Benthic shear stress and sediment condition

Aquacultural Engineering 21 (1999) 85 – 111 www.elsevier.nl/locate/aqua-online

Benthic shear stress and sediment condition Eric L. Peterson * School of Engineering and the Cooperati6e Research Centre for Aquaculture, James Cook Uni6ersity, Towns6ille 4811, Australia Received 17 March 1999; accepted 21 July 1999

Abstract This article presents a literature review and analysis which finds that the conditions in a shallow waterway are dependent on the underlying shear stress. Circulation and mixing have been recognised as somehow important to the health of the lower water column and sediment of a pond. Benthic shear stress is identified as one of the principal governors of sediment condition. Benthic shear stress regulates the convection of volatile substances such as oxygen across the sediment–water interface. Benthic shear stress is the primary determinant of where particulate matter scours, rolls, saltates, settles, and consolidates. The critical shear stress of very small particles tends to be determined by density rather than size. Excessive shear stress may cause organic material to become buried under a fallout of silt in locations with lower shear stress. Such organic matter trapped in a sludge blanket consumes oxygen faster than it can diffuse through the pores between grains of soil, resulting in anaerobic soils. The objective of pond aeration and circulation systems should be to optimise conditions for the growth of cultured stock. Better management of the epi-benthic habitat of shrimp and prawns would concurrently reduce the use of energy and soil. The finding is that pond sediment condition may be assessed in terms of benthic shear stress. Control of benthic shear stress would enable resuspension and oxygenation of organic detritus without making the situation worse by intermixing organic matter with mineral soil. Desirable benthic shear stresses are expected to exist in the range of 0.003 – 0.03 N/m2 where organic matter is gently maintained in an aerobic state. Locations having less than 0.001 N/m2 benthic shear stress are subject to burial under accumulating mineral silts. Excessive scour occurs in locations having more than 0.1 N/m2. High stress locations are the source of suspended solids which fallout on locations experiencing lower rates of benthic shear stress. The declining productivity of shrimp mariculture ponds is associated with excessive stocking and feeding because these practices necessitate intensive aeration, which results in high rates of pond circulation.

* Tel.: + 61-7-4781-4420; fax: +61-7-4775-1184. E-mail address: [email protected] (E.L. Peterson) 0144-8609/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 4 4 - 8 6 0 9 ( 9 9 ) 0 0 0 2 5 - 4

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The circulation causes soil to be scoured in some places while fallout covers the bottom in other places. Consequently intensive cropping of a pond causes feed pellets and other organic material to be buried in the soil, creating anaerobic conditions whereby bacterial metabolites are produced and released into the water column. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Pond circulation; Sediment condition; Sediment oxygen demand

1. Introduction Benthic shear stress is the tractive force applied over the area of sediment–water interface. This stress is a reaction to the applied force of wind, mechanical aeration, and water-exchange. It is hypothesised that the magnitude of this physical process strongly effects the condition of sediments found at the bottom of an aquaculture pond, or other shallow waterways. This article begins with a review of pond sediments, pond circulation, and fluid stress analysis. Analysis of the forced convection process at a boundary layer shows that mass transfer of dissolved substances is governed by shear stress at the banks and bottom of a waterway. The critical shear stress for the incipient motion of various classes of particulate matter varies according to particle size and density. The article concludes with a practical method to estimate benthic shear stress on the basis of surface velocity and depth of water.

1.1. Pond sediment The condition of the sediment found in an aquaculture pond is affected by many factors. Among these are stocking density, feed management, aeration practices and the materials of construction of the levee banks surrounding the periphery of the pond. Funge-Smith and Briggs (1994) found that bank erosion contributed the bulk of material to the sludge deposition in marine shrimp ponds in southern Thailand. Applied feed residue typically contributes about 5% of the sludge mass. The practice of excavating sludge effectively captures much of the organic matter originating from feed and primary production. Boyd (1995) reviewed a number of processes occurring at the sediment–water interface in aquaculture ponds. The sediment acts as a reservoir of nutrients and a sink of oxygen from the water column of a pond. Flooded soils change as a pond ages, despite periodic dry-out and liming treatments. Organic matter accumulates in the interstices between soil grains, and in the case of heavily fed ponds it may be impossible to diffuse oxygen into the soil as quickly as it is consumed. Aeration is used to counter this problem, but at very high feeding rates the soil tends to be completely anaerobic and toxic metabolites leach up into the water. Lin (1995) warned that the overstocking of ponds leads to increasing dependence on feed and aeration, and that a high proportion of the feed goes to waste, settling on the bottom to be decayed by bacteria. Jory (1995) identified the accumulation of detritus in pond bottom soils as a factor in disease outbreaks.

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Smith (1996) analysed sediment from penaeid growout ponds in eastern Australia. He characterised the sludge as a mixture of silt and clay with 5–10% amorphous oxides and 5 – 10% volatile compounds. There were significant gradients of soil properties along transits radially out from the centre of each pond. He attributed the pattern to circulation and mixing, comparing the peripheral zone of a pond to the well flushed banks of a mangrove creek. He found that the sludge from the centre of a pond is similar to the sediment taken from deeper in a mangrove forest. Moriarty (1997) implied that accurate modelling of microbial ecology and pond productivity would depend upon a realistic representation of the physics and biology involved. He emphasised the dramatic effect of sediment oxygenation, driven by wind or mechanical aeration. He explained that oxygen is depleted within the top millimetre of sediment due to bacterial growth and very slow diffusion through waterlogged soil. Fermentative bacteria release acids, alcohols and carbon dioxide, which are then utilised by sulphate reducers. An oxygen deficit is built up, and reduced species accumulate until harvest when the pond bottom is dried out. Burford et al. (1998) analysed sediments from a series of intensively aerated ponds at a tropical Australian prawn mariculture farm and found that the accumulated sludge had significantly higher bacteria counts than found in perimeter zones. Bacterial numbers were highly correlated with sediment grain size, probably because organic and mineral particles are both likely to fall out in dead spots such as the centre of a pond. The bacterial numbers and nutrient concentrations (C, N, and P) in accumulated sludge were found to be similar to mangrove soils. The higher organic loading rate of the ponds indicated that nutrients were mineralised more rapidly than in a mangrove estuary.

1.2. Pond circulation Aerators are named for their ability to force the convection of volatile substances across the air-water interface. Aerators may deliver oxygen, while also stripping carbon dioxide, and nitrogen. The same machines can also act to resuspend bottom particles and drive substances across the water–sediment interface. The process of pond circulation is poorly described in the literature, whereas many farmers practice ‘sediment-sweeping’, attempting to oxidise the soils at the bottom of a pond. The process of water-column aeration is well documented, based upon tank-tests with fresh water and no sediment, as reported by Boyd and Ahmad (1987). In contrast, the objectives of pond circulation are ad-hoc and less clearly defined in published literature, except for the general pond research ideas from Boyd (1995). Circulation is characterised by the transmission of horizontal momentum into a pond in a manner which creates a closed loop current parallel to the banks. This forcing causes the water column to overturn and mix as the primary flow advances. The rotating circumferential action causes secondary flow outwards along the surface and inwards near the bottom.

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During the course of the present research it was found that the aerators used in marine aquaculture ponds are invariably of the mechanical type, with some kind of paddle or propeller. Such devices are also very effective as pond circulators. It is possible that some may have attempted to deploy diffused-air systems in a sea water pond, but no commercially viable examples have been encountered by the author. Such systems would not be appropriate in a shallow pond because the entire bottom would need to be serviced with a dense network of piping, all the while delivering a less efficient aeration function. The very shallow aspect-ratio of a pond requires a concerted effort to establish circulation, and so any aerator which fails to produce strong circulation is perceived to be ineffective. Aquaculture research literature reveals a growing appreciation of the importance of circulation, as well as the requirement for oxygen transfer. Busch (1980) developed a non-aerating paddlewheel to minimise splashing, bubbling and spraying. This machine was deployed in a pond to test the effects of daylight circulation without aeration. Night-time dissolved oxygen near the bottom was sustained at higher concentrations than in an uncirculated pond. Currents were recognised as delivering oxygen from algae in the water column to decomposers in the benthos. Lawson and Wheaton (1982) described crawfish culturing in shallow flooded rice fields. They recognised that ‘dead’ areas needed to be avoided, and that conventional aerators would scour and cause problems. So uniform circulation was provided with baffle levees, creating convoluted raceways where dissolved oxygen was distributed from gravity aerators. Rogers (1989) emphasised that aeration and circulation are two distinct processes. Circulation transports oxygen within the pond system, from producers to consumers. The benefits of circulation were reported to include a reduction in sludge thickness and an increase in the proportion of the pond microcosm that is habitable for growout. Brune and Garcia (1991) asserted that circulation is the primary regulator of oxygen conditions in penaeid growout ponds. A case study of production failures led them to consider the commonly reported ‘biomass plateau’ in heavily stocked ponds. This was illustrated with a simple model of oxygen distribution in the benthic boundary layer. They found that the pond system cannot be assumed to be well mixed without artificial circulation. They concentrated their analysis on the diffusive boundary layer over the sediment, with the implication that the management of the diffusive boundary layer is the singular objective of pond circulation systems. Their discussion involved a review of circumstantial evidence that ponds require substantially more paddlewheels in the role of mixers than are required in their role as aerators. The stated implication was that aquaculture facilities should be designed with due respect to the physical interactions of pond geometry, aerator placement and benthic oxygen distribution. Fast and Boyd (1992) reviewed a number of investigations regarding the distinct effects attributable to aeration, circulation, and sediment manipulation in penaeid growout ponds. Aeration processes were very well defined, but complex issues prevented the quantification of the benefits of circulation. The circulation induced

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by aerators is normally directed around the periphery such that the sediments in this zone are well oxidised, with a light brown colour. Feed is thrown from banks to sink into the peripheral zone. The centre of such ponds tends to have a dead-spot where deposition occurs at a rate faster than it can be oxidised, resulting in a thick bed of black oxygen-starved sediment. Between crops the accumulated sludge is either excavated or spread out for exposure to air and solar radiation. Funge-Smith and Briggs (1994) recognised that erosion is caused by aeration and water circulation. They recommended that the peripheral zone should be lined because of the limited durability of earthen pond banks and perimeter areas of penaeid growout ponds. Boyd (1995) identified excessive aeration as the cause of erosion and deposition zones within a pond. Boyd pointed out that while these machines are designed to optimise water-column aeration, their effects on sediment–water interface should be improved. He suggested that aeration systems should be redesigned to produce a uniform gentle current that would resuspend only organic matter without disturbing soil particles. The analysis provided in the present article shows that there are two physical effects associated with pond circulation, and these both are quantified by the magnitude of benthic shear stress. The beneficial effect of benthic shear stress is the forced convection of dissolved substances across the sediment-water interface. Benthic shear stress becomes dangerous when it exceeds the threshold for soil erosion, and as the old saying goes: ‘what goes up must come down’. Suspended soil particles inevitably settle somewhere within the pond. The fallout of suspended sediment forms an overburden trapping organic material, such as feed pellets. Buried organic matter becomes anaerobic due to the slow rate of mass transfer in flooded soil. Strangely, these anaerobic conditions are the consequence of intensive aeration.

1.3. Viscosity and shear stress Background on fluid properties and processes is necessary to understand the distribution and condition of sediments found at the bottom of a shallow waterway. The objective of the present discussion is to review the role of viscosity, estimated from the components of stress: normal and tangential. The magnitude of shear stress is taken from the tangential components of stress, being related to the velocity gradient and viscosity at the particular surface of interest. Density is the fluid property denoted by r. The dynamic viscosity property, m, of a fluid is the proportionality factor between the magnitude of the shear stress and boundary velocity gradient: t=m(du/dz). Kinematic viscosity is denoted by n= m/r. In turbulent flow there appears a Reynolds stress, in addition to hydrostatic pressure and viscous stress. Reynolds stress is related to the eddy 6iscosity and the gradient of the time-averaged velocity field. Eddy viscosity varies with fluid processes. The eddy viscosity within a boundary layer has a maximum magnitude normal to the plane of maximum shear stress. Further afield, the eddy viscosity tends to be isotropic, acting equally in all directions. The eddy-viscosity approxima-

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tion (Boussinesq, 1877) and the RANS (Reynolds averaged Navier-Stokes, Reynolds, 1895) equations allow the application of an effecti6e 6iscosity to represent the turbulent effects on the mean flow field. Thereby, the ordinary velocity symbols (u, 6, w) are often taken to indicate the time-averaged mean of the components of velocity in the x-, y-, and z-directions. Similarly, the ordinary pressure and viscosity symbols (p and n) are often taken to include the effects of Reynolds stress. The k –o model is a computational fluid dynamic (CFD) scheme which simulates the behaviour of turbulent flows, as described by Ferziger and Peric (1996), and as implemented in FIDAP (Fluid Dynamics International, 1993). The k and o parameters provide an estimate of the effective viscosity, ne = n0 + Cm (k 2/o) and effective pressure, pe =p¯ +2/3rk, where r and n0 are the fluid density and viscosity properties, and Cm is a constant of 0.09. The reader is referred to Abbott and Basco (1989) for an introduction to CFD methods. The important point for the non-specialist is that turbulence operates on a wide range of spatial scales, as microcosms inter-fold within microcosms. These processes are observed from the macroscopic perspective as diffusion, expressed with the same physical units as viscosity. Section 2.1 details the relationship between viscosity and diffusivity. Shear derives from the noun for the common cutting implement, the pair of shears (scissors). As a verb, shear implies a cutting force that tends to cause two adjacent parts of a body to slide in opposite directions along their plane of contact. Stress is the aereal rate of force applied at the interface of contact between two adjacent bodies. The tangential component of force divided by the area of contact is the shear stress. The component of stress which is acting to press or pull apart the interface is termed normal stress. The combination of shear and normal components of force resolve the total force of interaction between the two parts. The resolved components of stress are dependent on the plane of contact and co-ordinate system. In the case of a fluid continuum there is no unique shearing plane, as the entire medium will deform under stress. Fluid stress components are usually given with Cartesian tensor notation (subscripts i and j ) of Eq. (1). sij (stress tensor) = − pdij (isotropic stress) +tij (viscous stress)+ru%i u%j (Reynolds stress) (1) Hydrostatic pressure is uniform in all directions, aptly named the isotropic stress tensor. The viscous stress tensor represents deviations from the isotropic pressure resulting from shear on a microscopic scale. The Reynolds stress represents the mean correlation of the orthogonal components of velocity fluctuations, which applies in turbulent flows, which is the predominant case for aquaculture ponds and natural waterways. The stress tensor is anisotropic whenever fluid is experiencing shear or otherwise forced to flow. Water is considered to be a Newtonian fluid since the viscous stress is proportional to shear rate tensor. For turbulent flow of water the strain rate tensor Sij is defined with Eq. (2). Sij =1/2(#u¯i /#xj +#u¯j /#xi )

(2)

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Application of the eddy viscosity hypothesis allows the components of stress to be simply arranged as Eq. (3a) so that all deviatoric effects are amalgamated together. sij (stress tensor) = −pedij (isotropic stress)+ 2r(n0 + nt)Sij

(3a)

For the purposes of illustration, the above tensors are expanded in Eq. (3b) with co-ordinates x, y and z representing the downstream, lateral and vertical co-ordinates, respectively. Similarly the downstream and lateral components of velocity are notated with u and 6, while any vertical component of motion is represented by w.

Á −p¯ − 23rk  0 0 2 sij = à 0 −p¯ − 3rk 0 Ã Ä 0 0 −p¯ − 23rk Å #u¯ Á 2(#x ) #6¯ ¯ +r(60 +6t )à #x + #u #y ¯ #u¯ Ä#w #x + #x

#u¯ #y

#6¯ + #x #6¯ 2(#y ) #w ¯ #6¯ #y + #z

¯ + #w #x  #w ¯ + #y à ¯ 2(#w #z ) Å

#u¯ #z #6¯ #z

(3b)

The specification of shear stress vector, ti, having components tx, ty, tz requires the assumption of a cutting plane with normal vector, nj, defined by components: nx ; ny ; and nz. The boundary of the fluid continuum is the obvious plane upon which to assess the shear stress. There is a no-slip condition at solid walls (u%= 6%= w% = 0), so the Reynolds stress vanishes. Turbulent kinetic energy, k= 0 at smooth walls, and k "0 at rough walls, but isotropic stress (effective pressure) does not effect the shear stress at any wall, because such forces act only in the direction of the normal. The forgoing apply for both smooth and rough walls with Eq. (4), where there is a defined normal surface, nj. #u¯ Át x  Á 2(#x ) #6¯ #u¯ Ãt y à =r6eà #x + #y ¯ #u¯ Ä t z Åwall Ä#w #x + #x

#6¯ + #x #6¯ 2(#y ) #w ¯ #6¯ + #y #z #u¯ #y

¯ + #w #x ÂÁn x  ¯ + #w #y Ãà n y à #w ¯ 2( #z ) ÅÄ n z Åwall

#u¯ #z #6¯ #z

(4)

As an example consider Fig. 1, with fully developed flow along a waterway having a level bottom. In this case, the normal vector nj is B0, 0, 1\ , and the flow is entirely aligned with the B1, 0, 0 \ direction, being parallel to the x-axis. The only non-zero velocity gradient is du¯ /dz, and so the shear stress vector may then be written as B rno (du¯ /dz), 0, 0 \. The shear stress magnitude is t = rno (du¯ /dz), where ne =n0 only in the case of a smooth wall. 2. Chemical transport This section refers to chemical transport literature and provides a formulation of the relationship between shear stress and the transfer of volatile substances at the sediment– water interface. The application of shear stress is necessary to force convection of momentum, heat and mass beyond those rates limited by molecular

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diffusion. The three molecular transport processes (momentum, heat, and mass transfer) all share the same form. The rate of transfer is determined by the ratio of driving-gradient to resistance, where the inverse of resistance is the diffusi6ity; which has units of length squared over time (m2/s). In Fig. 1 the transport of x-directed momentum through the bottom (normal to z) is the shear stress, tx. It was driven by the z-gradient of momentum, uxr while acting through the kinematic viscosity n. The forgoing illustration had the driving flow perfectly aligned with the x-axis and constant throughout the range of x (fully developed). This idealised alignment has been employed to simplify discussion. The magnitude of momentum and mass transfer at the sediment – water interface are not effected by the co-ordinate system employed to study the phenomena.

2.1. Diffusi6ity Referring again to the situation of Fig. 1, J *Az denotes the flux of dissolved species, A, through the bottom, in the z-direction, through the fluid solvent medium, B. Diffusive mass transport is driven by the z-gradient of the concentration of solute, CA (molA/m3) while acting against the molecular diffusivity, DAB (m2/s) as formulated in Eq. (5). J*Az = − DAB dCA/dz z = 0

(5)

Ficks law of diffusion lumps all non-advective transport as the product of concentration gradient and diffusivity. Anisotropic diffusive transport of a concentration field, CA, of dissolved species ‘A’ is modelled with Eq. (6), #CA #2CA #2CA #2CA =Dx +Dy +Dz 2 2 #t #x #y #z 2

Fig. 1. Illustration of benthic shear stress for fully developed flow.

(6)

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where the transport rate is assumed to be driven by the product of the concentration gradient and the effective diffusivity, De, with anisotropic variability in the directions x, y and z. Bowie et al. (1985) provided numerous empirical methods to estimate the diffusivities, Dx, Dy, and Dz for a wide variety of aquatic systems. Environmental flows are generally constrained by aspect ratios many orders of magnitude greater in the horizontal directions (x and y) where stratification effects limit motion in the vertical direction (z). Consequently the horizontal diffusivities, Dx and Dy, are generally several orders of magnitude greater than the vertical diffusivity, Dz. In spite of these effects it should also be noted that the vertical diffusivity, Dz, is generally many orders of magnitude greater than the molecular diffusivity of any particular solute-solvent pair. At the boundary layer the values of eddy diffusivities are dampened and approach the magnitude of molecular diffusivity. Boundary layer diffusivities and are the major topic of the present article because they act as a bottleneck to the transport of substances at the sediment–water interface. According to Tennekes and Lumley (1972), the kinematic viscosity as well as the heat and mass diffusivities are related to the eddy diffusivity by some quasi-constant proportion. The turbulent Schmidt number, Sct, is a quasi-constant of about 0.9 relating the turbulent mass diffusivity to the eddy diffusivity. The effective mass transfer diffusivity, De, is given in Eq. (7). De =DAB +nt/Sct

(7)

Substituting into the foregoing and assuming density is constant, Eq. (8) gives a relationship between shear stress and mass diffusivity for pure shear with a velocity gradient only in the vertical direction, du/dz. De =

tx n +DAB − 0 r(#u/#z)Sct Sct

(8)

Turbulent diffusivity is proportional to the shear stress magnitude, and inversely proportional to the velocity gradient. Molecular diffusion is the controlling factor within the viscous sub-layer immediately adjoining a boundary wall, while shear stress acts to thin this layer. According to Jørgensen and Des Marais (1990), forced sediment aeration encounters a bottleneck in the diffusive boundary layer, dD, defined as the thickness within which the eddy diffusivity is less than the molecular diffusivity. The diffusive boundary layer, dD, was found to be 0.59 mm thick for a 0.0003 N/m2 shear stress. The dD was cut down to only 0.16 mm thick when the shear stress was increased to 0.0077 N/m2. The flux of oxygen increased 2.5-fold when shear stress was increased 25 times. Shaw and Hanratty (1977) conducted experiments and provided an empirical relation between the turbulent viscosity and shear velocity at a wall (u*= t/r) with Eq. (9), nt = cn0(zu*/n0)n

(9)

Shaw and Hanratty found the parameters, c =0.000463 and n=3.38, are constant over a wide range of conditions. Eq. (9) may be solved for that point in the

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Fig. 2. Effective mass transfer diffusivity, illustrating Eqs. (7) and (9).

z-direction where the eddy viscosity and molecular diffusivity share an equal magnitude. The distance from the wall to this point is the diffusi6e boundary layer thickness, dD, as given in Eq. (10). − 1/n dD = n 1 − 1/n · u* − 1 · D 1/n AB · c

(10)

For example, assume properties of water are r= 998 kg/m and n0 = 10 m2/s. Furthermore allow the molecular diffusivity of any solute in the solvent, DAB = 10 − 9 m2/s. For a shear stress of 0.1 N/m2 the corresponding shear velocity is u* = 0.01 m/s, and so the height where eddy viscosity equals molecular diffusivity is dD =0.125 mm. Effective diffusivity begins at a minimum of DAB at the wall surface, and then accelerates with distance to the 3.38 power. Fig. 2 plots the estimated effective mass transfer diffusivity, De, with the Schmidt number, Sct = 0.9 for a range of wall shear stresses, t, and heights, z, applying Eqs. (7) and (9). 3

−6

2.2. Deri6ation of chemical flux 6elocity at the sediment–water interface Extending on the findings of Shaw and Hanratty, a one-dimensional computational approach has been employed to predict the flux of dissolved oxygen into sediment. This accounts for the increase in turbulent diffusivity with respect to increasing position out of the boundary layer. The mass transport of dissolved species ‘A’ from the water column ( ) into the sediment (0) is hereby formulated in Eq. (11).

&

z

0

dz =− De

&

E.L. Peterson / Aquacultural Engineering 21 (1999) 85–111 CA,

C A,0

dCA J*Az

95

(11)

The integral on the right hand side is straightforward: (CA,0 –CA, )/J *Az, where the numerator expresses the concentration difference between the water column and the sediment. Within the diffusive boundary layer there is a minimum value of diffusivity which is nearly constant at DAB and then curves up to only twice this value at the outermost level of the boundary layer. Assuming a quasi-constant diffusivity of DAB within the boundary layer thickness, dD, there is a simple approximate solution for the mass flux of dissolved species through the pond bottom, as given in Eq. (12). J*Az /(CA,0 −CA, ) : DAB/dD

(12)

More precisely, the left hand side of Eq. (11) may be expanded in terms of Eq. (9), to give Eq. (13a).

& 

z

0

dz = DAB +(nt/Sct)



z · 2F1

&

z

0

dz =− DAB +(c60(u*z/n0)n/Sct)

1 1 nt , 1; 1 + ; − n n DAB · Sct

nn

z

=− 0

&

CA,

C A,0

dCA J*Az

&

CA,

C A,0

dCA J*Az

(13a) (13b)

The Wolfram Research Inc. (1996) computer program Mathematica was used to compute the left hand side of Eq. (13b). The integration was conducted with nt expanded as a function of z, and the result was in the form of a Gaussian hypergeometric function. Numerical estimation of the hypergeometric requires a prohibitive number of iterations, but it was promptly evaluated by Mathematica’s symbolic logic kernel provided the lower limit of the integrand was adjusted to be diminutively above zero. Therefore the lower limit was taken as z/r, where r was assigned a large nominal value of 106. Calculations were based on a unit of driving concentration differential, DCA = 1 g/m3 :1 ppm. For the example of 0.1 N/m2 shear stress then the hypergeometric integration gave a result of 9.5 ×10 − 6 g/m2 per s at the dD height of 0.00012546 m. Integration to 10× dD height resulted in 7.0991× 10 − 6, while integration to 100 × dD and 1000 ×dD both resulted in 7.0892 × 10 − 6 g/m2 per s. Beyond such distances from the wall it appears that mixing may be represented as a continuously stirred tank reactor. Without assuming a concentration potential DC the results may be expressed in terms of flux 6elocity, kL (m/s). Fig. 3 displays results of hypergeometric integrations applied to calculate kL = J*Az /DCA for various values of shear stress at the top of the diffusive boundary layer dD as well as at 1000 times that height: 1000 × dD. The dD curve gives the highest mass flux because the concentration potential DC is applied over a shorter distance than 1000× dD. Fig. 3 also includes a plot of the approximation J*Az : DAB/dD, from Eq. (12). This curve also applies the concentration DCA to the shorter distance dD. The approximation conveys a lesser mass flux than the hypergeometric integration of dD because eddy diffusivity is neglected. It should be noted that the eddy diffusivity

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was involved in the calculation of dD in Eq. (10), and so the approximation of Eq. (12) is understandably close to the mark. The hypergeometric results 1× dD and 1000× dD are parallel to, and envelope around, the approximation curve of Eq. (12). An additional hypergeometric integration through 100 ×dD (one tenth of 1000 × dD) yielded results matching the 1000 × dD with five significant figures of precision in the range of shear stress from 0.0001 to 1 N/m2. The 1000×dD curve is concluded to characterise the bulk mass transfer of dissolved substances between the water column and benthos of a pond. A linear regression analysis of the 1000× dD results provided a correlation coefficient squared of 1.0000000 when fit to a power law formulation. It was found that this curve may be reported with Eq. (14). kL =J*Az /DCA − 1/n =0.8894 · c 1/n · D 1AB · n 1/n − 1 · r − 1/2 · t 1/2

=0.09175(DAB/n)0.704 u*

(14)

The 0.8894 factor appears because the 1000 × dD results are 11.06% lower than the approximation. This is a reasonable result because the fluid outside of 1× dD offers some resistance to mass transfer, although this effect drops away very quickly owing to the power n increase in diffusivity with the distance parameter, y+ z t/ r/n.

Fig. 3. Forced convection of dissolved substances at the bottom of a pond.

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When aerating fresh water at 20°C, then kL : u*/1410 : t · 2.242 × 10 − 5 m3/2 kg − 1/2.

2.3. Limitation of sediment oxygen demand The respiration of sediment may be limited by the availability of oxygen and other electron acceptors, as well as nutrients such as organic carbon. The consumption of oxygen is often termed the sediment-oxygen-demand (SOD). Whenever nutrients are available in excess the bottleneck establishing SOD must be the availability of dissolved oxygen. This is thought to be the case in most aquaculture ponds and other eutrophic waterways. Eq. (14) predicts a limitation in the flux of a dissolved substance through the sediment– water interface at the bottom of a shallow waterway. The formula has now been derived from Shaw and Hanratty’s (1977) model of diffusivity in a boundary layer, with coefficient c= 0.000463 and power n= 3.38. The formula predicts the flux velocity, kL =J *Az/DCDO. The mass transfer limit may be determined on the basis of area and concentration potential, DCDO. Given a benthic shear stress of 0.0001 N/m2 in the dead zone at the centre of a pond, then a solute having a molecular diffusivity of 10 − 9 m2/s would be limited to a maximum flux velocity of 2.2×10 − 7 m/s (0.22 mm/s). If the concentration of dissolved oxygen in the water column was 5 mg/l while the sediment was anaerobic then DCDO = 5 g/m3, and so the mass flux of oxygen would be limited to 1.12× 10 − 6 g/m2 per s (0.1 g/m2 per day). In the turbulent jet emanating from an aerator there would be a zone of substantially more intense benthic shear stress, on the order of 1 N/m2. Assuming molecular diffusivity of oxygen is 10 − 9 m2/s and the concentration potential is 5 mg/l then the resulting mass flux of dissolved oxygen could go as high as 1.12× 10 − 4 g/m2 per s (10 g/m2 per day). But respiration in such locations may be more limited by the availability of carbon and other nutrients. It is interesting to note that a 10 000 fold increase in benthic shear stress would result in only 100 times the mass transfer capacity. This is because of the rate is controlled by the square root of the shear stress. This explains the use of shear 6elocity in fluid mechanics literature, which is defined as the square root of shear stress divided by square root of fluid density: u* t/r. This is confirmed by Boudreau (1997), who found that most models of benthic boundary layer dynamics represent eddy diffusion in proportion to shear velocity. Wainright and Hopkinson (1997) provided a literature review which supports the present assertion that Eq. (14) is generally appropriate. They cited 24 studies of sediment respiration in marine estuaries and offshore locations where reporting ranged 0.02 – 2.4 g C/m2 per day, with a mean value of 0.55 g C/m2 per day. The spread of the values is taken to be a result of diverse hydrodynamic and environmental circumstances. The equivalent SOD values were in a range from 0.5× 10 − 6 up to 10 − 4 g O2/m2 per s, with a mean of 1.4×10 − 4 g O2/m2 per s. To compare with Eq. (14), the oxygen concentration potential might be assumed to be 5 g/m3, in which case the respiration rates tabulated by Wainright and

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Fig. 4. Traditional Shields curve, after Yalin 1977.

Hopkinson suggest a range of benthic shear stress rates from 2× 10-5 up to 0.8 N/m2, with a value of 0.016 N/m2 corresponding to the mean respiration rate. These are very similar to the range of stress conditions found in a pond, and they are not unlike the range of conditions expected in natural waterways. Wainright and Hopkinson simplified hydrodynamics in terms of a ‘resuspension magnitude’ to simulated benthic processes, apparently without regard to quantifying benthic shear stress or shear velocity. Jahnke and Jackson (1992) quantified sediment respiration in the abysmal depths of the oceans, finding correlation with the rate of organic carbon supplied by settlement from the surface waters. They found benthic fluxes of O2 in the range 0.001–0.1 g/m2 per day. Corresponding benthic shear stress could have been from 10 − 8 to 10 − 4 N/m2, and not limit the respiration rates they observed. So there is no obvious contradiction with the present article.

3. Sediment transport This section analyses sediment transport literature and finds that incipient motion is more strongly related to particle density than particle size. Herein it is determined that a benthic shear stress of 0.01 N/m2 is sufficient to keep all organic matter in suspension, all the while allowing mineral particles to remain undisturbed. Critical shear stress is that intensity of traction which would trigger the movement of a particular class of sediment particle. This stress determines when banks erode, how feed is distributed, and where detritus settles. Suspended particles experience substantially higher rates of diffusive exchange with the water than they would when flocculated and settled on the bottom. Since 1936 the Shields curve has provided prediction of dimensionless mobility number, u, as a function of grain size Reynolds number, Re* (Shields, 1936). The Shields curve is illustrated in Fig. 4 with axes defined by Eqs. (15) and (16). Erosion

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99

generally occurs when the mobility number is above the curve, whereas sedimentation is expected for conditions below the curve. Mobility number: Grain size number:

u=

t (rs −r)gd

Re* =

t/rd n0

(15) (16)

Yalin (1977) provided theoretical reasoning why sediment particles remain lodged on the bottom until some critical threshold forcing transpires. Furthermore he made the case that fine muddy material has such a small grain size that the ‘individuality’ of particles tends to be obliterated. He argued particle diameter disappears as a parameter of critical shear stress when grain size approaches zero. The Shields curve of very fine sediments having a grain size Re* less than unity plots on log – log co-ordinates with a slope of − 1:1, because particle diameter appears in both the denominator of the u-axis and in the numerator of the Re*-axis. Miller et al. (1977) found that the exact prediction of the threshold stress is not so simple, but there remains a certain tendency to sort benthic material according to density. They extended the Shields curve for Re* conditions less than unity by conducting an exhaustive review of experimental data of very fine particles of various densities and sizes. They searched literature across disciplines in science and engineering to generalise the principles of sediment transport so that planetary dust models could be formulated for Mars, where gravitational acceleration and the atmosphere are quite unlike anything on earth. The traditional Shields curve was developed for hydraulic engineers who are concerned with the bulk movement of sand and gravel in rivers. Only recently have other aquatic and terrestrial applications become apparent. Some phenomena are hardly perceptible, and the importance of such processes may not have been viewed as worthy of research. In recent years there came to be a desire to better understand processes at the sediment– water interface. The nepheloid layer of suspended flocs at the bottom of many aquatic systems consists of particulate organic matter (POM) having a relative specific gravity of only about 0.05. Siliceous mineral particles, known of as particle inorganic matter (PIM), have a relative specific gravity of about 1.65 relative to water. The relative specific gravity of various particles may be determined from Stokes law if settling velocity and diameter are observed. Assuming the properties of sea water at 25°C then Stokes law is D= 16.6w/d 2 where D= (rp − r)/ r is the relative specific gravity of particles, w is settling velocity expressed in m/day and d is size in mm. For example, a 1 mm diameter aquaculture pond feed pellet which settles through 1 m of water column in 15 s would have D= 0.08. The present review may be criticised as simplistic for assuming particulate matter is either organic or mineral in nature, as there are a class of agglomerate particles termed marine snow, composed of minerals and all sorts of living and dead biota bonded by mucus. But the tangled form of such particles has a relatively low

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wet-density, which may behave like POM. Syvitski et al. (1995) measured the properties of marine snow, finding relative specific gravities in the range of 0.01 to 0.09 depending upon season and locality. Gloor et al. (1994) plotted a variety of PIM and POM particles on the extended Shields diagram extended by Miller et al. to show there is more than an order of magnitude difference in the relative critical shear stress for organic and mineral particles. Bloesch (1995) reviewed limnological methods and results by many researchers, finding that resuspended sediments are largely organic, and that the physical process of resuspension is of crucial importance to the health of an aquatic ecosystem. For brevity Peterson (1998) applied Yalin’s assumption that small particles exist completely within the viscous sublayer such that their incipient motion curve has a slope of − 45o on logarithmic paper given log10 ucr = − 1− log10 Re*cr. This is rearranged to estimate the critical shear stress, tcr, with Eq. (17), tcr = (g 2s n 2r/100)1/3

(17)

where the specific weight of the particle is gs = g(rp − r), the density of water is taken to be on the order of r $1000 kg/m3, and the viscosity of water is about n0 $ 10 − 6 m2/s. For example, organic flocs are assumed to have a particle density r(POM) $1048 kg/m3, whereby the critical shear stress for resuspension would be tcr(POM) $ 0.01 N/m2. By contrast, siliceous mineral soil particles have a density of r(PIM) $2650 kg/m3, therefore the critical shear stress for scouring would be tcr(PIM) $ 0.1 N/m2. A more involved analysis of critical shear stress applicable to POM and PIM finds that results actually do vary slightly with particle size, but that particle density remains a dominant parameter of incipient motion. A comprehensive review by Miller et al. (1977) extended the Shields diagram for small particle Reynolds numbers, Re* B 1. Gloor et al. (1994) plotted shear velocities of 2 and 7 cm/s for PIM and POM on the extended Shields diagram of Miller et al. to show there are differences of more than an order of magnitude between the relative critical shear stress for each class of particles. Gloor et al. were observing the velocity profiles in a large seiching lake without resolving shear stress, whereas the present study of smaller ponds is directed to quantifying shear stress. They assumed DPIM = 1.65 and DPOM =0.05. Fig. 5 plots shear stresses of 0.01 and 0.1 Pa for both PIM and POM on the extended Shields diagram in a fashion mimicking Gloor et al.’s plotting of seiching shear velocities. The Shields diagram uses two dimensionless co-ordinates: particle Reynolds number, Re* on the x-axis versus relati6e shear stress, u on the y-axis. Miller et al. reviewed experimental data by others and plotted them to extend the incipient data for Re*B 1. The threshold of movement was observed to scatter within two parallel curves, where the uppermost represents a high probability of scour, while the lower represents a high probability of settling. The incipient curves and data points were graphically interpolated from the illustrations of Miller et al. and then transcribed to Table 1. Various possible sediment conditions are plotted on Fig. 5 on the following basis:

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“ “

particle sizes ranging as noted on the diagram; particle density of POM and PIM assumed to be 1048 and 2650 kg/m3, respectively; “ water density of r = 998 kg/m3; “ water viscosity of n0 =10 − 6 m2/s; and “ benthic shear stress of t =0.01 and 0.1 N/m2. Conditions lying below the incipient curves are representative of sedimentation. Sediment conditions between the incipient curves are likely in locations of scouring, while only cohesive materials might endure conditions above the curves.

3.1. Analysis of the critical shear stress This section extends on the estimation of critical shear stresses for PIM and POM offered by Peterson (1998), such that particle size has a secondary effect on critical shear stress. Data points were interpolated from the Miller et al. curve are presented in Table 1. It appears that the specific recommendation for the management of benthic shear stress at 0.01 N/m2 is confirmed. Fig. 5 shows that such a stress would cause organic particles to experience incipient tumbling or rise into suspension, while all classes of mineral soil particles would be completely undisturbed.

Fig. 5. Organic and mineral particle shear stress 0.01 and 0.1 Pa curves plotted on Miller et al. (1977) extension of Shields diagram after Gloor et al. (1994).

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Table 1 Incipient motion data points taken from Miller et al. (1977)

Natural sediment in oil

Crushed silica Natural sediment in oil Natural sediment Natural sediment Lead-glass ballotini Natural sediment Natural sediment Natural sediment in oil Crushed silica Natural sediment Natural sediment Glass beads Natural sediment Lead-glass ballotini Lead-glass ballotini Fine Mersey sand (quartz) Fine Mersey sand (quartz)

Re*

ucr

0.03 0.05 0.05 0.08 0.1 0.16 0.16 0.17 0.18 0.2 0.2 0.23 0.25 0.29 0.4 0.42 0.7 0.9 0.92 0.78 0.88

0.23 0.28 0.25 0.23 0.16 0.17 0.12 0.13 0.15 0.11 0.1 0.16 0.12 0.14 0.14 0.23 0.08 0.07 0.07 0.14 0.15

The hypothesised 45° decline on a log–log plot of the Shields diagram described in the literature review is not supported by evidence. Whilst a regression analysis of the data in Table 1 form a decline of about 16°, they must be considered in the context of the established Shields curve at higher particle Reynolds numbers, Re*, where the slope turns up into a positive incline and later levels out. Miller et al. drew both the high and low probability curves of incipient motion with a 27° decline between 0.04BRe* B 1.0. As a matter of engineering practice, a deterministic relation is needed to represent the threshold of sediment movement, midway between Miller et al.’s scouring and settling curves. Ten samples points were taken from these curves in the range 0.04BRe* B 1.0 and entered into a linear regression analysis. The result indicates a slope of − 0.5:1 (atan 0.5= 27°) with an intercept of −1.16 projected onto log10 u. Therefore the Miller et al. extended Shields curves are taken together to be represented with Eq. (18), log10 ucr = − 1.16 −0.5 log10 Re*cr

(18)

This may be expressed as Eq. (19), ucr = 10 − 1.16/100.5(log Re*) =0.06918/(10log Re*)1/2 = 0.06918/Re* 1/2

(19)

which was incidentally noted in the upper left of Fig. 4. Substituting for ucr from Eq. (15) and Re* from Eq. (16) thereby yields Eq. (20) as follows,

E.L. Peterson / Aquacultural Engineering 21 (1999) 85–111

tcr = 0.11803rD0.8g 0.8d 0.4n 0.4

103

(20)

which is applicable in the range 0.04B Re*B1. No data were available for Re*B 0.04. Below this condition the critical shear stress is expected to be enveloped by some quantum of confidence taken above and below the prediction of Eq. (20) An ad-hoc criterion has been adopted whereby the level of confidence diverges in proportion to the ratio of Re*/0.04. The results of Eq. (20) are plotted in Fig. 6 with enveloping divergence of confidence for Re* B 0.04. Fortunately the uncertainty does not obscure the critical shear stresses expected for incipient motion at higher Re*. It is clear that benthic shear stress of about 0.01 N/m2 will suffice to keep organics in suspension, while assuring mineral particles are undisturbed. Shear stresses over 0.1 N/m2 plainly cause all silt particles to be scoured. Between 0.01 and 0.03 N/m2 benthic shear stress all classes of organic matter would be resuspended, while silts and sands remain undisturbed. Feed particles and large flocs of algae would start to settle out of suspension in locations with shear stress decreases from 0.01 to 0.003 N/m2.

4. Conclusions This paper has enhanced the understanding of the literature addressing aquaculture pond circulation in general and the condition of the sediment–water interface

Fig. 6. Incipient motion criteria for organic and mineral particles. Plot of critical shear stress in N/m2 for organic and mineral particles having a range of diameters. This figure employs Eq. (20), which is derived from Miller et al. (1977) extended Shields curve. Relative specific gravity of particles, D = (rp − r)/r.

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in particular. The analytical results of the present paper have distilled useful engineering formulae from the work of earlier researchers. Eqs. (14) and (20) quantify the capacity for dissolved and particulate matter to cross the sediment– water interface of a shallow waterway. These formulae are both based upon a common determinant: benthic shear stress. Eq. (14) quantifies the limit of sediment oxygen demand, whereby respiration may be limited by the hydrodynamics. Eq. (20) predicts that 0.01 N/m2 benthic shear stress is sufficient to resuspend most organic matter in an aerobic state, yet not so excessive as to scour mineral particles. Higher stress rates cause erosion along banks, which results in burial of organic matter in lower stress ‘dead spots’. Equation further suggests that benthic shear stress should be controlled at about 0.003 N/m2 when feeding epi-benthic shrimp so that high protein pellets will rest on top of soil, while lighter organic matter is kept moving. It is suggested that aeration and circulation could be increased, as determined with Eq. (20), to meet sediment respiration requirements, but only at night, after the completion of daily feeding. Admittedly, there is a lack of confidence in the assumed composition of sediments, but the present formulations provide a model with which future research could be directed. Specifically, there had been a dearth of publications regarding the physical properties of ‘marine snow’, aquacultural feed pellets, faecal pellets, and other forms of particulate organic matter (POM). It is suggested that POM be characterised with regard to constituent ‘bins’, reported with a conjugation of parameters: diameter; settling velocity; and wet density. Ideally, some additional measure of cohesiveness would also be advantageous. Taken together, the benthic shear stress and size of sediment found at a particular location describe the local state of the sediment-water interface. Shear stress alone acts as an indicator of likely conditions, but there is some uncertainty about sediment quality without information about mineral deposition from the water column above. Since the stated objective is to avoid scouring mineral soil, then fallout would be less significant in a well managed pond, and so benthic shear stress would act as the singular governor of sediment condition. This could be termed the well managed pond hypothesis. In such a pond there would no erosion, achieved either with low-stress aerators, or by lining the banks and bottom with durable materials.

4.1. Appraisal of sediment condition Having demonstrated that the processes of chemical and sediment transport are strongly influenced by benthic shear stress it is arguable that sediment condition may be largely quantified by this single physical factor. To this end a classification scheme is proposed to measure six distinct zones of sediment condition: dead, cells, feed, clay, silt, and sand. Table 2 outlines the supposed conditions in each zone.

4.1.1. Dead zone Dead spots are expected where benthic shear stress is less than 0.001 N/m2. Sediment scouring is insignificant in this zone, while the process of sedimentation

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Table 2 Sediment stress zones

Sand Silt Clay Feed Cells Dead

Benthic shear stress t (N/m2)

Grain size d (mm)

Sediment aerationa J*Az (g/m2 per day)

Min

Max

Min

Max

Min

Max

0.1 0.03 0.01 0.003 0.001 0

2.3 0.1 0.03 0.01 0.003 0.001

63 4 0.1 12 1 0

3,000 63 4 100 12 1

3.1 1.7 1 0.5 0.3 0

14 3.1 1.7 1 0.5 0.3

a The sediment aeration rate is based on the assumption that the water column offers a concentration potential of 5 mg/l with respect to surface of the sediment.

would progress for all classes of particulate matter. Accumulated sludge beds contain a mixture of organic and mineral matter. Oxygen diffusion would be about 0.25 g/m2 per day on the basis of 5 mg/l in the water. Day light conditions improve with photosynthesis of settled algae. The author has observed P. monodon in the dead zones of ponds at midday, where they appeared to be delving into the sediment in search of food and shelter. Due to the extreme thickness of the diffusive boundary layer and breakneck respiration of bacteria, it is expected that stocking capacity of the dead zone is near zero at night.

4.1.2. Cell zone Single cells and small algal particles would tumble along from 0.001 to 0.003 N/m2. The cell zone is sub-optimal because larger flocs of algae may form mats on the bottom subject to burial by fallout of silt. Oxygen diffusion would be about 0.5 g/m2 per day if there were 5 mg/l in the water. The diffusive boundary layer in this zone would be about 1 mm thick, suggesting that the gills of prawns could reach up into the oxygen-bearing waters of the water column. 4.1.3. Feed zone Larger algal flocs and feed pellets would initiate motion from 0.003 to 0.01 N/m2. The upper end of this range would be optimum because all edible material would be suspended or tumbling along, while no mineral particles would be disturbed. A problem would exist if there were other zones at higher stresses which would cause fallout of silt in places with shear stress less than 0.01 N/m2. The ‘conveyor-belt’ phenomenon was described by Boudreau (1997) whereby remote scouring processes may causes sludge to be dumped on an area of the bottom. Oxygen diffusion would be up to 0.7 g/m2per day given 5 mg/l in the water column.

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4.1.4. Clay zone A stress of 0.01 – 0.03 N/m2 is expected to move non-cohesive clay sized particles, while it is acknowledged that the cohesive properties of clays may be much more durable. Conversely it could be postulated that clay colloids already in suspension would be able to settle out of suspension where local benthic shear stress drops into the range of 0.01 – 0.03 N/m2. Except in the case of an especially well managed pond, the clay zone is likely to receive silt fallout which would mix with the bed flows of flocculating clay and organic matter. Dissolved organic substances may be involved in clay mineral chemistry. Oxygen diffusion would be about 1.2 g/m2 per day assuming a bulk pond concentration of 5 mg/l. 4.1.5. Silt zone Non-cohesive particles in the size range of silts would begin scour in the range of 0.03–0.1 N/m2. Silts finer than 10 or 20 mm are mobilised more easily and so they are the most common constituent in dead zone sludge. Larger silt particles would tumble along in bed flows. Soil in this zone would be scoured away with time. Oxygen diffusion would be near 2.5 g/m2 per day on the basis of an anaerobic bottom and 5 mg/l in the water. 4.1.6. Sand zone Sand begins to move with a shear stress of 0.1 N/m2. All lighter materials would be absent. Oxygen diffusion would be up to 5 g/m2 per day on the basis of 5 mg/l concentration potential, although soil may already be aerobic, without driving potential. The oxygen diffusion capacity of the sandy zone compares to a stocking density of 30 PL/m2 on the basis of 200 mg O2/kg animal/ h respiration rate (Boyd, 1995) and 35 g harvest size. Thereby the oxygen demand of stock is estimated at about 0.168 g of O2/day per animal. It would appear there is a problem in the other zones of the benthos of such an intensively stocked pond, indicating that stock must somehow force sufficient flow over their gills. 4.2. Implications for sediment quality Notice that the names of the zones adopted in the previous section are not necessarily identical with the materials actually found at such locations. Zone names identify the class of particles which would tumble along on the verge of resuspension into the water column. For example, fine silt may be displaced from the silt zone, leaving coarse silt and sand. The appraisal of sediment quality depends upon two-tiered reasoning. In the first instance it is essential to determine the base material properties of silt and sand zones which thereby affect the sediment load at the lower stress zones of the same pond. If locations subjected to high stress are not armoured then it is likely that scouring will be an ongoing problem. The best-case scenario is applicable to ponds with exceptional armour and less intensive circulation. The later situation is referred to as the well managed pond.

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The well managed pond scenario would apply only in cases where pond levees are armoured against erosion due to circulation and the breaking of wind-driven waves. The author has found that levee banks are usually repaired between crop cycles, providing a continuous source of erosion. Other farms have parent soil contained a sufficiently high proportion of stones and gravel that lighter material eventually washes out by the processes of aeration and water exchange, converting pond banks into stone walls. Some managers cover pond banks with plastic or concrete and place sand on the bottom. The magnitude of benthic shear stress may be used to indicate the likely sediment quality at each zone after the armouring status of the pond has been characterised. Table 3 summarises the author’s opinion of the combined effect of pond classification (as eroding or armoured) and local benthic shear stress.

4.3. Practical estimation of benthic shear stress Aquaculturalists need a straightforward method to assess benthic shear stress. This can be achieved by observing the surface speed, u and measuring the depth of water column. Possible methods include time-tracking the displacement of floating particles, such as orange citrus fruit. Benthic shear stress is represented by the shear velocity, u* = t/r. Peterson (1999) reworked formulae reviewed by Henderson (1966), finding the ratio of surface speed to shear velocity magnitude is proportional to the square root of the Fanning friction factor, f, and also as the ratio of water depth to roughness, h/ks, all as formulated in Eq. (21) u /u* = 8/f =4 2 log10(12h/ks)

(21)

For example, a one metre deep pond has a sandy soil with a characteristic roughness of about 1 mm. Then ks = 0.001 m and so u /u*: 23. If pond Table 3 Conjectural appraisal of sediment quality

Sand Silt Clay Feed Cells Dead a

Benthic shear stress t (N/m2)

Eroding pondsa (intensive circulation)

Armoured pondsb (and less intensive circulation)

Min

Max

Surface soil

Deep soil

Surface soil

Deep soil

0.1 0.03 0.01 0.003 0.001 0

2.3 0.1 0.03 0.01 0.003 0.001

Aerobic Aerobic Borderline Anaerobic Anaerobic Anaerobic

Aerobic Borderline Anaerobic Anaerobic Anaerobic Anaerobic

Aerobic Aerobic Aerobic Aerobic Borderline Anaerobic

Concrete Sand Aerobic Borderline Anaerobic Anaerobic

Levee banks composed of loose soil, steep, and requiring regular reconstruction. The special case of a well managed pond by various means: Stone or concrete affixed on steep banks, gravel placed downstream of each aerator, and sand laid on all other peripheral portions of pond bottom; or soil ponds with minimal scouring achieved by other means (less intensive circulation or uniform distribution of stress). b

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Table 4 Practical estimation of benthic shear stress Density, r = 998 kg/m3

Estimated benthic shear stress (N/m2) as a function of water column

0.6 m Surface speed (m/s) 0.010 0.00021 0.015 0.00047 0.02 0.00084 0.03 0.0019 0.04 0.0034 0.06 0.0075 0.08 0.013 0.10 0.021 0.12 0.030 0.15 0.047 0.2 0.084 0.3 0.19 0.4 0.34 Adjustment for roughness ks =0.01 m +82% increases t ks =0.001 m As above tabulated t ks =0.0001m −37% decreases t

0.8 m

1.0 m

1.2 m

1.5 m

2.0 m

0.00020 0.00044 0.00079 0.0018 0.0031 0.0071 0.013 0.020 0.028 0.044 0.079 0.18 0.31

0.00019 0.00042 0.00075 0.0017 0.0030 0.0067 0.012 0.019 0.027 0.042 0.075 0.17 0.30

0.00018 0.00041 0.00072 0.0016 0.0029 0.0065 0.012 0.018 0.026 0.041 0.072 0.16 0.29

0.00017 0.00039 0.00069 0.0016 0.0028 0.0062 0.011 0.017 0.025 0.039 0.069 0.16 0.28

0.00016 0.00037 0.00065 0.0015 0.0026 0.0059 0.010 0.016 0.023 0.037 0.065 0.15 0.26

+78%

+75%

+73%

+71%

+68%

As above

As above

As above

As above

As above

−36%

−36%

−35%

−34%

−34%

circulation were 0.1 m/s then the shear velocity would be 4.3 mm/s, and the magnitude of the benthic shear stress would be about 0.02 N/m2 (‘clay zone’). Table 4 applies this relationship over an array of surface speeds and water column depths normally found in aquaculture ponds. Surface speeds in the range 3–4 cm/s would stress the bottom between 0.001 and 0.003 N/m2, creating ‘cell zone’ conditions. Such conditions are recommended when feeding epibenthic shrimp species.

Acknowledgements This research was made possible with funding from the Pond and Effluent Project of the Aquaculture CRC (Australia). The following entities at James Cook University were helpful for the reasons noted: academic supervision from Lal Wadhwa and Jonathan Harris; particle sizing at the Sedimentology Laboratory and the Geomechanics Laboratory; and chemical analysis at the Advanced Analytical Centre. I further wish to commemorate my late grandfather Bertel Peterson for demonstrating the importance of river sediments.

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Appendix A. List of symbols a c CA CDO CDO,entity CSS CSS,bed Cm D d50 du/dz De DAB Dx, Dy, Dz D* f g h J *Az K ks kL Kla n nj p −pdij Re* Sct Sij 2r(n+nt)Sij ui u=u1 u u¯ u% u+ u* 6=u2 w=u3 wSS x y

mass transfer area (m2) Shaw and Hanratty coefficient (0.000463) concentration of general species A (molA/m3) actual dissolved O2 concentration (mg O2/l) DO concentration in given entity (mg O2/l) suspended sediment in water column (m3 SS/m3 water) bed fraction as suspended sediment(m3 SS/m3 sediment bed) turbulent viscosity factor (0.09) particle size (m) mean particle size (m) vertical velocity gradient (s-1) effective mass transfer diffusivity (m2/s) diffusivity of A in solvent B (m2/s) anisotropic diffusivity (m2/s) non-dimensional grain size (-) Fanning friction factor (-) acceleration due to gravity (9.81 m/s2) depth of pond (m) flux of species A in z direction (molA/m2 per s or gA/m2 per s) turbulent kinetic energy (m2/s2) bottom roughness (m) mass transfer velocity at interface (m/s) kL/h actual transfer coefficient (s-1) Shaw and Hanratty exponent (3.38) normal vector (-) pressure (N/m2) isotropic stress (N/m2) u* · d/n0 grain size number (-) turbulent Schmidt number (0.9) 0.5(#u¯i /#xj+#u¯j /#xi ) strain rate (s-1) deviatoric stress (N/m2) general velocity vector (m/s) x-component of velocity (m/s) general velocity along streamline (m/s) time averaged mean velocity (m/s) velocity fluctuations (m/s) u/u* log-law wall velocity profile (-)

t/r shear velocity (m/s) y-component of velocity (m/s) z-component of velocity (m/s) settling velocity of solid particles (m/s) northward Cartesian co-ordinate (m) westward Cartesian co-ordinate (m)

109

110

y+ z dD dij

D DCDO o k ne nt n0 u ucr r rs rentity ru%i u%j sij t tcr tij

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y-plus Reynolds number (-) vertical Cartesian co-ordinate (m) diffusive boundary layer thickness (m) Ã1 0 0Ã Kronecker delta Ã0 1 0Ã Ã0 0 1Ã (rs−r)/r relative specific gravity (-) concentration driving potential (mg O2/l) dissipation of kinetic energy(m2/s3) von Karman constant (0.41) n0+nt effective viscosity (m2/s) eddy viscosity (m2/s) molecular viscosity (m2/s) tr -1D-1g -1d -1Shields mobility (-) critical mobility number (-) density of water (kg/m3) density of sediment (kg/m3) density of given entity (kg/m3) Reynolds stress (N/m2) stress tensor (N/m2) local shear stress at wall or bottom (N/m2) critical shear stress for resuspension (N/m2) shear stress tensor (N/m2)

References Abbott, M.B., Basco, D.R., 1989. Computational Fluid Dynamics: an Introduction for Engineers. Longman Scientific and Technical, Essex, UK, p. 425. Bloesch, J., 1995. Mechanisms, measurements and importance of sediment resuspension in lakes. Mar. Freshw. Res. 46, 295–304. Boudreau, B.P., 1997. A one-dimensional model for bed-boundary layer particle exchange. J. Mar. Systems 11, 279–303. Boussinesq, J., 1877. Me´m. pre´s. par div. savant a` l’acad. sci. Paris 23, 46. Bowie, G.L., Mills, W.B., Porcella, D.B., et al., 1985. Rates, Constants, and Kinetic Formulations in Surface Water Quality Modeling, second ed., EPA/600/3-85/040, US Environmental Protection Agency, Athens, GA. Boyd, C.E., 1995. Bottom Soils, Sediment, and Pond Aquaculture. Chapman and Hall, New York, p. 348. Boyd, C.E., Ahmad, T., 1987. Evaluation of aerators for channel catfish farming. Bulletin 584, Alabama Agricultural Experiment Station, Auburn, AL, p. 52. Brune, D.E., Garcia III, A., 1991. Transport limitation of oxygen in shrimp culture ponds. Aquac. Eng. 10, 269 –279. Burford, M, Peterson, E.L., Bianio, J., Preston, N., 1998. Bacteria in shrimp pond sediments-their role in mineralising nutrients and some suggested sampling strategies. Aquac. Res. 29, 843 – 850.

E.L. Peterson / Aquacultural Engineering 21 (1999) 85–111

111

Busch, C.D., 1980. Water circulation for pond aeration and energy conservation. Proc. World Maric. Soc. 11, 93 – 101. Fast, A.W., Boyd, C.E., 1992. Water circulation, aeration and other management practices. In: Fast, A.W., Lester, J.L. (Eds.), Marine Shrimp Culture: Principles and Practices. Elsevier, Amsterdam, pp. 457 – 495. Ferziger, J.H., Peric, M., 1996. Computational Methods for Fluid Dynamics. Springer-Verlag, Berlin, p. 356. Fluid Dynamics International, 1993. Fluid Dynamics Analysis Package FIDAP. Fluid Dynamics International, Evanston, IL. Funge-Smith, S.J., Briggs, M.R.P., 1994. The origins and fate of solids and suspended solids in intensive marine shrimp ponds. Summary report from the Songkla Region of Thailand, Institute of Aquaculture, Stirling, Scotland, UK, p. 20. Gloor, M., Wuest, A., Munnich, M., 1994. Benthic boundary mixing and resuspension induced by internal seiches. Hydrobiologia 284, 59–68. Henderson, F.M., 1966. Open Channel Flow. MacMillan, New York, p. 522. Jahnke, R.A., Jackson, G.A., 1992. The spatial distribution of sea floor oxygen consumption in the Atlantic and Pacific Oceans. In: Rowe, G.T., Pariente, V. (Eds.), Deep-Sea Food Chains and the Global Carbon Cycle. Kluwer Academic, Dordrecht, The Netherlands, pp. 295 – 307. Jørgensen, B.B., Des Marais, D.J., 1990. The diffusive boundary layer of sediments: oxygen microgradients over a microbial mat. Limnol. Oceanogr. 35, 1343 – 1355. Jory, D.E., 1995. Feed management practices for a healthy pond environment. In: Browdy, C.L., Hopkins, J.S. (Eds.), Swimming Through Troubled Waters, proceedings of the Special Session on Shrimp Farming, Aquaculture ’95. World Aquaculture Society, Baton Rouge, Louisiana. Lawson, T.B., Wheaton, F.W., 1982. Pond culturing of crawfish in the Southern United States. Aquac. Eng. 1, 311–317. Lin, C.K., 1995. Progression of intensive marine shrimp culture in Thailand. In: Browdy, C.L., Hopkins, J.S. (Eds.), Swimming Through Troubled Water, proceedings of the Special Session on Shrimp Farming, Aquaculture ‘95. World Aquaculture Society, Baton Rouge, LA. Miller, M.C., McCave, I.N., Komar, P.D., 1977. Threshold of sediment motion under unidirectional currents. Sedimentology 24, 507–527. Moriarty, D.J.W., 1997. The role of microorganisms in aquaculture ponds. Aquaculture 151, 333 – 349. Peterson, E.L., 1998. Benthic shear stress and sediment quality. In: World Aquaculture ‘98 Book of Abstracts, World Aquaculture Society, Las Vegas, p. 413. Peterson, E.L., 1999. The Effect of Aerators on the Benthic Shear Stress in a Pond. PhD thesis. The Library, James Cook University, Townsville, Australia. Reynolds, O., 1895. On the dynamical theory of incompressible viscous fluids and the determinations of the criterion. Philos. Trans. R. Soc. London A 186, 123. Rogers, G.L., 1989. Aeration and circulation for effective aquaculture pond management. Aquac. Eng. 8, 349 – 355. Shaw, D.A., Hanratty, T.J., 1977. Turbulent mass transfer rates to a wall for large Schmidt number. AIChE J. 23 (1), 28–37. Shields, A., 1936. Anwendung der Aehnichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung, Mitteilungen der Preussischen Versuchsanstalt fur Wasserbau and Schiffbau, Berline. Translation by Ott, W.P., van Uchelen, J.C., 1936. Application of similarity principles and turbulence research to bed-load movement, Soil Conservation Service Cooperative Laboratory, California Institute of Technology, Pasadena, CA. Smith, P.T., 1996. Physical and chemical characteristics of sediments from prawn farms and mangrove habitats on the Clarence River, Australia. Aquaculture 146, 47 – 83. Syvitski, J.P.M., Asprey, K.W., Leblanc, K.W.G., 1995. In-situ characteristic of particles settling within a deep-water estuary. Deep-Sea Res. Part 2, 42, 223 – 256. Tennekes, H., Lumley, J.L., 1972. A First Course in Turbulence. Massachusetts Institute of Technology, Cambridge, MA. Wainright, S.C., Hopkinson Jr, C.S., 1997. Effects of sediment resuspension on organic matter processing in coastal environments: a simulation model. J. Mar. Syst. 11, 353 – 368. Wolfram Research, Inc., 1996. Mathematica 3.0, Wolfram Research, Champaign, IL. Yalin, M.S., 1977. Mechanics of Sediment Transport, second ed., Pergamon, Oxford, p. 298.