The structure of dissipation in the western Irish Sea front

Journal of Marine Systems 77 (2009) 428–440

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Journal of Marine Systems j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j m a r s y s

The structure of dissipation in the western Irish Sea front John H. Simpson a,⁎, J.A. Mattias Green a, Tom P. Rippeth a, Thomas R. Osborn b, W. Alex M. Nimmo-Smith c a b c

School of Ocean Sciences, College of Natural Sciences, Bangor University, UK Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, MD, USA School of Earth, Ocean & Environmental Sciences, University of Plymouth, UK

a r t i c l e

i n f o

Article history: Received 6 December 2007 Accepted 29 October 2008 Available online 11 November 2008 Keywords: Tidal mixing front Turbulence Dissipation Autosub Irish Sea

a b s t r a c t We report on an intensive campaign in the summer of 2006 to observe turbulent energy dissipation in the vicinity of a tidal mixing front which separates well mixed and seasonally stratified regimes in the western Irish Sea. The rate of turbulent dissipation ε was observed on a section across the front by a combination of vertical profiles with the FLY dissipation profiler and horizontal profiles by shear sensors mounted on an AUV (Autosub). Mean flow conditions and stratification were obtained from a bed mounted ADCP and a vertical chain of thermistors on a mooring. During an Autosub mission of 60 h, the vehicle, moving at a speed of ~ 1.2 m s− 1, completed 10 useable frontal crossings between end points which were allowed to move with the mean flow. The results were combined with parallel measurements of the vertical profile of ε which were made using FLY for periods of up to 13 h at positions along the Autosub track. The two data sets, which show a satisfactory degree of consistency, were combined to elucidate the space–time variation of dissipation in the frontal zone. Using harmonic analysis, the spatial structure of dissipation was separated from the strong time dependent signal at the M4 tidal frequency to yield a picture of the cross-frontal distribution of energy dissipation. A complementary picture of the frontal velocity field was obtained from a moored ADCP and estimates of the mean velocity derived from the thermal wind using the observed density distribution. which indicated the presence of a strong (0.2 m s− 1) jet-like flow in the high gradient region of the front. Under neap tidal conditions, mean dissipation varied across the section by 3 orders of magnitude exceeding 10− 2 W m− 3 near the seabed in the mixed regime and decreasing to 10− 5 W m− 3. in the strongly stratified interior regime. The spatial pattern of dissipation is consistent in general form with the predictions of models of tidal mixing and does not reflect any strong influence by the frontal jet. © 2008 Published by Elsevier B.V.

1. Introduction Tidal mixing (TM) fronts are the boundaries between seasonally stratified and well-mixed regimes. They occur widely in regions of the continental shelf which experience a combination of high tidal dissipation and a large seasonal heat exchange. The shelf seas of north-western Europe satisfy both of these conditions and are host to a number of prominent frontal ⁎ Corresponding author. School of Ocean Sciences, Bangor University, Menai Bridge, Anglesey, LL59 5AB, UK. Tel.: +44 01248 38 28 44. E-mail address: [email protected] (J.H. Simpson). 0924-7963/$ – see front matter © 2008 Published by Elsevier B.V. doi:10.1016/j.jmarsys.2008.10.014

features which have been the subject of extensive study. The basic theory of the heating–stirring competition which underlies the formation of these fronts and controls their geographical positions (Simpson and Hunter, 1974) has been utilised in combination with numerical models of tidal flow to predict the positions of fronts (e.g. Pingree and Griffiths,1978; Garrett et al., 1978; Lie, 1989; Glorioso and Simpson, 1994). Tidal mixing theory has been extended to allow for the influence of the fortnightly cycle in tidal stirring and the contribution from wind mixing (Simpson and Bowers, 1981) as well as the effects of the Earth's rotation (Simpson and Sharples, 1994; Simpson and Tinker, in press). The internal dynamics of fronts have also been

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Fig. 1. Autosub at the end of mission in the recovery gantry on MS Terschelling. Insert shows the nose-mounted airfoil shear probes which sense transverse velocity on a scale of b 1 cm. Autosub is 7 m long and has a diameter of 0.9 m.

explored in numerical models (e.g. Garrett and Loder, 1981; James, 1984) which indicate the presence of a frontal jet and a weak cross-frontal circulation. Direct observations of the frontal jet have been obtained in a number of tidal mixing fronts (e.g. Lwiza et al., 1991; Brown et al., 2003) while evidence of the cross-frontal circulation has been obtained from dye dispersal experiments by Houghton, 2002. More generally the contribution of the density driven-flows produced by heating and tidal stirring to the summer circulation in shelf seas has been elucidated by Hill et al. (1997). Direct measurements of the gradients in tidally forced turbulence which are responsible for generating and maintaining TM fronts became practical with the advent of shear profilers (Oakey, 1982; Dewey et al., 1987). An extensive series of measurements with the FLY profiler have elucidated the structure of turbulent dissipation and mixing in the characteristic mixed and seasonally stratified regimes of the European shelf seas (Simpson et al., 1996; Rippeth, 2005; Rippeth et al., 2005). Generally there is a pronounced M4 cycle in dissipation in the tidally-driven bottom boundary layer (bbl) which, in the mixed regime, extends up to the surface where it merges with the surface mixed layer. In the seasonally stratified regime, the bbl is limited to a fraction of the water depth, and dissipation shows a marked phase lag increasing with height above the bed (Simpson et al., 2000). Most of the observed profiles of dissipation can be understood in terms of energy inputs at the top and bottom boundaries of the water column, although in strongly stratified conditions there are clear indications of additional energy inputs in midwater whose origin remains uncertain and is the subject of ongoing investigations (e.g. Rippeth et al., 2005). While the seasonally stratified and well-mixed regimes have now been extensively studied through vertical profiles, there have been very few measurements of the horizontal

variability of turbulent processes. In particular, determining the structure of turbulence in the tidal mixing fronts between stratified and mixed regimes has proved difficult with vertical shear profilers because of complicated space–time pattern of dissipation in these structures. In addition to the time evolution on M2 and M4 time scales the whole frontal structure is subject to tidal advection with an excursion of ~5 km or more. Observing a TM front therefore requires an extended sampling scheme as in the pioneering measurements by Oakey and Pettipas (1992) based on a series of 98 anchor stations on a section through the Georges Bank TM front. In this contribution we report a series of observations of the turbulent dissipation rate ε in a TM front based on a new approach in which we used a combination of horizontal transects across the front combined with vertical profiles of dissipation and mooring measurements of the vertical structure of density and velocity. The measurements are combined and analysed to give as full a picture as possible of the space–time evolution of dissipation in the frontal zone. The paper is structured so that in Sections 2 and 3 we briefly describe the measurement methods and the observational campaign before describing the density and velocity fields (Section 4) which set the physical context for the turbulence measurements. We then present the main results in Sections 5–8, and conclude with a summary and a brief discussion of their implications in Section 9. 2. Measurement methods The measurements reported here were obtained through a two ship campaign in the Irish Sea during the period July 11–23 2006. The M. S. Terschelling carried the Autosub team and acted as mother vessel to the autonomous underwater vehicle (AUV)

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Autosub (Millard et al., 1998), while the RV Prince Madog undertook the deployment of moorings and the vertical profiles of turbulence using FLY. During the eight days of Autosub operation (July 13–21), three separate Autosub missions were successfully accomplished in Mixed, Stratified and Frontal regimes. In this paper, we focus on the results from the frontal zone study which was undertaken in a 3 day period just before the time of neap tides which occurred on July 21. Predictably this frontal mission proved the most challenging of the three. Results from the other regimes are to be reported elsewhere (Thorpe et al., 2008). As in previous studies, vertical profiles of dissipation were obtained from the FLY system which measures the vertical shear of the horizontal velocity on a scale of b1 cm, from which the rate of energy dissipation may be calculated assuming that the turbulence is isotropic at these scales. The noise floor for the determination of dissipation by FLY is ~10− 6 W m− 3. In addition to the shear sensors, FLY is also equipped with sensors for temperature and conductivity. The profiler falls freely at a speed of ~0.7 m s− 1 and is furnished with a probe guard which allows measurements to continue to ~15 cm above the bed when the profiler impacts with the bottom. After each profile, FLY is hauled back to the surface by a Kevlar sheathed cable which provides a twisted-pair cable link for the transmission of digital data back to the research vessel. For details of the FLY instrumentation and data processing methods, see Dewey et al. (1987) and Simpson et al. (1996). In the observations described here, FLY was used to obtain groups of 5–6 consecutive profiles during each hour with a break of ~20 min to allow for recharging of the internal batteries. Horizontal profiling of turbulence was achieved by fitting shear probes of the same type as those used on the FLY profiler to the Autosub. The shear sensors, along with a fast response temperature sensor, were attached to a frame mounted on the nose of Autosub (Fig. 1). The turbulence package was essentially the same as that employed in a series of turbulence measurements in the surface mixed layer (Thorpe et al., 2003), which demonstrated the impressively low noise levels (~10− 5 W m− 3) which can be achieved on the Autosub vehicle while moving at horizontal speed of ~1.25 m s− 1. The two probes were oriented so as to obtain measurements of ∂v/∂x and ∂w/∂x, i.e. the horizontal and vertical velocity shear components directed across Autosub's line of travel. In addition to the turbulence measurements, the standard instrument suite on Autosub provided data samples every second on the velocity field from upward and downward looking ADCPs (300 and 150 kHz, respectively) and temperature and salinity from a Seabird 911 CTD system. Autosub navigates using GPS fixes while running at the surface, and dead reckoning based on the ADCP bottom tracking when operating at depth. The accuracy of the bottom track positioning system is estimated as b1% of the distance travelled, or in our case b2.5 km at the end of a mission (although in practice it proved to be more accurate). The navigational data from Autosub, i.e. position, heading, speed over ground, propeller RPM, along with depth, pitch, roll and heave, were logged at 1 s intervals. Autosub logs data from five different systems: the internal navigation, the two ADCPs, the CTD, and the turbulence package. In order to proceed with analysis, data from the different systems had to be aligned to a common time frame. First, the data from Autosub's CTD were aligned to the

Fig. 2. a) A satellite IR image of the Irish Sea temperature during the observational campaign (courtesy of Plymouth Marine Laboratory) with the 50 and 100 m isobaths marked as dotted white lines. The image shown is a composite and shows the average of the SST for the period between July 15– 21, 2006. Note the location of moorings SWIS and FR and the full Autosub track starting near FR. The dashed black line marks the 14 °C isotherm (i.e. the boundary between blue and green colouring). Note that the stratified region is the warm patch located between the front and the Irish Coast, and that the other warm areas (e.g. along the west coast of the UK) are not stratified. b) The track of Autosub during mission FR. The locations of the moorings (SWIS and FR) are marked together with the FLY stations FR–FR3. The arrows mark direction of travel, with travel westwards at 45 m depth and travel eastwards (from stratified to mixed) at 15 m depth. The roman numerals mark the order of the turning points and label the legs (i.e. leg II starts turning point II). The dotted line marks an average position of the front as seen at 15 m depth (note that the front cuts the surface further to the east in panel a). The track started at Year day 199.16 at point I and ended at Year day 201.21 at point XI. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

turbulence package (TP) timebase, which was chosen as reference, using markers in the pressure signals from the two systems. Autosub's navigation and ADCP data were then aligned to each other and to the TP timebase using the inertial navigation system pitch and ADCP pitch signals. Corrections were next made for the misalignments from the horizontal plane of the two ADCPs and hence to the ADCP velocities used to

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describe the motion of Autosub after application of a 1 minute filter to remove noise. The through-water speed was finally calculated from the calibrated propeller RPM, using periods of good ADCP data and a weighted average to account for vertical shear. It was assumed that there is a linear relationship between the RPM/ADCP forward velocities over the ranges of values within the data set. Time-series of 1 second averages of all the Autosub data, including navigation, were then produced. The temperature and pressure series from the turbulence package were enhanced using the method described in Mudge and Lueck (1994), using a convolution between the series and its derivative. The time series of the navigation was used to identify the periods when Autosub was running straight. For these periods, shear and accelerometer spectra over 240 s were generated and plotted to identify vibrations and determine the

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level of despiking. These spectra were taken from both active and quiescent periods to identify the signal and the noise levels. The dissipation rates were then calculated, with a 10-second resolution, by integrating the shear spectra for the despiked data-set, and account for limits in integration and shear probe responses (see Thorpe et al., 2003, for details). 3. Observational campaign The observations were focussed on a section of the TM front in the western Irish Sea (Fig. 2a). Moorings, which were deployed prior to the Autosub missions at the FR and SWIS sites, each consisted of a bed mounted 300 kHz ADCP together with a vertical string of temperature sensors to determine the flow and density structure respectively. The ADCP was set to have a

Fig. 3. Temperature and density from (a–b) mooring FR and (c–d) mooring SWIS. All panels show 5-minute averages.

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Fig. 4. The plates show the 5-minute averages of (a) the along-frontal and (b) the cross-frontal velocities at station FR.

vertical bin size of 2 m, while the temperature sensors were spaced to cover the water column with separations of ~2–10 m (with denser coverage over the thermocline). Two SeaCat CTDs were also deployed at each mooring: one was attached to the surface marker buoy at ~0.5 m depth, and one was located ~2 m above the sea bed. The temperature loggers and CTDs recorded data samples every 2 min, whereas the ADCP recorded data every 2 s. All data were averaged and interpolated to a common 5-minute grid in time during the post-cruise processing., The ADCP did not record data within ~4.5 m from the bed, nor from the ~10–15 m closest to the sea-surface. The location of the FR mooring was chosen to correspond to the centre of the frontal region on the basis of the known tidal stirring distribution and satellite I–R imagery. Its correct location in the high gradient region was confirmed by a composite of imagery during the observation period (Fig. 2b). The mooring at SWIS was deployed on July 11 2006 and recovered on July 22 (year days 191–202), while the FR mooring was deployed on July 12 and recovered on July 21 (days 192–201). The strategy for the Autosub measurements was based on the idea of sampling across the front at two vertical levels which were representative of conditions above and below the pycnocline. On the basis of the anticipated depth of the mixed layer, these levels were fixed at 15 m and 45 m depth. The choice of track for the Autosub presented something of a dilemma. In order to separate out time dependence from spatial structure we needed Autosub to sample repeatedly across a frontal section of more than 20 km. This can be done either by travelling between geographically fixed way points (as we used in the studies of the mixed and stratified regimes) or by having the vehicle travel on a fixed bearing for a fixed time and then switch to the reciprocal course for the same time and so on. In principle, this latter approach should enable Autosub to move with the tidal flow and sample approximately the same section of water across the front. This is the approach we eventually selected. Autosub then operated for 5 h at a certain depth, travelling at a constant speed on a heading of 104° or 284°. After

5 h, the sub turned to the reciprocal heading, changed its operating depth, and started another 5-hour run. In this way we could obtain 12 passages of the front during the mission, 6 each at 15 and 45 m of depth. The weakness of the fixed bearing approach is that the chosen frontal section may also be subject to residual, non-tidal advection so that, over the course of the 60 hour Autosub mission the chosen frontal section may be displaced significantly from its original position. This is what happened, as can be seen in Fig. 2b–c, when, following the start of the start of the first frontal section, there was a significant displacement to the north-east which continued for the rest of the mission. This displacement corresponds to a residual flow of ~0.1–0.2 m s− 1 and is, as we shall see, mainly attributable to the baroclinic flow associated with the front. Since the sub experienced a particularly strong drift during the first and last of the legs, these sections have not been used in the subsequent analysis which concentrates on the ten Autosub legs shown in Fig. 2b. To complement the horizontal sections with Autosub, we undertook a series of FLY profile time series with durations of 11–13 h, at fixed locations, starting at the frontal position (FR) and working eastwards (FR2-3) with the aim of determining the time dependence of dissipation at points along the tidal stirring gradient. Our observational campaign was favoured by generally light winds and a tranquil sea state which facilitated the Autosub deployment and recovery operations. Rather unusually for the Irish Sea at this time of year, skies were clear sufficiently often to allow good I–R coverage. 4. Density structure and tidal flow In this region of the Irish Sea, density variations and the associated stratification are almost completely controlled by temperature. At the time of our observations the strong thermal stratification, evident at SWIS (Fig. 3b), was only slightly modified by vertical differences in salinity, which did not exceed 0.3 over the extent of the water column at any

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Fig. 5. a) A synthesized density section from mooring SWIS, across the front, to station FR3. Data consisted of time averages of the measurements from the moorings at FR and SWIS, and from CTD and FLY profiles at FR, FR2 and FR3. b) Mean velocity across the frontal section deduced from the thermal wind relation (Eq. (1)) using the density data in panel (a). c) The time-averaged along-front velocity profile from mooring FR (dotted) and the velocity profiles from the thermal wind equation at section s1–s3 (see figure legend).

time. The consistently strong stability at SWIS, which is representative of the stratified regime, contrasts with the weaker stability at FR (Fig. 3a) which exhibits a marked semidiurnal fluctuation as cross frontal advection moves the frontal gradients past the mooring position. The magnitude of

the cross-frontal excursion can be estimated from the velocities at FR measured by the ADCP (Fig. 4b). Over much of the water column, there is a tidal oscillation of magnitude ~0.2 m s− 1 which corresponds to a cross-tidal excursion of ~ 2.8 km. In the lower half of the water column, the

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Fig. 6. Time series of dissipation ε (W m− 3) obtained using FLY. (a) at station SWIS. (b) at FR–FR3 (sections of data from left to right). In all cases contour plots are based on hourly averages of 5–6 individual profiles.

temperature varies by ~ 1 °C which indicates a cross-front density gradient of ∂ρ/∂x ~ 7 × 10− 5 kg m− 4 which implies considerable vertical shear. These gradients are also apparent in the cross-frontal section of Fig. 5 which is based on timeaverages of the density obtained from the moorings, FLY, and CTD data from stations SWIS to FR3. Applying the thermal wind balance: Av g Δρ = − Az ρf Δ x

ð1Þ

to these horizontal gradients, with the condition that the density driven flow has zero velocity at the bed, we see (Fig. 5b) that there is a pronounced jet like flow in the front with velocities of up to ~ 0.2 m s− 1. A further verification was made by using the time-series of the vertical density structure at mooring FR and calculating the horizontal density gradient from the time-derivative and cross-frontal flow velocity. Applying the density gradients obtained in this way in Eq. (1) gave a time-averaged vertical shear consistent with the observed time-averaged shear at mooring FR. These calculations support a jet-like flow of ~0.2 m s− 1 along the front. The existence of this residual flow is also evident in the ADCP record of the along front flow (Fig. 4a) which shows consistently higher velocities in flow to the north-east than in the reverse phase of the tidal flow. The time mean of the observed along front flow at FR is closely similar to the velocity profile deduced from thermal wind near the same station (Fig. 5c). 5. Vertical structure of dissipation in the stratified and frontal regimes The tidal cycle of turbulence was observed with the FLY Profiler at stations SWIS, FR and FR2-3. A continuous series of 50 h sampling was acquired at the reference stratified station SWIS, between days 196 and 198, because of its importance in

the stratified regime campaign. It also serves in the present context as an end point in transition from fully mixed to fully stratified conditions. The regular M4 cycle in dissipation is here clearly defined in the bottom boundary layer and extends up to ~ 40 m above the bed with a phase delay which increases with height above the bed (Fig. 6a). Above this level there is a region of very low dissipation with ε rarely exceeding 10− 4 W m− 3 and frequently close to the noise level of 10− 6 W m− 3. At the frontal stations FR, FR2–3, the time series exhibit rather similar behaviour (see Fig. 6b). However, a positive trend in the magnitude of dissipation and a progressively increasing upward penetration of the dissipation from the bottom boundary are evident as we move from station FR through FR2 and FR3 towards the well mixed water column in the east. We did not acquire a FLY time series from the fully mixed regime during this campaign but the form of the profile for this case is well known and would be similar to that of FR3 with the M4 variation in the boundary layer extending up close to the surface. 6. Horizontal structure from Autosub transects We now consider the dissipation estimates obtained from the Autosub turbulence sensors as the sub moved at fixed depths of 15 m and 45 m back and forth across the frontal zone along the legs indicated in Fig. 2b. Fig. 7 shows ε, averaged over 10 s (~12 m along track), for leg II (south-eastward at 15 m) and leg III (north-eastward at 45 m). At the lower level, a clear trend in dissipation is discernable with the values generally increasing towards the south-east by approximately two orders of magnitude. and peak dissipation at the south-eastern end of the section exceeding 10− 2 W m− 3. At the north-western end, values were mostly low, falling, for a period, close to the system noise level of the (10− 5 W m− 3). In identifying this trend, we should remember that, as each leg takes 5 h, these dissipation plots are not synoptic pictures of turbulent activity but include significant time variability imposed largely by the tide. At the

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Fig. 7. Dissipation ε (as 10 second averages) from legs I and II of the Autosub track (see Fig. 2b) at depths of (a) 15 m and (b) 45 m. Panel (c) shows the temperature observations from Autosub during the two tracks while panel (d) is a plot of the pressure signal from Autosub's CTD during leg II. Data are plotted versus distance from the north-western turning point.

15 m level there is significant spatial variability but no clear indication of a trend in ε with values mostly in the range 10− 5– 10− 3 W m− 3. The temperature record from these sections

(Fig. 7c) shows temperature difference between 15 and 45 m increasing markedly towards the north-western limit of the section with ΔT approaching 3 °C. This sharp increase in stability

Fig. 8. The dissipation of turbulent kinetic energy as observed by Autosub for all ten legs. Black lines represent data from 15 m depth, travelling eastwards (from left to right), whereas red lines refer to data from 45 m depth, travelling from east to west (right to left in the plates). Data are plotted versus distance from the northwestern turning point. The triangular symbols indicate the time of low water (▽) and high water (△) respectively, with black colour marking that Autosub was at 15 m depth and red that it operated at 45 m depth.

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Fig. 9. M4-harmonic fit to the dissipation data. (a) average dissipation, ε0. (b M4-amplitude of the dissipation ε4. (c) phase lead, l4. The solid lines show the phase lead. Black colour refers to data from 15 m depth, red colour represent data from 45 m depth. Solid lines show the tidal fit to 20-minute averages of the Autosub data. Open circles denote the results from the tidal fit to hourly averages of the FLY data from 15 m depth and open diamonds show the fit to FLY data from 45 m depth. The red star indicates the phase of the barotropic current determined from ADCP data and the vertical bars in panels (a) and (b) mark the 95% confidence limit. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

here may be associated with the reduction of ε at 45 m to the noise level for much of the last 4 km of leg III. The complete set of dissipation data along the ten legs of the Autosub mission (Fig. 8) confirms the picture based on Fig. 7 alone. At 45 m depth, dissipation values are generally higher at the north-western ends of the sections than at the south eastern end points where ε is frequently at, or close to, the noise floor of 10− 5 W m− 3. Dissipation at 15 m tends to be generally lower than at 45 m and does not exhibit a strong trend along the track except at the south eastern end where values are, on average somewhat higher than on the rest of the track. At both levels there is considerable variability on a variety of scales with a few occasions (e.g. legs 3 and 4 at 17 km along track) when dissipation is apparently greater at 15 m than at 45 m. We should note, however, that these observations differ in time by ~ 2.5 h so that significant differences due to tidal modulation may be involved. To separate such spatial and time dependent effects we need to apply harmonic analysis which we consider in Section 7. Comparison of the along-track dissipation data with the depth monitoring signal from the Autosub system reveals an interesting influence of turbulent motions on the motion of the body. Under tranquil conditions Autosub is designed to maintain the specified depth to within 0.2 m or better but, as can be seen in Fig. 7d, considerably larger displacements of up to 1.5 m peak to peak were experienced during leg II. The observed spatial pattern of vertical displacements is closely correlated with the intensity of dissipation. (Fig. 7b). More

extreme examples of vertical displacement by turbulent motions were observed in the Autosub mission in the mixed regime where energy levels are considerably higher and large scale vertical eddies (boils) were encountered (see Thorpe et al., 2008). 7. Synthesis of cross-frontal structure In order to achieve a synthesis of the structure of dissipation from the horizontal sampling by Autosub and the vertical profiles from FLY, we sought harmonic fits to both data sets. For the Autosub data, we first smoothed ε with a 20-minute average corresponding to spatial resolution of ~1500 m. With data from five legs at each depth during the mission, it was then possible to fit a quarter-diurnal harmonic function of the form: e = e0 + e4 cosðω4 t + u4 Þ

ð2Þ

Here, ω4 was taken as twice the average of the frequencies for M2 and S2. By using least squares to fit the observed data, we obtained estimates of mean dissipation ε0 as well as the amplitude ε4 and the phase φ4 of the tidally oscillating component. We also fitted Eq. (2) to hourly averages of the FLY dissipation data for each of the stations SWIS, FR, FR2 and FR3 to determine the vertical structure of dissipation. The results of the tidal fitting procedure for the Autosub data at 15 m and 45 m depth plotted against along track distance are shown in Fig. 9 together with the results for the same depths from the FLY analysis. At 45 m depth, both the mean dissipation

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ε0 and the amplitude ε4 are seen to exhibit a more or less steady increase across the frontal section by ~1.5 and ~2 orders of magnitude respectively. At 15 m both parameters are lower than at 45 m almost everywhere across the section. and the trend across the section at this depth is significantly weaker. At 45 m depth the M4 fit was good enough to allow the phase lead φ4 to be reasonably well determined and these values are shown in Fig. 9c together with the results from the FLY analysis. There is fair agreement between the along track values and the more statistically robust estimates from FLY. The observed trend in φ4 from N120° at ~5 km from the north-western end of the section to near zero at the south-eastern end corresponds to a time difference of ~2 h. This change is consistent with the difference between strongly stratified conditions where the phase lag at 45 m depth is ~2–3 h (see Fig. 6) and well-mixed where the phase of dissipation is close to the barotropic current phase i.e. maximum dissipation occurs at maximum current speed as is apparent at the south-eastern end of the section. The correlation of the M4-fit with data varied over the transect, but was significant for the fit at 45 m over the entire transect

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(r2 N 0.5). The fit from 15 m correlated well in the mixed part, but showed only a weak correlation with data in the stratified part (r2 b 0.3), as would be expected from the limited upward penetration of turbulence in the bottom boundary layer of the stratified regime. Combining all the mean dissipation data from the M4 fits, we can synthesise a cross-frontal picture of the average dissipation rate, ε0 (Fig.10a). Here we have used all the horizontal data from Autosub and the vertical profile fits from FLY. The contouring has been completed by fitting the Autosub profiles at the southeastern end of the section to the profile form for the mixed regime since there was no profile series at this end of the front. Combined with density and mean velocity data of Fig. 5, we see an overall picture of the frontal structure in which tidal stirring increases from stratified to mixed. As it does so, dissipation in the bottom boundary layer increases, and with it, the thickness of the layer increases until it occupies the whole water column. With increasing mixing, thermal stratification decreases, with resulting horizontal gradients of temperature and density in the lower part of the water column. These gradients are responsible

Fig. 10. The mean dissipation ε0 on a transect from SWIS to the south-eastern end of the Autosub tracks. The dotted vertical lines show the locations of each of the FLY stations while horizontal dotted lines denote the Autosub tracks. Note the (front-parallel) westernmost turning points used in previous figures correspond to a distance of ~ 5 km in the present figure. The lower panels are Fig. 5 repeated.

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Fig. 11. Current components relative to the front experienced by Autosub (continuous black line), and the depth averaged currents at the FR mooring (grey dotted line). The top plate shows the along front current component and the lower plate shows the across front current. The thick horizontal lines at 0.7 and − 0.7 m s− 1 in the lower plate indicate periods when Autosub was at 15 and 45 m depth, respectively. The triangles in panel a) mark times of frontal crossings at 15 m depth.

for a geostrophically balanced flow normal to the section with speeds of ~0.2 m s− 1 in a rather narrow (~5 km wide) jet. Most mixing in this picture has its origin in the frictional effects in tidal flow over the bed. In view of the calm light winds experienced during the survey, energy inputs from the surface were minimal. There is, however, some evidence of enhanced dissipation at the pycnocline in the otherwise tranquil interior of the stratified regime at station SWIS. There is no clear indication of the influence of the frontal jet on the distribution of dissipation although the fact that values of ε N 10− 3.5 W m− 3 extend further up the water column at FR than at FR2 may be indicative of such influence. 8. Velocities from the Autosub track An interesting bonus from the Autosub operation was an additional sampling of the velocity field which was made possible by our chosen mode of operation. Autosub was set to travel at a constant speed of ~ 1.2 m s− 1 at a constant heading of 104°/284°. The local current field deflected its track relative to the seabed while Autosub maintained its intended heading and speed. The recorded velocity of Autosub relative to the seabed, which is deduced from the ADCP bottom track system, can then be assumed to be a vector sum of (i) Autosub's intended heading and speed, and (ii) an advective component due to the local current field. An estimate of the current speed can thus be obtained by vector subtraction. The resulting Lagrangian sampling of the velocity field, resolved into along front and cross-front components, is compared with the Eulerian series from the ADCP observations at FR in Fig. 11. The two series show the M2 tidal flow with closely similar phase but the Lagrangian series includes larger

along-front speeds as Autosub moves further to the north-east. Autosub also sampled a number of large positive (along front to the north-east) velocity peaks, e.g. around Year day 199.75, 200.2, and 200.7, with an amplitude of ~0.2 m s− 1 and a typical duration of ~1.6 h which implies a spatial extend of ~7 km. We interpret these features as crossings of the frontal jet. The large across-front gradient of the along-front velocity matches that predicted by tidal models of the area (Simpson, 1997). A slight complication arises from the fact that alternate legs are at 15 and 45 m depth as indicated in Fig. 11 but the effect of this depth change should be small as this is a region of relatively low shear in the jet flow. In the cross-frontal direction, there is fair agreement between Eulerian and Lagrangian samples of the flow reflecting the fact that the weaker tidal component in this direction is less variable across the section and unaffected by the front-parallel jet. 9. Summary and discussion The Autosub vehicle has been used to observe, for the first time, the detail of the cross-frontal distribution of dissipation in a tidal mixing front. By combining horizontal sections across the front at fixed depth from Autosub with vertical profiles over a tidal cycle from the FLY shear probe, we have been able to achieve a first order separation of spatial and time dependent changes in dissipation to give a picture of the mean energy dissipation in an x–z plot across the front. This picture is complemented by an equivalent cross-frontal section of the horizontal flow based on measurements by a moored ADCP and velocities deduced from the observed density field in the front. Both indicate the presence of a pronounced jet-like flow embedded within the front.

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The mean dissipation is found to vary across the section by 3 orders of magnitude. The largest values near the seabed in the mixed regime exceed 10− 2 W m− 3 in contrast to minimum values in the stratified interior where mean ε falls to 10− 5 W m− 3. These are the magnitudes of dissipation observed around the period of neap tides. At spring tides, when tidal flows are ~1.8 times larger, dissipation values will typically be ~ 0.6 of a decade larger. The observed spatial pattern of dissipation is consistent in general form with what was expected from tidal mixing models (e.g. Sharples and Simpson, 1995). The present results indicate that the presence of the jet does not substantially alter the dissipation pattern within the frontal zone. This is in contrast to the finding by Avicola et al. (2007), who report on significantly enhanced dissipation rates in the coastal upwelling jet on the Oregon shelf. The dissipation is then confined to thin, elongated patches which coincide with regions of constructive interference between inertial, tidal and wind shear. The jet at the Oregon shelf has a maximum velocity ~40 cm s− 1, on which substantial windinduced shear is superposed. In the present investigation the predominant flow is tidal and the baroclinic jet has its maximum in mid-water and so makes only a small contribution to enhancing mixing near the bed. At the same time wind forcing was very weak and the frontal jet was significantly weaker than that at the Oregon Shelf. There are some caveats to be noted in relation to the above conclusions. In the analysis we have been forced to make a number of simplifying assumptions. In particular we have assumed that the front is essentially two dimensional in structure so that we have implicitly ignored along-frontal variation. This approach may be compromised if the front is meandering with significant curvature at the location of the observed section. There are indications in the observed I–R (see Fig. 1b) that this may have been the case, at least in the surface manifestation of the front. There are also limitations in resolution which must be taken into account. Because of the need to extract the tidal signals, we acquired vertical profiles only at a limited number of stations and horizontal profiles only at two depths. Increasing the number of FLY stations and using more survey depths for Autosub would result in an unrealistically long campaign. It should also be noted that while the FLY stations remained fixed relative to the seabed, the Autosub results were for a section moving with the water, so there is some smearing out of the data in the cross-frontal direction on the scale of the tidal displacement (~3 km) which effectively degrades the horizontal resolution. In spite of these limitations, we consider that this study has demonstrated the considerable benefit of employing an AUV in conjunction with more conventional instrumentation to study spatially complex systems like that of the tidal mixing front. There is clearly scope in such studies for examining alternative survey strategies and analysis techniques for teasing apart the spatial structure and the time dependence of the processes involved but, whatever the strategy, data from a roving AUV provides an invaluable additional dimension to the study. The present Autosub is large and demanding in terms of support services but as AUVs become smaller and easier to manage, there is the prospect of improving sampling by using more than one AUV working in

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parallel with moorings and conventional shipboard measurements in a well-designed survey. Acknowledgements The expertise and professionalism of the officers, crews, and scientific crews of RV Prince Madog and MS Terschelling were vital to the success of the operations described here. Ben Powell, Ray Wilton, and the Autosub team under Steve McPhail provided invaluable technical and operational support. Peter Miller at Plymouth Marine Laboratory kindly granted access to the satellite imagery from the Irish Sea. The comments from two anonymous reviewers helped improve the manuscript. Funding was provided by the British National Environmental Research Council through grant NER/D/S2002/00965. References Avicola, G.S., Moum, J.N., Perlin, A., Levine, M.D., 2007. Enhanced turbulence due to the superposition of internal gravity waves and a coastal upwelling jet. Journal of Geophysical Research 112, C06024. doi:10.1029/2006JC003831. Brown, J., Carrillo, L., Fernand, L., Horsburgh, K.J., Hill, A.E., Young, E.F., Medler, K.J., 2003. Observations of the physical structure and seasonal jet-like circulation of the Celtic Sea and St. George's Channel of the Irish Sea. Continental Shelf Research 23, 533–561. Dewey, R.K., Gargett, A.E., Oakley, N.S., 1987. A microstructure instrument for profiling oceanic turbulence in coastal bottom boundary layers. Journal of Atmospheric and Oceanic Technology 4, 288–297. Garrett, C.J.R., Keeley, J.R., Greenberg, D.A., 1978. Tidal mixing versus thermal stratification in the Gulf of Maine. Atmosphere and Ocean 16 (4), 403–423. Garrett, C.J.R., Loder, J.W., 1981. Dynamical aspects of shallow sea fronts. Philosophical Transaction of the Royal Society of London, Series A— Mathematical Physical and Engineering Sciences 302, 563–581. Glorioso, P.D., Simpson, J.H., 1994. Numerical modelling of the M2 tide on the Patagonian shelf. Continental Shelf Research 14, 267–278. Hill, A.E., Brown, J., Fernand, L., 1997. The summer gyre in the western Irish Sea: Shelf sea paradigms and management implications. Estuarine, Coastal and Shelf Science 44, 83–95. Houghton, R.W., 2002. Diapycnal flow through a tidal front: a dye tracer study on Georges Bank. Journal of Marine Systems 37, 31–46. James, I.D., 1984. A three-dimensional numerical shelf-sea front model with variable eddy viscosity and diffusivity. Continental Shelf Research 3, 69–98. Lie, H.J., 1989. Tidal fronts in the south-eastern Hwanghae (Yellow Sea). Continental Shelf Research 9, 527–546. Lwiza, K., Bowers, D.G., Simpson, J.H., 1991. Residual and tidal flows at a tidal mixing front in the North Sea. Continental Shelf Research 11, 1379–1395. Millard, N.W., Griffiths, G., Finnegan, G., McPhail, S.D., Meldrum, D.T., Pebody, M., Perrett, J.R., Stevenson, P., Webb, A.T., 1998. Versatile autonomous submersibles — the realising and testing of a practical vehicle. Underwater Technology 23, 7–17. Mudge, T.T., Lueck, R.G., 1994. Digital signal processing to enhance oceanographic observations. Journal of Atmospheric and Oceanic Technology 11, 825–836. Oakey, N.S., 1982. Determination of the rate of dissipation of turbulent kinetic energy from simultaneous temperature and velocity shear microstructure measurements. Journal of Physical Oceanography 12, 256–271. Oakey, N.S., Pettipas, R.G., 1992. Vertical mixing rates on Georges Bank during June, July and October, 1988. Canadian Data Report Hydrography and Ocean Science, vol. 110. 225 pp. Pingree, R.D., Griffiths, D.K., 1978. Tidal fronts on the shelf seas around the British Isles. Journal of Geophysical Research 83, 4615–4622. Rippeth, T.P., 2005. Mixing in seasonally stratified shelf seas: a shifting paradigm. Philosophical Transaction of the Royal Society of London, Series A—Mathematical Physical and Engineering Sciences 363, 2837–2854. doi:10.1098/rsta.2005.1662. Rippeth, T.P., Palmer, M.R., Simpson, J.H., Fisher, N.R., Sharples, J., 2005. Thermocline mixing in summer stratified continental shelf seas. Geophysical Research Letters 32, L05602. doi:10.1029/2004GL022104. Sharples, J., Simpson, J.H., 1995. Semi-diurnal and longer period stability cycles in the Liverpool Bay ROFI. Continental Shelf Research 15 (2/3), 295–314. Simpson, J.H., 1997. Tidal processes in shelf seas. In: Brink, K.H., Robinson, A.R. (Eds.), The Sea, vol. 10, pp. 113–150.

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