A numerical study of marine larval dispersal in the presence of an axial convergent front

Estuarine, Coastal and Shelf Science 100 (2012) 172e185

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A numerical study of marine larval dispersal in the presence of an axial convergent front P.E. Robins*, S.P. Neill, L. Giménez School of Ocean Sciences, Bangor University, Menai Bridge, Anglesey LL59 5AB, UK

a r t i c l e i n f o

a b s t r a c t

Article history: Received 13 September 2011 Accepted 2 February 2012 Available online 13 February 2012

Estuarine axial convergent fronts generate strong secondary (cross-estuary) flows which can be important for larval dispersal and settlement, and have been shown in this research to aid estuarine retention of natal populations which will promote production. This paper explores several larval migratory strategies, synchronised by sensory cues such as pressure, velocity, salinity and solar radiation, in relation to an estuarine axial convergent front e an important circulatory mechanism that forms in many coastal regions where larvae are concentrated; hence these results have implications for fisheries management. A three-dimensional hydrodynamic model is applied to an idealised channel, parameterised from observations of a well documented axial convergent front in the Conwy Estuary, UK. The model simulates the bilateral cross-sectional circulation of the front, attributed to the interaction of lateral shear of the longitudinal currents with the axial salinity gradient. Axial surface convergence develops during the flood phase of the tide and (weaker) surface divergence during the ebb phase. Lagrangian Particle Tracking Models subsequently use velocities from a range of simulated tidal and climatic scenarios to track larvae in the estuary. The results show that axial convergent fronts aid estuarine retention of larvae. Specifically retention is enhanced for larvae that experience tidal stream transport and diel migration. Tidally-synchronised larvae exhibit the strongest landward dispersal while the modelled copepod (a combination of tidal and salinity cues) exhibits ‘full retention’ in the midestuary release location. Finally, the vertical migration speed of the larvae must exceed the background vertical velocities in order to get the greatest enhancement of retention. Ó 2012 Elsevier Ltd. All rights reserved.

Keywords: larval transport larval dispersal axial convergent front estuaries Conwy Irish Sea

1. Introduction The persistence of estuarine populations of many aquatic invertebrates depends on strategies and adaption to respond to variations in tidal and freshwater flow (e.g. Cronin and Forward, 1979, 1986; DiBacco et al., 2001). Some organisms, such as copepods and amphipods, develop behaviours to migrate vertically in response to the tide (Hough and Naylor, 1991, 1992a, 1992b) to aid retention near their spawning site; in other systems copepods appear to behave passively (Castel and Veiga, 1990). Vertical migration is also found in larval stages of some decapod crustaceans that respond to tidal variations using a series of environmental cues (hydrostatic pressure, wave agitation, flow-induced turbulence, salinity and temperature) to retain larvae within the estuary (e.g. Rhithropanopeus harrisii : Cronin and Forward, 1979; Petrolisthes armatus: Tilburg et al., 2010). In other species of

* Corresponding author. E-mail address: [email protected] (P.E. Robins). 0272-7714/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ecss.2012.02.001

estuarine decapod crustaceans, females migrate to the coastal zone so that larvae hatch and develop outside the estuaries; however, the final larval stage re-colonizes estuaries through a mechanism known as selective tidal stream transport by which larvae migrate towards surface waters during the flood tidal phase and remain in deeper waters during the ebb phase (Queiroga, 1998). Most of the proposed mechanisms about how tidal and freshwater flows affect the transport of organisms within an estuary abstract the process of transport as occurring in a system of two dimensions given by the vertical axis and a horizontal axis along the estuary. However, a series of secondary flows are common in estuaries, and they are modelled correctly only in a threedimensional system. Secondary flows are often associated with fronts, regions of sharp gradients between two water masses. Such fronts are common and persistent features of many estuaries and can be further-classified as tidal mixing fronts, plume fronts, shear fronts, and axial convergent fronts - based on the mechanism controlling the horizontal density gradient (Simpson and Turrell, 1986; O’Donnell, 1993; Neill, 2009). While several studies have investigated phytoplankton blooms at tidal mixing and plume

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fronts (e.g. LeFevre, 1986; Franks, 1992; Sharples and Simpson, 1993; Largier, 1993), and at open-ocean fronts (e.g. Yoder et al., 1994), little is known about how larvae respond to axial convergent fronts in estuaries (Largier, 1993; Queiroga and Blanton, 2005). This is important, because estuarine fronts are often associated with secondary flows that can significantly affect the local circulation and hence the distribution of planktonic organisms and their exposure to more favourable settling grounds at the shoals of the estuary (Largier, 1993). An example of an axial convergent front is illustrated in Fig. 1; an idealised estuarine simulation which is explained further in Section 2. The front occurs in estuarine systems where across-estuary (lateral) density variations are generated which lead to crosssectional bilateral baroclinic circulation (secondary flow). This takes place where there is an axial salinity gradient (as is the case in most estuaries as saline water meets fresh water) and also a bathymetry which enhances lateral shear in the longitudinal velocity. In such a circumstance, densities in the centre of the channel are greater than over the shoals for a period of a few hours during the flood phase of the tide, due to the interaction of lateral shear of the longitudinal currents (stronger in the deeper central channel) and the axial salinity gradient (Fig. 1a). Consequently, secondary baroclinic circulation develops, producing surface convergence along the main axis of the estuary (Fig. 1b), often visible due to the accumulation of organic matter and an intense foam line (Nunes and Simpson, 1985; Brown et al., 1991; Turrell et al., 1996), with a corresponding divergence at the bed. Conversely, axial surface divergence will theoretically occur during the ebb tide, but observations of this phenomenon are rare. Such fronts can be maintained when the estuary is well mixed vertically. Axial convergent front mechanisms were originally explained by Nunes and Simpson (1985) after their observations in the Conwy Estuary, UK. Axial convergent fronts are ubiquitous features of estuarine systems, evidenced by many studies in the literature (e.g.

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Huzzey and Braubaker, 1988; Brown et al., 1991; Swift et al., 1996; Eggleston et al., 1998; Lerczak and Geeyer, 2004). Secondary flows associated with axial convergent fronts can be of order 20% of the longitudinal flows (e.g. Brown et al., 1991) and may significantly influence the transport and dispersal of estuarine planktonic organisms, in addition to contributing to the mixing processes. Eggleston et al. (1998) investigated the distribution and transport of Dungeness crab Cancer magister in an axial convergent front in Grays Harbour Estuary, USA. They noted that the secondary circulation may act as a cross-frontal barrier and lead to strong along-frontal flows, which may serve as a larval conduit, funnelling larvae accumulating at the front to potential settlement locations. In the present paper, we are interested in evaluating the potential effects of axial convergent fronts on the distribution of planktonic organisms. We addressed this objective through particle tracking models (PTMs) that incorporate and evaluate the role of migration strategies on planktonic dispersal. The interaction of hydrodynamic models and PTMs has been used extensively in recent years to understand the transport and dispersal of larval stages of marine organisms. In this prevalent area of research, most studies have concentrated on large scale movements and connectivity between geographically distinct sites and species (e.g. Cowen et al., 2006; Levin, 2006). Banas et al. (2009) is one of the few papers addressing the question of larval transport in an estuarine site with the help of a three-dimensional model. However, they were concerned primarily with the biological consequences of the patterns of larval retention rather than the physical causes of these patterns. PTM studies of larval dispersal in Scottish sea lochs (e.g. Gillibrand and Willis, 2007; Amundrud and Murray, 2009) has been undertaken, though these environments are dissimilar to shallow, well mixed estuaries. Therefore, the present study explores larval transport within an estuarine axial convergent front; a region of high importance for larval transport and growth (e.g. Wolanski and Hamner, 1988; Eggleston et al., 1998; North et al., 2006). In this

Fig. 1. Output from the hydrodynamic model (see Section 2), which illustrates an axial convergent front in an idealised estuarine channel. During flood tides, longitudinal surface velocity vectors and densities are plotted in (a); the interaction of lateral shear of the longitudinal velocities (parabolic lateral velocity profile) with the axial salinity (density) gradient causes a wedge-shaped advecting plume. The vertical slice plane (AeB) at X ¼ 10 km is plotted in (b), which shows lateral density variations and bilateral cross-sectional circulation in the velocity vectors. Points x1ex5 indicate the locations of velocity time series plotted in Fig. 3. The longitudinal velocity vectors in (a) are a factor of 20 greater than the lateral vectors (b).

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environment, the secondary baroclinic circulation fundamentally influences the probability of settlement and recruitment of larvae. Furthermore, a crucial trait of planktonic organisms is that their migration behaviour will influence their dispersal and, therefore, behaviour must be incorporated into the particle tracking algorithm. The vertical position of planktonic organisms within the water column (especially for estuaries where an axial convergent front forms) influences their advection, feeding success, predation risk, growth, and ability to detect sensory cues (North et al., 2006). In this study, we model the dispersal of organisms in the Conwy Estuary, a region where there are a number of species that may be affected by an axial convergent front. Two key planktonic species, the copepod Eurytemora affinis and the amphipod Gammarus zaddachi appear to be retained within the Conwy Estuary through a combination of vertical migration behaviours (Hough and Naylor, 1991, 1992a, 1992b). The copepod E. affinis follows a complex pattern of migration: individuals located towards the seaward end of the estuary swim upwards on the flood tide and hence are transported up-estuary in the stronger surface currents, while those located towards the head of the estuary swim upwards on the ebb tide (reverse tidal migration). In consequence, the population is concentrated towards the centre of the estuary (Hough and Naylor, 1991, 1992a). For the amphipod G. zaddachi, individuals change their vertical migration behaviour through the season: juveniles migrate upstream in August by swimming upwards during the flood tides; adults migrate downstream in winter and spring by swimming upwards during the ebb tides. This pattern also varies with the position of individuals along the estuary (Hough and Naylor, 1992b), as in E. affinis. In addition the last larval stage (megalopa) of the shore crab Carcinus maenas is known to invade estuaries of the North European coast through tidal vertical migration (Queiroga, 1998; Queiroga et al., 2006). Larvae of the great scallop Pecten maximus appear to follow diel vertical migrations with higher positions in the water column during periods of darkness (Kaartvedt et al., 1987), trapping these organisms in the estuarine waters. Diel migration occurs for several reasons, e.g. predator avoidance or stimulation of digestion (Wurtsbaugh and Neverman, 1988). As a first step we describe the three-dimensional hydrodynamical model and then a more detailed account of its application to an idealised estuarine channel, parameterised on the Conwy Estuary (see “Methods”). Also in this section, development of the PTMs and the experimental programme are explained. Next (see “Results”), we describe simulations designed to investigate specific aspects of the estuarine circulation and transport of planktonic organisms. For the PTM simulations, vertical migrations which represent the above organisms were implemented: selective tidal stream transport, or tidal migration (Carcinus maenas, Eurytemora affinis and Gammarus zaddachi), diel migration (Pecten maximus) and passive particles with no vertical migration. The migration strategies have been compared to assess their relative importance in terms of larval transport. In Section 4 (see “Discussions”), we consider the consequences of behavioural strategies for transport in estuarine axial convergent fronts of different strengths. In the final section, conclusions of the research are presented. 2. Methods Three-dimensional hydrodynamic simulations of axial convergent fronts were generated to drive PTMs so that larval transport could be investigated through a modelling approach. A set of climatic simulations were designed which represent the likely changes in estuarine circulation, in contrast to a baseline test case which has been parameterised on the present-day axial convergence that has been observed in the Conwy Estuary (Nunes and Simpson, 1985).

2.1. Hydrodynamic model description The Stony Brook Parallel Ocean Model (sbPOM1) is a parallelised version of the 3D, primitive equation, sigma-coordinate, free-surface Princeton Ocean Model (POM). The model (in its non-parallel form, POM) is described in detail by Blumberg and Mellor (1987) and, hence, is only outlined briefly here. POM incorporates Mellor and Yamada (1982) turbulence closure which yields more realistic Ekman surface and bottom layers. The Level 2.5 closure model is used together with a prognostic equation for the turbulence macroscale. The standard prognostic variables (e.g. velocity, temperature, salinity, turbulence) are solved using finite-difference discretization on a staggered, orthogonal Arakawa-C grid in the horizontal, and using sigma-coordinates in the vertical. An implicit numerical scheme in the vertical and a mode-splitting technique in time have been adopted for computational efficiency. Horizontal diffusion is calculated using the Smagorinsky Diffusivity (Smagorinsky, 1963), based on a non-dimensional coefficient that has the advantage of reduced diffusivities with increased grid resolution. It is assumed that the weight of the fluid identically balances the pressure (hydrostatic assumption) and also that density differences are neglected unless the differences are multiplied by gravity (Boussinesq approximation). The former assumption is valid provided that the vertical accelerations do not get too large, such as flow near steep bathymetric gradients. Pressure gradient errors associated with computing variables along steep sigma-coordinates are reduced by subtracting the area-averaged density from the horizontal pressure gradient terms in the momentum equations (Mellor et al., 1994). Increasing the vertical resolution and bathymetric smoothing also help avoid such errors (e.g. Robins and Elliott, 2009). 2.2. Hydrodynamic model application The model was parameterised from observations of the axial convergent front which occurs in the Conwy Estuary, UK (Fig. 2). Nunes and Simpson (1985) observed that during the flood phase of the tide, lateral parabolic current profiles are generated with stronger flow in the centre of the channel (due to less frictional influence), which advects dense off-shore water up-estuary quicker than at the shallower edges of the channel. During a mean flood tide, a lateral density difference is created (of order 0.32 kg m3) until the currents begin to diminish approaching high water. During this period, lateral baroclinic forcing generates crosschannel convergence and near-bed divergence forming an axial convergent front. During the latter half of the ebb tide, the reverse baroclinic forcing occurs (surface divergence, near-bed convergence), since the mid-channel waters are less dense than on the shoals. Tidal ranges in the macro-tidal Conwy Estuary are 3.8 m (neaps) and 6.9 m (springs), generating spring tidal currents into the estuary exceeding 1 m s1 (Nunes and Simpson, 1985; Pelegrí, 1988). Lateral velocities were observed by Nunes and Simpson (1985) to reach 0.1 m s1, or 20% of the local axial velocity. Tidal volume exchange exceeded mean river input by a factor of 20 (Simpson et al., 2001), ensuring that the majority of the estuary is vertically mixed. However, the longitudinal salinity gradients are large; of order 5e10 km1 (Turrell et al., 1996). An idealised channel geometry (Fig. 1) was created which resembles a cross-section of the Conwy Estuary, 2 km south of Conwy Bridge and mid-way down the estuary (see Fig. 2): a Gaussian channel profile in the across-channel direction with maximum and minimum depths of 10 m and 4 m (relative to mean

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URL: http://www.imedea.uib-csic.es/users/toni/sbpom/.

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Further simulations were performed to act as sensitivity tests which determine the relative importance of the axial salinity gradient. All the hydrodynamical runs simulated a typical larval period of 28 days and are summarised in Table 1. For comparative purposes, a diagnostic simulation, where an axial convergent front does not form, was performed (sbPOM-2). Salinity was fixed in space and time at 32. All other conditions were identical to the baseline simulation. For the remaining hydrodynamic simulations, the salinity forcing at the estuary-head was varied to represent (indirectly) changes in river flow (or rainfall) and simulate corresponding changes in baroclinic circulation. Some of the predicted consequences of climate change are increased precipitation in winter (Oliver et al., 2008) and also increased periods of drought in summer (Reaney and Fowler, 2008), leading to extreme high and low flow events in rivers, respectively, which in turn alter the longitudinal salinity gradient. Therefore, an extreme low longitudinal salinity gradient of 1 km1 representing drought conditions (sbPOM-3), and an extreme high longitudinal salinity gradient of 10 km1 representing high rainfall (sbPOM-4), scenario were devised (Table 1). 2.4. Simulating the transport of planktonic organisms

Fig. 2. Map of the Conwy Estuary, North Wales (boxed region in inset map of the UK). The location of the modelled cross-section is shown.

sea level), respectively, and of width 400 m. The along- and acrosschannel resolutions were 100 m and 10 m, respectively. The crosschannel Gaussian profile does not vary throughout the 40 km length of the idealised channel. There are 20 equally segmented terrain-following sigma layers in the model, giving a maximum vertical resolution of 0.2 m over the shoals and 0.5 m over the channel. Principal semi-diurnal M2 and S2 harmonic tidal constituents were applied at the mouth of the channel and allowed to dissipate out of the domain at the opposite boundary (head of the channel). In order to isolate tidal and buoyancy-driven components to the circulation, surface wind stress was omitted from the simulations. A similar approach was adopted by Neill (2009), where a 2D Gaussian cross-sectional model of the Conwy was applied to investigate sediment dynamics in the axial convergent front. 2.3. Hydrodynamic model simulations An initial (baseline case) simulation was performed (sbPOM-1) in order to reproduce the axial convergence under similar conditions to those observed in the Conwy Estuary (Nunes and Simpson, 1985), although a transect further downstream was used in this idealised application, so an exact parameterisation has not been made. M2 and S2 tidal elevation amplitudes of 2.5 m and 0.6 m, respectively, were applied at the estuary mouth, generating longitudinal surface velocities of 1.25 m s1 during springs. Salinity forcing was set to 22 at the head and 32 at the mouth of the channel (after discussions with J.H. Simpson), generating an axial salinity gradient across the frontal zone at slack water of w5 km1. Temperatures were spatially fixed at 10  C (for all simulations hereafter) so that variations in density are solely a function of salinity. The model was spun up for two tidal cycles (a test simulation showed velocities to reach a steady state after 1 tidal cycle), then run for a typical larval stage of 28 days. The larval stage of marine species has been shown to range from weeks to months (Garland et al., 2002), though our research of the literature found that 28 days was typical.

Lagrangian particle tracking models trace the individual movement of particles (in this case representing larvae) through space and time, based on advection, sub-grid scale turbulent mixing, and vertical larval swimming behaviour. From these models, the transport of larvae originating from a release or spawning site can be mapped and their dispersal range calculated. The PTM uses 3D velocity and diffusivity outputs from the hydrodynamic simulations, but are run off-line from the main computation, so that a single hydrodynamic simulation can be used for multiple particle release scenarios. The velocities are linearly interpolated from the hydrodynamic model spatial scales to the position of each particle, and the hydrodynamic output temporal resolution of 15 min is increased to 5 min for the PTM. Each particle is then iteratively advected horizontally and vertically. The particles are mixed locally through sub-grid scale turbulence, based on random displacement models (random walks), where the longitudinal change in position, Δx(m), over a PTM time step Δt(s) are given by (e.g. Proctor et al., 1994; Ross and Sharples, 2004):

R r

Dx ¼ $cosð2pRÞð2Kx DtÞ1=2

(1a)

where R is a random number in the range [0,1] pffiffiffi and r is the standard deviation of Rcos(2pR) with a value of 1= 6. The expression (R/r) cos(2pR) thus has the necessary properties of a mean of zero and a standard deviation of unity (Ross and Sharples, 2004). A similar expression for lateral diffusion is given by:

R r



Dy ¼ $sinð2pRÞ 2Ky Dt

1=2

(1b)

Table 1 Summary of hydrodynamic model simulations. Model simulation

Umax (m s1)

Axial frontal salinity gradient (km1)

sbPOM-1

Baseline: mean axial salinity gradient Uniform:zero axial salinity gradient Drought: reduced axial salinity gradient High rainfall: increased axial salinity gradient

w1.25

w5

w1.25

0

w1.25

w1

w1.25

w10

sbPOM-2 sbPOM-3 sbPOM-4

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Spatially and temporally varying horizontal diffusivities, Kx and Ky (m2 s1), were output from the hydrodynamic model and linearly interpolated in the same way as the velocities. A random displacement model (Visser, 1997; North et al., 2006) was used to simulate sub-grid scale vertical turbulence:

R r

Dz ¼ Kz0 Dt þ ð2Kz DtÞ1=2

(2)

where Kz (m2 s1) is the vertical diffusivity, outputted from the hydrodynamic model and linearly interpolated to the particle position, z, in the PTM algorithm, and Kz0 ¼ vKz =vz is evaluated at z. In order to ensure that sufficient numbers of particles were released so that the trajectories are not polluted by statistical outliers, a simple test was performed. Using velocities from the baseline hydrodynamic simulation, a large number of particles (1  106) were released from the centre of the channel (at the surface) and the concentrations of particles occurring in each grid cell after 28 days was calculated. No vertical migration was simulated. The PTM run was repeated, reducing the number of release particles, until the concentration in each cell, as a function of the total number of particles, started to fluctuate significantly (i.e. varied by more than 10% of the initial concentrations). The experiment was then repeated for different release depths (mid-depth and near-bed) and it was found that, overall, a cohort of approximately 1  104 particles is sufficient to satisfactorily represent larval dispersal. For each of the hydrodynamic scenarios (see Section 2.3), a range of PTM simulations were produced: 1  104 larvae were released instantaneously from either the sea surface or the bed, across the width of the channel, and equidistant from the head and mouth of the estuary. Their positions were tracked for 28 days. This time period covers two spring-neap tidal cycles and, although it is longer than the developmental time of the megalopae of Carcinus maenas, other planktonic organisms will remain in the water column. The following vertical migration strategies were modelled: (i) tidally-synchronised migration representing Carcinus maenas

megalopa and Gammarus zaddachi, (ii) normal/reverse tidal migration of the copepod Eurytemora affinis, (iii) diel migration representing the behaviour exhibited by Pecten maximus larvae, and (iv) passive (drifting) particles with no vertical migration. For the migration of the copepod we followed findings of Hough and Naylor (1991, 1992a): E. affinis, individuals located towards the seaward end of the estuary swim upwards on the flood tide (normal tidal migration), while those located towards the head of the estuary swim upwards on the ebb tide (reverse tidal migration). The simulations also included a variety of swimming speeds, leading to a total of 26 PTM runs, summarised in Table 2. For the tidally-synchronised PTM, particles swim upwards on the flood tide (where longitudinal velocity is the cue, rather than pressure) and downwards on the ebb, while for the daily (equinox)-synchronised model, particles swim upwards after 17:00 GMT and downwards after 05:00 GMT each day (i.e. equal amounts of time in the surface and at the bottom). To examine sensitivity, a summer solstice version of the PTM was designed whereby particles swim upwards after 20:00 GMT and downwards after 02:00 GMT (causing the particles to remain near the bed for longer). Provided the larval stage is a factor of the fortnightly semi-diurnal cycle (i.e. 28 days in this case), larvae will experience all states of the circulation with respect to their position. In some regions, however, the S2 tidal component dominates the flow and the daily and tidal cycles become synchronized (Hill, 1991a, 1991b) whereby the fate of diel larvae in an axial convergent front will be similar to that of tidallysynchronised larvae. The vertical swimming speed of passive larvae was set to zero, while for the former cases, the swimming speed was varied in the range 5  104e3  103 m s-1, to encompass swimming speeds reported in the literature (e.g. Shanks, 1995; North et al., 2008; Tian et al., 2009; Michalec et al., 2010; Seuront, 2010; Souissi et al., 2010). In water depths of 10 m, particles with this swimming speed range would therefore take between 1 and 6 h to swim from the surface to the bed. Particles which passed onto land (possible only due to diffusion) were

Table 2 Summary of PTM simulations. PTM run PTM-1.1 PTM-1.2 PTM-1.3 PTM-1.4 PTM-1.5 PTM-1.6 PTM-1.7 PTM-1.8 PTM-1.9 PTM-1.10 PTM-1.11 PTM-2.1 PTM-2.2 PTM-2.3 PTM-2.4 PTM-2.5 PTM-3.1 PTM-3.2 PTM-3.3 PTM-3.4 PTM-3.5 PTM-4.1 PTM-4.2 PTM-4.3 PTM-4.4 PTM-4.5

Hydrodynamic simulation

Vertical migration

Vertical migration speed (m/s)

Passive Tidal

0.0 0.0005 0.001 0.003 0.003 0.0005 0.001 0.003 0.0005 0.001 0.03

Surface/bottom

sbPOM-2 Horizontally uniform salinity

Passive Tidal Copepod Diel (equinox) Diel (solstice)

0.0 0.003 0.003 0.003 0.003

Surface/bottom Bottom Bottom Bottom Bottom

sbPOM-3 Reduced axial salinity gradient (drought)

Passive Tidal Copepod Diel (equinox) Diel (solstice)

0.003

Bottom

sbPOM-4 Increased axial salinity gradient (high rainfall)

Passive Tidal Copepod Diel (equinox) Diel (solstice)

0.003

Bottom

sbPOM-1 Baseline

Copepod (E. affinis) Diel (equinox)

Diel (solstice)

Release depth

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reflected back into the domain (normal to the boundary), rather than settle, since it is the potential dispersal at the end of the simulations that we are interested in. To isolate the effects of circulation and planktonic behaviour on the trajectories, other processes such as mortality, predation, and settlement (in case of larvae) were not considered in this idealised study. However, these additional processes should be incorporated into PTMs for accurate simulations in actual case studies, although such information is not readily available and there are only a few estimates of early lifestage mortality (e.g. Peterson and Wrobleski, 1984; Hirst and Kiørboe, 2002; Houde, 2002). For all PTM simulations, the maximum patch-averaged horizontal dispersal (in both landwards and seawards directions) and net migration over the 28-day period were calculated. The patchaveraged horizontal dispersal, at each time step, is defined: n X xi i¼1

n

(3)

where xi is the longitudinal position of particle i, and n is the total number of particles in the patch. A maximum value over the simulation indicates the landwards extent of dispersal whereas a minimum value indicates the seaward extent of dispersal. 3. Results 3.1. Simulation of the frontal zone and circulation An axial convergent front was successfully simulated for the baseline scenario (sbPOM-1; see Figs. 1 and 3), where the crosschannel bathymetric profile and velocities were parameterised for observations in the Conwy Estuary. During the flood tide, the model simulated lateral shear of the longitudinal currents (producing a cross-channel parabolic velocity profile), leading to cross-channel density variations that were comparable to observations by Nunes and Simpson (1985), and bilateral circulation with surface convergence and near-bed divergence (Fig. 3b). Longitudinal surface velocities reached 1.25 m s1 during spring tides, and near-bed longitudinal velocities were half as strong (Fig. 3a). Maximum lateral surface currents were 0.06 m s1 (Fig. 3b) which was approximately 5% of the longitudinal flow. On the ebb tide, the flow pattern reversed, generating surface axial divergence with peak lateral surface velocities of 0.05 m s1 (Fig. 3b). There is much less evidence of axial divergent fronts in the literature as they are generally weaker (and there is less indication of their existence at the surface due to the absence of a foam line), although they are inferred by Brown et al. (1991) and O’Donnell (1993). Axial convergent fronts were evidenced throughout the spring-neap cycle, enhanced during spring tides by approximately 25%, compared with neaps. Spring tide vertical velocities in the deepest part of the channel (Fig. 3c) reach 3.0  103 m s1 (downwards during the flood phase) and 5.0  103 m s1 (upwards during the ebb phase). Again, these magnitudes reduce by approximately 25% during neap tides. Secondary (lateral) flow was not simulated for the diagnostic scenario (sbPOM-2) where there was no axial salinity/density gradient (Fig. 3b). This demonstrates that, in this application, axial convergence is a function of the axial density gradient, as postulated by the observational research (Nunes and Simpson, 1985; Turrell et al., 1996), and not generated by topographic frictional effects alone. However, fronts and secondary flows can exist where the water column is uniform, such as where there are steep gradients in bathymetry (e.g. Neill et al., 2004), flow round meandering channels (e.g. Nidzieko et al., 2009) or flow separation around headlands and islands (e.g. Wolanski and Hamner, 1988). A

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simulation with the baseline salinities and constant depth (of 10 m) was performed (results not presented) and an axial convergent flow did not develop, demonstrating that lateral velocity shear is required to generate lateral density differences. For the extreme low longitudinal salinity gradient (drought) and high longitudinal salinity gradient (high rainfall) scenarios (sbPOM-3 and sbPOM-4), the maximum lateral density difference was 0.15 kg m3 and 0.5 kg m3, respectively, occurring at the surface during peak flood tide. Longitudinal velocities (Fig. 3a) were similar in magnitude to the uniform salinity simulation during the flood phase but slightly weaker during the ebb phase due to surface divergence. For all simulations with an axial salinity gradient, lateral flows were generated at all phases of the spring-neap cycle, and were approximately 5% of the longitudinal velocities. Vertical velocities at the centre of the channel were also similar in magnitude to the baseline simulation. 3.2. Transport of planktonic organisms Figs. 4e7 show larval trajectories within the channel domain, both in lateral slice and plan views. Several of the key simulations have been presented during convergent and divergent fronts, and as final distribution maps. Results from the PTM simulations, in terms of maximum axial dispersal, are summarised in Fig. 8 as a series of bar graphs illustrating the patch-averaged axial dispersal (Eq. (3)) from the origin. Therefore each bar represents two values: the maximum landward dispersal of the patch-averaged particle, and the maximum seaward dispersal. The patch-averaged net migration over the 28 day period is also shown. Shorter bars suggest high retention at the release zone. The bar graphs are grouped (and some repeated) according to the hydrodynamic conditions and biological traits, so that comparisons can more easily be visualised. Patch-averaged longitudinal and lateral distances travelled (i.e. absolute along- and across-channel path lengths), per tidal cycle, are also shown (Fig. 9). The PTM simulations are summarised in Table 2. 3.2.1. Larval trajectories and distribution With an axial convergent front present, the larval trajectories could be thought of as spiralling, or cork-screwing, longitudinally. During the flood phase, passive particles converged towards the channel centre and were then advected to the bottom due to bilateral convection (Fig. 4aeb). During the ebb phase, reversedconvection caused individuals to be advected back to the surface where they diverged to the shoals (Fig. 4ced). In the horizontal plane, particles oscillated along the channel with tidal flow and their lateral transport varied according to the scenario: lateral dispersal was higher when an axial convergent front was present as compared to the uniform salinity scenario (Fig. 4eeh). Fig. 9 also shows increased lateral distance travelled, per tidal cycle, when an axial convergent front forms. This behaviour results in passive particles spreading laterally so that they occupy the whole width of the estuary (Fig. 4). The transport described above is not applicable if the tidal oscillations become asymmetrical in character; for example, due to nonlinear friction in shallow estuaries (Pugh, 1987) or strong vertical stratification (Robins and Elliott, 2009). For all simulations with the baseline hydrodynamics (PTM-1.1-1.11), the depth of release made negligible difference to dispersal after 28 days. This was also the case for PTM-2.1. The release depth was only significant during the initial few tidal cycles and, therefore, it would only affect early settlers in the case of larval stages. For this reason, particles were released from near the bed only for the remaining scenarios. Tidally-synchronised particles migrating upwards during flood flow (and downwards during ebb flow) appeared to move up and down in the centre of the channel and showed reduced lateral

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transport; the result is that these particles did not disperse laterally (Fig. 5) as in the case of passive particles (Fig. 4). For example, passive particles travelled laterally 100e500 m, over a tidal cycle, whereas tidally-synchronised particles travelled less than 100 m (Fig. 9). Axial convergence and surface larval migration during flood flow caused particles to congregate in the centre of the channel (Fig. 5a) and disperse longitudinally along the channel (Fig. 5b). Convergence near the bed during ebb flow caused the downward swimming individuals to remain in the central axis of the channel (Fig. 5ced). Increased swimming speeds, relative to the background vertical velocities, enhanced this process (Fig. 5; Fig. 8b) as the larvae spent less time travelling through the water column. Again, longitudinal dispersal (Fig. 8c), and longitudinal transport over a tidal cycle (Fig. 9), were higher in scenarios with an axial convergent front present. The extreme situation is given by particles simulating the behaviour of the copepod Eurytemora affinis, where longitudinal dispersal was at a minimum (Fig. 6; Fig. 8d). In this case, salinity

was used as an additional sensory cue to pressure; when each particle experienced salinities that were in the lower half of the longitudinal salinity range (in the upper half of the estuary), reverse-tidal migration occurred. When particles were located seaward of the origin, they behaved in an identical manner to that shown in Fig. 5a and c, i.e. swimming towards the surface on the flood phase and converging in the channel centre, and swimming towards the bed on the ebb, and the net result is landwards migration over a tidal cycle. When the particles travelled upestuary of the origin, however, the reverse vertical transport occurred: particles moving up-estuary during the flood tide descended towards the (weaker) near-bed currents and diverged towards the banks and, therefore, their up-estuary migration was severely curtailed. The following ebb tide caused the particles to swim back to the surface where they remained near the banks due to surface divergence. Once the particles were located seaward of the origin, they were transported towards the bed and converged towards the channel centre until high water whence they were

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Fig. 4. Instantaneous distributions of 10,000 passive larvae-particles (green particles) after 15 days during the flood tide (a and b) and the ebb tide (c and d), for the baseline hydrodynamic simulation (axial convergent front present; PTM-1.1). The corresponding cross-channel (a and c) and surface (b and d) isopycnals and velocity vectors are also shown (longitudinal velocity vectors in b and d have been reduced by a factor of 20). The dotted lines in (b) and (d) indicate the particle release origin. The final distribution of particles after 28 days is shown in (e) and (f). The additional dotted lines in (f) show the patch-averaged landwards and seawards dispersal distances after the 28 day period (i.e. corresponding to the bar lengths in Fig. 8). The final two panels (g and h) depict the final distributions of the corresponding passive particles when there is no axial convergent front present (PTM-2.1), showing less axial convergence, less lateral dispersal and reduced longitudinal transport. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

transported back towards the surface and completed the cycle (Fig. 6ae6d). This migratory regime had a significant impact on the patch-dispersal, effectively using the lateral baroclinic flow to minimise axial dispersal range and net dispersal of the patch (Fig. 6eef; Fig. 8d). This behaviour is advantageous in terms of reducing salinity and temperature ranges and remaining close to the parent population, all of which could increase the likelihood of settlement and production. Particles which followed diel migration (Fig. 7) exhibited considerable lateral dispersal; particles travelled laterally 200e500 km, over a tidal cycle, when an axial convergent front was present (Fig. 9). Particles at the surface converged towards the channel centre during the flood tide and moved towards the banks during the ebb tide (Fig. 7a and b, respectively). Consequently, they travelled in stronger currents during the flood than the ebb. The opposite process occurred near the bed (Fig. 7c and d), but the nearbed currents are weaker and hence the overall net migration of the larvae patch was up-estuary (Fig. 8eef), since equal amounts of day and night occurred (equinox). Longitudinal dispersal during the solstice, however, was less (Fig. 7f; Fig. 8eef) because, during summer months, larvae spend more time in the (weaker) near-bed currents. Net seaward dispersal of the larvae patch was also apparent during the solstice (and in many individual larvae regardless of the season), in contrast to tidally-synchronised particles, suggesting that diel larvae have a greater chance of exiting the estuary. Stronger swimmers relative to the vertical velocities oscillated readily between the surface and bottom,

whereas weaker swimmers were dispersed more evenly throughout the water column and were influenced significantly by the currents (i.e. they drifted in a similar way to passive particles). 3.2.2. Longitudinal transport and dispersal Passive particles drifted back and forth along the channel with the tidal currents (Fig. 4) and their absolute longitudinal transport distance, per tidal cycle, was 20e25 km, according to the longitudinal salinity gradient; a stronger gradient produced more axial transport (Fig. 9). Maximum axial dispersal was 7e8 km (both landward and seaward); again, a stronger salinity gradient produced more dispersal (Fig. 8a). By contrast, tidally-synchronized particles (Fig. 5) showed a net transport up-estuary. Patch-averaged up-estuary transport increased with vertical swimming speed (relative to the background vertical velocity), from 2.5 km for slower swimmers to 8 km for faster swimmers (Fig. 8b). Up-estuary transport of tidal particles also increased with a greater longitudinal salinity gradient, from 6.5 km for the mixed case to 8 km for the high rain scenario (Fig. 8c). However, tidally-synchronised particles travelled similar longitudinal distances to passive particles, over a tidal cycle (Fig. 9). Uniform salinity conditions (Fig. 4geh; Fig. 8) also lead to up-estuary migration because flood velocities were stronger than ebb velocities (as there is less frictional influence during peak flood flow due to a velocity-elevation phase lag (Pugh, 1987)). However, the effect of the axial convergent front on dispersal of tidally migrating larvae is to increase upestuary transport. Particles simulating the strategy of the

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Fig. 5. Instantaneous distribution of tidally-synchronised larvae-particles after 15 days during the flood tide (a and b) and the ebb tide (c and d) during the baseline hydrodynamic simulation. Each particle colour represents a patch of 10,000 organisms with swimming speeds of 0.0005 m s1 (green; PTM-1.2), 0.001 m s1 (red; PTM-1.3), and 0.003 m s1 (blue; PTM-1.4). The larvae swim to the surface and converge in the channel centre during the flood (a) and swim to the bed and converge during the ebb (c), and migrate landwards over a tidal cycle (b) and (d). The cross-channel (a and c) and surface (b and d) isopycnals and velocity vectors, corresponding to a mean tidal regime, are also shown (longitudinal velocity vectors in b and d have been reduced by a factor of 20). The dotted lines in (b) and (d) indicate the particle release origin. The final distribution of particles after 28 days is shown in (e) and (f). The additional, colour-coded, dotted lines in (f) show the patch-averaged landwards and seawards dispersal distances after the 28 day period (i.e. corresponding to the bar lengths in Fig. 8). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

copepod Eurytemora affinis (tidal stream transport downstream and reverse-tidal stream transport upstream; see Fig. 6) also migrated up-estuary (Fig. 8d), slightly, but contrary to the other strategies, there was significantly reduced axial dispersal (maximum dispersal of 2e3 km from the origin (Fig. 8d) and absolute transport of 4e5 km, per tidal cycle (Fig. 9). Again, increasing the longitudinal salinity gradient increased dispersal of the copepod patch along the channel. Diel migration (Fig. 7) resulted in up-estuary net axial migration (of the order 2e5 km), during the equinox (Fig. 8eef), which is less than tidally migrating organisms. Axial dispersal (Fig. 8eef) and axial transport (Fig. 9) of diel larvae tended to be less than that of passive and tidal particles. For example, daily-synchronised particles during the equinox travelled 17e19 km (depending on axial salinity gradient), over a tidal cycle, whereas passive and tidal particles travelled 20e26 km (Fig. 9). However, in all diel scenarios, dispersal and transport were lower during the solstice, when particles spent longer in the deeper waters characterised by weaker currents (Fig. 8eef and Fig. 9). Higher swimming speeds resulted in increased up-estuary dispersal during the equinox (net dispersal increased from 2 km to 4 km), but not during the solstice, when net dispersal was relatively small and sometimes seaward (Fig. 8e). Particles in uniform axial salinity waters displayed less longitudinal dispersal (approximately half) than those within an axial convergent front (Fig. 8f). In summary, for most larval strategies, the results show that the axial convergent front enhances up-estuary larval transport. 4. Discussion This work highlights the importance of axial convergent fronts for the transport of planktonic organisms within estuaries. We simulated circulation patterns and transport of planktonic

organisms within an idealised estuary (parameterized on the Conwy Estuary, UK), under a variety of physical conditions (tidal phase, photoperiod, and longitudinal salinity gradient) and behavioural strategies (passive particles, tidally-synchronised vertical migration, and diel migration). Firstly, the model successfully reproduced the structure and velocities of an axial convergent front and it therefore captured key aspects of the circulation in the Conwy Estuary, where an axial convergent front is well documented. Secondly, we showed that the behavioural strategies interact with the environmental conditions to define the magnitude of up-estuary and down-estuary migration, dispersal, transport towards the banks and estuarine retention at the release location. Our results are consistent with previous findings (see next section) about the importance of tidally-mediated migration for estuarine retention and colonization. Additionally, we demonstrate that the formation of the axial convergent front will aid retention in the case of both tidal and diel migration. This work has also revealed a series of patterns resulting from lateral transport that should affect the colonization of the intertidal zone for settling larvae as well as the general distribution of planktonic organisms across the estuary. 4.1. Consequences of behavioural strategies for transport in an estuarine axial convergent front The first main conclusion is that the axial convergence front does not significantly alter the longitudinal dispersal of passive transport but does enhance lateral transport. Organisms behaving like passive particles would oscillate along the estuarine longitudinal axis and disperse vertically and across the channel. Therefore, retention or estuarine colonization is not ensured by passive transport. This is consistent with the fact that many estuarine organisms have some type of behavioural strategy either to be

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Fig. 6. Instantaneous distribution of 10,000 copepod E. affinis larvae-particles after 15 days during the flood tide (a and b) and the ebb tide (c and d) during the baseline hydrodynamic simulation (PTM-1.5). The cross-channel (a and c) and surface (b and d) isopycnals and velocity vectors, corresponding to a mean tidal regime, are also shown (longitudinal velocity vectors in b and d have been reduced by a factor of 20). The dotted lines in (b) and (d) indicate the particle release origin. The final distribution of particles after 28 days is shown in (e) and (f). The additional dotted lines in (f) show the patch-averaged landwards and seawards dispersal distances after the 28 day period (i.e. corresponding to the bar lengths in Fig. 8). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

retained (e.g. Hough and Naylor, 1991), or to be exported away from the estuary (e.g. DiBacco et al., 2001). Transport to the less energetic banks is enhanced because of the front and may provide the larvae of benthic organisms with a greater opportunity to find a suitable settling ground, but may also expose other planktonic organisms to hazards such as being washed up on tidal flats or gravel beaches. Behavioural strategies lead to different patterns of transport as compared with the passive set up, but the effect depends on swimming speed relative to the background vertical velocities. For the Conwy Estuary, the critical swimming speed was ca. 3  103 m s1, as this was the magnitude of the vertical velocities. For the case of tidally-synchronised individuals (upward flood migration; downward ebb migration), the predicted transport was up-estuary, hence retention within estuarine waters, because they are predominantly exposed to axial convergence and so travel in the stronger mid-channel currents. This is consistent with the hypothesis put forward by Eggleston et al. (1998) that axial convergent fronts act as a ‘larval conduit’ system. For the Conwy Estuary, this system would constitute a conduit for Carcinus maenas megalopa, but also may affect other planktonic organisms such as Gammarus zaddachi and Eurytemora affinis. Furthermore, for the case of the copepod E. affinis, the change in strategy according to the along-estuary position (or salinity) would further contribute to their retention at the release location within the mid-estuary. This finding is consistent with that observed by Hough and Naylor (1991) for E. affinis. These authors found that the centre of the population distribution is located at an intermediate point in the estuary. For the case of daily-synchronised vertical migration, estuarine retention may be achieved if organisms migrate upwards during

dusk and night, and downwards during dawn. At night, when individuals swim to the surface, they converge to the stronger axial currents during the flood tide and diverge to the estuary banks during the ebb, leading to a net up-estuary migration, albeit at a lesser rate than for tidally-synchronised organisms. The result assumes that the observation period equals the lunar cycle (e.g. 28 days) so that the organisms experience all states of the tidal circulation with respect to time of day. However, in estuaries where the solar semi-diurnal tidal constituent (S2) is prominent, the vertical migration phase can become coupled with the periodicity of the tidal flow (Hill, 1991a, 1991b). In this case, up-estuary migration will be enhanced. Net longitudinal migration was generally small, however, for diel larvae, so changing the larval stage by typically a few days (to, say, 25 or 33 days) would not influence the overall distribution significantly. This was indeed the case for diel distributions a few days before the final distributions that were presented here. Nevertheless, a key result is that dailysynchronised larvae such as the great scallop Pectin maximus are more likely to be retained within an estuary where an axial convergent front forms, relative to uniform axial salinity conditions. Over the 28-day period, the up-estuary dispersal during night-time flood currents dominates the distribution of larvae and, therefore, diel migration in estuaries with axial convergent fronts strongly aids estuarine retention. The amount of time that the organisms spend in the more energetic, and flood-dominated surface waters, is reduced in summer and, hence, dispersal distances are also reduced. For strong swimmers and with equal amounts of day and night, net dispersal is seaward. Since P. maximus larvae spawn throughout the summer months (Brand et al., 1980; Cochard and Devauchelle, 1993), the prediction is

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Fig. 7. (aed): Instantaneous distribution of 10,000 daily-synchronised larvae-particles (during the equinox and with vertical swimming speeds of 0.003 m s1; PTM-1.8) after 15 days for the baseline hydrodynamic simulation. The larvae swim to the surface during night-time, and converge in the channel centre during the flood (a) and diverge towards the banks during the ebb (b). During daylight, the larvae swim towards the bed and diverge during the flood (c) and converge during the ebb (d). The cross-channel and surface isopycnals and velocity vectors, corresponding to the mean tidal case, are also shown. The final distribution of particles after 28 days is shown in (e) and (f), for the equinox simulation (red particles; PTM-1.8) and also for the solstice simulation (blue particles; PTM-1.11). The dotted lines in (f) show the origin and the patch-averaged landward and seaward dispersal distances after the 28 day period (i.e. corresponding to the bar lengths in Fig. 8). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

that dispersal distances will be approximately half that of tidallysynchronised larvae, under the same hydrodynamical conditions. Our simulations also highlight the importance of migration strategies for lateral movements, of which little is known. In the case of tidally-synchronised migrators, high swimming speeds reduce the magnitude of lateral transport. By contrast, organisms exhibiting daily migrations should be regularly advected towards the banks and the intertidal zone. In case of holoplanktonic organisms, such as copepods, reduced lateral transport may ensure that individuals keep away from the shallow areas where they may be exposed to benthic predators or remain stranded at low tide. However, for species settling in the intertidal zones, such as many estuarine crabs, strong swimming associated with tidally-timed migrations may reduce the chances to access the appropriate settling habitat. In order to reach the intertidal zone megalopa of these crabs would have to rely on a more flexible behavioural strategy where swimming speed and direction respond to signals from the appropriate intertidal environment (e.g. lower salinity at the side of the estuary, chemicals from macroalgae, seagrass or conspecifics). Megalopa of many intertidal species are indeed able to respond to chemical gradients either to orient swimming (Diaz et al., 1999) or metamorphose (Forward et al., 2001; Anderson and Epifanio, 2010). Successful settlement may rely on modifications of behaviour in the proximity of the intertidal zones. 4.2. The importance of variations in the strength of the axial convergent front Model simulations show that under weak or no-axial front conditions, the capacity for retention or up-estuary migration is

reduced in the case of the strategies evaluated here. If the front does not develop, tidally-synchronised organisms will still migrate up-estuary but at a lower speed, compared with the axial front (up to 20% less up-estuary dispersal than with the front). Dailysynchronised strategies would however not result in retention: these organisms would travel back and forth with the tidal currents, as do passive individuals. Seaward transport during the ebb phase would cause individuals to leave the estuary. Variations in the strength of the axial front should result from changes in salinity gradients that are driven by variations in rainfall at the scale of the river catchment. Future changes in climate are predicted to generate increased periods of precipitation in winter (Oliver et al., 2008) and also periods of drought in summer (Reaney and Fowler, 2008). Consequently, we can expect increased periods of high and low river flow, and associated high and low longitudinal salinity gradients in the River-Estuary Transitional Zone (RETZ). The hydrodynamic simulations here have shown that weak longitudinal salinity gradients (drought) will weaken the formation of the front, whereas strong salinity gradients due to high rainfall will generate the front (provided the water column stays vertically mixed), but not necessarily strengthen the lateral velocities, compared with typical presentday salinity gradients. Therefore, we can speculate that formation of estuarine axial convergent fronts may become more sporadic in the future, especially during summer months, thereby limiting up-estuary migration. Variations in the strength of the circulation may be also relevant for fertilization in broadcast spawners. In these species, gamete fertilization depends on processes of transport and diffusion that govern the time gamete remain mixed together at appropriate

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Fig. 9. Bar graphs showing longitudinal distance travelled per tidal cycle. The length of each bar represents patch-averaged particle distance, averaged over each tidal cycle, and the error bars denote the standard deviation within each patch of 10,000 organisms. The width of each bar is proportioned to represent patch-averaged lateral distance travelled, i.e. thicker bars indicate organisms that dispersed further laterally (back and forth across the channel), relative to thinner bars. For organisms with migratory strategies, only simulations where vertical swimming speeds equal 3  103 m s1 are shown. The coloured bars isolate different larval migratory strategies and corresponds to Fig. 8.

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concentrations (Levitan, 1995). Broadcast spawners appear to develop a series of adaptations to increase that time (Yund, 2000), e.g. by releasing gametes at times of minimum diffusion by wind stress (van Woesik, 2010). Habitats characterised by low diffusion rates appear to increase rates of fertilization (Simon and Levitan, 2011). Estuaries with an axial convergent front may constitute habitats that favour fertilization through accumulation of gametes at the front during flood tide. This process is widespread among estuarine habitats if axial fronts are a common feature: for instance, in the UK, out 26 main estuaries, 21 develop an axial convergent front (Brown et al., 1991). Thus, the importance of axial convergent fronts on the dynamics of fertilization appears as a further area of investigation. 5. Conclusions Realistic 3D modelling of larval transport has revealed the potentially intricate nature of planktonic life history stages. In summary, axial convergent fronts aid estuarine retention of larvae, particularly for larvae that experience tidal stream transport and diel migration. The results presented in this paper represent some standardised trajectories for the most common marine organisms that are expected in the presence of an axial convergent front; many of the physical (e.g. local bathymetry, wind stress and surface waves), and biological (e.g. mortality, predation and settling criteria) factors which have not been included will become more important for case-specific investigations. The formation of an axial convergent front requires an axial salinity gradient and deeper mid-channel water than the banks. Mid-channel velocities are enhanced relative to the banks due to frictional effects. This shear of the longitudinal velocities thus generates lateral density gradients. Barotropic surface velocities are enhanced in the channel centre during the flood tidal phase by drawing in energy from the banks via lateral flows that are 5% of the axial flow. Divergence near the bed will dissipate the axial flow laterally. The reverse circulation has been simulated during the ebb phase, however, this process has not been observed elsewhere in the literature and further observations are therefore required. When the axial convergent front is formed, up-estuarine transport is achieved if vertical migration behaviours are synchronised with the tidal currents, with individuals migrating upwards during flood tidal velocities and downwards during ebb flow. Retention within the estuary is achieved with diel vertical migration where organisms remain in surface waters during night and near the bottom during daylight; seaward migration is common during the solstice. Full retention, i.e. retention at a specific location within the estuary, is achieved by strategies such as those exhibited by the copepod Eurytemora affinis which switches from tidally-synchronised migration in the lower estuary to reverse-tidal migration in the upper estuary, i.e. synchronised by a combination of tidal and salinity cues. Also, the vertical migration speed of the larvae must exceed the background vertical velocities in order to get the greatest enhancement of retention. Lateral dispersal varies inversely with up-estuary migration (e.g. lateral transport is reduced for tidally-synchronised organisms) so that colonization of the intertidal areas and banks may result from the balance of organisms being present in the estuary and the speed of flood tide currents. Reduced lateral dispersal in holoplanktonic organisms (e.g. copepods) may result in less exposure to predators. However, stages attempting to reach the intertidal zone to settle should rely on a flexible behavioural strategy based perhaps on chemical cues. If the axial convergent front is not formed, up-estuarine migration and estuarine retention is only achieved by tidally-synchronised vertical migration. Both passive

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