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  • View in gallery

    Irish Sea Location map showing the position at which the time series was collected, (LB2) (*) and the positions of the CTD stations (+)

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    The water column structure running west–northwest from the mouth of the river Mersey to the north of Anglesey and across the western Irish Sea front. The arrow indicates the position of station LB2. The three sections are (a) temperature (°C), (b) salinity (psu), and (c) σT (kg m−3)

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    Evolution of the water column and current structure at LB2 for a 24-h period on 5 and 6 of Jul 1999. (a) Temperature (°C) and (b) salinity measured by profiling with the FLY profiler and CTD; (c) u velocity and (d) υ velocity components (m s−1) measured using the seabed-mounted ADCP

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    Evolution of the density structure [given as σT (kg m−3) and calculated from the temperature and salinity as shown in Figs. 3a and 3b] is overlain on top of a plot of the evolution of the rate of dissipation of turbulent kinetic energy (log10 − W m−3) measured using the FLY profiler at station LB2

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    Individual profiles of temperature (°C), σT (kg m−3), ϵ (W m−3), and the u and υ velocity components (m s−1): (a) taken 1 h before the local low water and (b) taken 45 min before high water. The temperature profile has a vertical resolution of ∼4 cm

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    Vertical and error velocity estimates made using the ADCP. The modulus of 1-min ensemble values of (a) vertical velocity and (b) error velocity for the depth bins centered at 23.5, 19.5, 15.5, 10.5, and 6.5 mab, respectively, above the seabed

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    Summary plot: (a) the U velocity component measured in the upper (25 mab; solid line) and lower layers (5 mab; dashed line), (b) rate of change of ϕ due to straining estimated from the vertical shear in the u velocity, as measured by the ADCP [Eq. (2)], (c) the difference in salinity between 2 mab and just below the surface, (d) depth-averaged salinity, (e) vertical turbulent buoyancy flux [Eq. (10)], (f) hourly mean ϕ value calculated from the profiles of temperature and salinity made using FLY [Eq. (1)], (g) hourly mean ∂ϕ/∂t estimated from the values of ϕ given in (e), (h) vertically averaged rate of dissipation over between 15 mab and 5 m below the sea surface (near-surface region), and (i) vertically averaged rate of dissipation between the heights of 0.15 and 15 mab (near-bed region)

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The Cycle of Turbulent Dissipation in the Presence of Tidal Straining

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  • 1 School of Ocean Sciences, University of Wales Bangor, Menai Bridge, Anglesey, United Kingdom
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Abstract

In regions of large horizontal density gradient, tidal straining acts to produce a periodic component of stratification that interacts with turbulent mixing to control water column structure and flow. A 25-h series of measurements of the rate of dissipation of turbulent kinetic energy (ϵ) in the Liverpool Bay region of freshwater influence (ROFI) have revealed the form of this interaction and indicate substantial differences from regions where horizontal gradients are weak. In the ROFI system there is a pronounced difference between flood and ebb regimes. During the ebb the water column stratifies and strong dissipation is confined to the lower half of the water column. By contrast, during the flood, stratification is eroded with complete vertical mixing occurring at high water and high values of dissipation (3 mW m−3) extending throughout the water column. The cycle of dissipation is therefore predominantly semidiurnal in the upper layers whereas, near the bottom boundary, the principal variation is at the M4 frequency as observed in regions of horizontal uniformity. Toward the end of the flood phase of the cycle, tidal straining produces instabilities in the water column that release additional energy for convective mixing. Confirmation of increased vertical motions throughout the water column during the late flood and at high water is provided by measurements of vertical velocity and the error velocity from a bottom-mounted acoustic Doppler current profiler.

Corresponding author address: Tom Rippeth, School of Ocean Sciences, University of Wales Bangor, Menai Bridge, Anglesey LL59 5EY, United Kingdom. Email: t.p.rippeth@bangor.ac.uk

Abstract

In regions of large horizontal density gradient, tidal straining acts to produce a periodic component of stratification that interacts with turbulent mixing to control water column structure and flow. A 25-h series of measurements of the rate of dissipation of turbulent kinetic energy (ϵ) in the Liverpool Bay region of freshwater influence (ROFI) have revealed the form of this interaction and indicate substantial differences from regions where horizontal gradients are weak. In the ROFI system there is a pronounced difference between flood and ebb regimes. During the ebb the water column stratifies and strong dissipation is confined to the lower half of the water column. By contrast, during the flood, stratification is eroded with complete vertical mixing occurring at high water and high values of dissipation (3 mW m−3) extending throughout the water column. The cycle of dissipation is therefore predominantly semidiurnal in the upper layers whereas, near the bottom boundary, the principal variation is at the M4 frequency as observed in regions of horizontal uniformity. Toward the end of the flood phase of the cycle, tidal straining produces instabilities in the water column that release additional energy for convective mixing. Confirmation of increased vertical motions throughout the water column during the late flood and at high water is provided by measurements of vertical velocity and the error velocity from a bottom-mounted acoustic Doppler current profiler.

Corresponding author address: Tom Rippeth, School of Ocean Sciences, University of Wales Bangor, Menai Bridge, Anglesey LL59 5EY, United Kingdom. Email: t.p.rippeth@bangor.ac.uk

1. Introduction

Understanding the processes controlling the spreading of freshwater runoff, and the lateral dispersion of riverine pollutant and nutrient loads, is a key element in the development of predictive models on which management strategies for many coastal areas are increasingly dependent. Buoyancy input as freshwater is an important contributor to the dynamics and a dominant stratifying influence, not only in most estuarine environments but also over large areas of the shelf seas, referred to as ROFIs (regions of freshwater influence: Simpson 1997). Significant density gradients may extend tens or even hundreds of kilometers from major estuarine sources creating an environment in the ROFI radically different from that over the rest of the shelf, where the exchange of heat through the sea surface tends to dominate the buoyancy flux.

The buoyancy input tends to drive an estuarine circulation in which lighter water is moved seaward over heavier fluid moving landward below. This stratifying influence competes with stirring by tides and wind stress to control the structure of the water column. When the buoyancy supply, from freshwater, is steady, the regular variations in tidal stirring over the spring–neap cycle acts to produce a fortnightly variation in stratification. This stratification cycle, together with related changes in the circulation, modulates the transport of buoyancy as was demonstrated in the laboratory experiments of Linden and Simpson (1988). During periods when the level of turbulence is sufficient to mix the water column completely, the salt flux can be an order of magnitude less than during periods when the level of turbulence is sufficiently weak to allow runaway stratification to develop (Linden and Simpson 1988). This modulation of horizontal transport by vertical mixing has been observed in ROFIs, for example, through the spring–neap cycle in San Francisco Bay (Monismith et al. 1996) and Spencer Gulf (Nunes et al. 1989).

In addition to this fortnightly cycle, the horizontal density gradients may interact with vertical shear in the tidal flow to induce periodic stratification at the M2 frequency (Simpson et al. 1990; Simpson and Souza 1995). Complete vertical mixing may occur during periods when the contribution of the straining destabilizes the water column, followed by periods of stratification when the vertical shear stratifies the water column. The switching between the stratified and mixed states over a single tidal cycle, termed strain-induced periodic stratification (SIPS), has been observed in a wide variety of estuarine and ROFI systems, for example, the Rhine outflow area of the North Sea (Simpson and Souza 1995); the York River estuary, Virginia (Sharples et al. 1994); San Francisco Bay (Stacey et al. 1999); the Columbia River (Jay and Smith 1990); and the Hudson River (Nepf and Geyer 1996).

Where the tidal motion has the character of a standing wave, the maximum stratification in the SIPS cycle occurs at low water after the ebb flow when fresher water in the upper layers has moved seaward over saltier water in the deeper layers. During the flood, this process is reversed with tidal straining acting to reduce the stability of the water column with complete vertical mixing occurring near high water. SIPS behavior was originally reported for the Liverpool Bay ROFI in the Irish Sea (Simpson et al. 1990) and this area has been the focus of efforts to understand and model the temporal evolution of vertical structure and flow over the semidiurnal and fortnightly cycles (e.g., Sharples and Simpson 1995). One-dimensional vertical structure models driven by tidal forcing and density gradients and utilizing Mellor–Yamada turbulence closure schemes have provided credible, first-order accounts of the system including predictions of the variation of turbulent energy intensity and dissipation over the SIPS cycle.

Understanding the interaction between turbulence, stratification, and shear has been the target of a number of recent observational campaigns in shelf seas (Simpson et al. 1996; Inall et al. 2000) and estuaries (Peters 1997; Stacey et al. 1999), which make use of the new generation of instruments capable of measuring turbulence parameters in these regimes. In this contribution we present new measurements made with the FLY Dissipation Profiler, which have enabled us, for the first time, to directly measure the rate of dissipation of turbulent kinetic energy ϵ through the water column in the Liverpool Bay ROFI system. Particular interest centers on the period, toward the end of the flood phase of the tide, when the tidal straining mechanism induces unstable conditions in the water column that will promote convective turbulent mixing, a process not fully represented in the turbulence closure schemes.

2. The energetics of tidal straining

The operation of the tidal straining mechanism and its influence on water column stability and mixing can be understood in terms of the energetics model of Simpson et al. (1990) in which the stratification of the water column is specified in terms of the potential energy anomaly ϕ, defined in terms of the density profile ρ(z) as
i1520-0485-31-8-2458-e1
where h is the depth; ϕ increases positively with water column stability and represents the amount of work (J m−3) needed to mix the water column. Density-driven and tidal shear flows interact with the horizontal density gradient to produce or erode stratification. If the local density changes are due only to advection in the x direction, it is readily shown that the change in ϕ is given by
i1520-0485-31-8-2458-e2
where ∂ρ/∂x is the horizontal density gradient, u(z) is the velocity profile, and u the depth-averaged velocity.
For the steady-state estuarine circulation, u(z) may be taken as the well-known solution of Hansen and Rattray (e.g., Officer 1976, p. 118) for a constant eddy viscosity Nz, which when substituted in Eq. (2) leads to the rate of increase in ϕ due to the density-driven circulation (∂ϕ/∂t)E. Comparing this quantity to the mean rate of tidal stirring over the tidal cycle, we have as the condition for the maintenance of stratification:
i1520-0485-31-8-2458-e3
where δ ≈ 0.004 is the efficiency of tidal stirring by currents of amplitude uT and k = 0.0025 is the quadratic bottom drag coefficient. Setting Nz = 0.0033huT (Bowden 1953), the criterion for estuarine stratification becomes
i1520-0485-31-8-2458-e4
This result serves as a practical test for the occurrence of estuarine stratification on timescales longer than the semidiurnal cycle (Nunes and Lennon 1987). Of more interest here is the application of Eq. (2) to the changes in stratification arising from the interaction between shear in the tidal flow and the density gradient. As a simple representation of the tidal velocity profile we use the quadratic formula of Bowden and Fairbairn (1952):
i1520-0485-31-8-2458-e5
which implies a rate of change of ϕ given by
i1520-0485-31-8-2458-e6
This term acts to increase stratification when the flow is directed with the density gradient during the ebb and reduces it on the flood. In the absence of vertical mixing, there would be a reversible cycle of stratification induced by straining superimposed on any longer term estuarine stratification. If the latter is negligible, stirring by winds and tides produces mixing, which means that by the end of the flood flow the water column may become vertically mixed and the straining mechanism then tends to induce instability in the water column with consequent release of energy for convective mixing. This tendency to induce “overmixing” will be most marked during periods when the tidal range is increasing.
Significant stratification will only occur on the ebb if the straining mechanism out-competes the tidal stirring; the criterion is found by comparing the net input from straining with the mean stirring power available on the ebb; that is,
i1520-0485-31-8-2458-e7
which, on substituting numerical values, reduces to
i1520-0485-31-8-2458-e8
This result is of the same form as Eq. (4) but implies that SIPS will occur at density gradients an order of magnitude weaker than is required for the maintenance of longer period stratification.

3. The northern Irish Sea

Liverpool Bay in the northern Irish Sea (Fig. 1) is host to an extensive ROFI, driven by freshwater discharge from the rivers Mersey, Dee, Ribble, and other smaller sources along the Lancashire coast. The region is one of very large tides that take the form of a standing wave associated with reflection of the Kelvin wave at the Lancashire coast. The springs range at the port of Liverpool is ∼10 m with correspondingly strong currents (>1 m s−1) over much of the eastern Irish Sea that, away from the ROFI, maintain a well-mixed regime. By contrast, in the western Irish Sea the currents fall to a minimum in the deep water to the southwest of the Isle of Man with correspondingly low levels of vertical mixing.

In order to set the context of the new observations, we first present a section across the Irish Sea (Fig. 1) made immediately on completion (7 July 1999) of the 24-h cycle of observations. The section, running from east to west, starts near the mouth of the rivers Mersey and Dee, and extends into the center of the western Irish Sea. The section was started approximately one hour after high water, and the ship had reached a point 70 km along the section by low water, with the final part of the survey (70–160 km) undertaken during the flood tide.

The section (Fig. 2) shows the characteristic summer regimes of the Irish Sea, with a thermally stratified area to the northwest, where surface temperatures of ∼16°C overlie deeper water of temperatures <12°C, with little variation in salinity with depth. This area is separated from the vertically well-mixed regime by a region of strong temperature gradient, the western Irish Sea tidal mixing front (Simpson 1981). Within the central region of the section (60–120 km offshore) the horizontal gradients in both temperature and salinity are weak. Details of the vertical structure of turbulent dissipation in these two contrasting regimes have been given elsewhere (Simpson et al. 1996, 2000).

Between 60 km offshore and the shoreward end of the transect, the water column shoals (bottom slope is ≈8 × 10−4) and the ROFI regime is identified by a strong offshore salinity gradient (∂S/∂x ≈ 7 × 10−5 m) and temperature gradients (∂T/∂x ≈ 7 × 10−5 m−1), which combine to form a density gradient of ∼7 × 10−5 kg m−4. The time series measurements to be presented in section 4 were collected at the position LB2, in the middle of this high horizontal gradient section where the mean water depth is 32 m and the tidal current amplitude uT varies between 0.5 m s−1 at neap tide and 1.2 m s−1 at spring; at the time of the observations uT was ≈0.6 m s−1.

Applying these values in the stratification criteria [Eqs. (4) and (8)], we find that the horizontal gradient of density is insufficient to support enduring stratification, but the condition for SIPS is satisfied so that we might anticipate significant periodic changes in water column stability.

4. Time series observations

High-resolution measurements were made over two tidal cycles on 5–6 July 1999 at a position in the Liverpool Bay area of the Irish Sea (53°28.4′N, 3°39.2′W; Fig. 1) using a FLY4 ϵ probe, a conventional CTD, and a moored ADCP (acoustic Doppler current profiler). During the period of the observations, the weather was calm with a clear sky and the sea state varied from smooth to slight. The tide was waning, after the spring tide, which occurred on 2 July, three days before the measurements began.

The free-falling FLY4 probe provides microstructure measurements of velocity shear from two piezoelectric shear probes mounted on the instrument nose, which are sampled at an operating frequency of 280 Hz and can resolve horizontal velocity fluctuations whose vertical wavelengths are between ∼1 cm and 1 m. Within the range of dissipation rates measurable using this instrument, ϵ ≈ 10−6–10−1 W m−3, the potential error in the measurement is estimated to be of order ±50% (Dewey et al. 1987; Simpson et al. 1996). The data from the instrument consists of profiles starting at 5 m below the sea surface. In the surface 5 m of the water column, the data may be corrupted as the probe is still accelerating and the water column turbulence may be contaminated by the ship's wake. Measurement continues down the water column until 15 cm above the seabed when a protective guard impacts on the bottom.

Temperature and conductivity sensors mounted on the FLY4 are recorded at an operating frequency of 20 Hz. The temperature sensor is a Thermometric P60 thermistor mounted on the probe nose, with a response time of 0.3 s, and the conductivity sensor is an (unpumped) SeaBird SBE-04 (response time of 0.34 s) attached to the probe body approximately 20 cm behind the nose. Although a first-order correction for the spatial mismatch between the temperature and conductivity measurements has been applied, the salinity finestructure is not sufficiently resolved to determine the Thorpe scale reliably.

The mode of operation was to profile continuously with FLY4 for 40 minutes out of every hour, with each profile taking about 5-min to complete. During the remaining 20 min the ship was repositioned. A profile was taken with a Neil Brown Mark IIIB CTD every second hour. The CTD was calibrated directly using reversing thermometers and water bottle samples. The FLY4 temperature and salinity sensors were then calibrated against the CTD.

The flow structure in the water column was observed using an RDI 600-kHz ADCP deployed on the seabed. The instrument was set up so that ensembles of velocity data for depth bins of 1 m, each comprising approximately 158 pings, were recorded every minute. The data consisted of two horizontal components u and υ, the vertical velocity w, and an “error” velocity e. We estimate the standard deviation in the ensemble mean velocity measurements to be 0.005 m s−1. Operational constraints unfortunately meant that the ADCP had to be recovered 2 h before the end of the measurement period.

5. Results

a. The cycles of stratification and dissipation

The evolution of the temperature, salinity, and velocity structure are shown in Figs. 3a–d on which the sea surface elevation, estimated from the ADCP backscatter data, has also been plotted to indicate the state of the tide. There is a clear semidiurnal signal in the structure of the water column with almost complete vertical mixing around each of the three high waters sampled. As the tide ebbs, the water column begins to stratify. Stratification continues throughout the ebb with maximum levels of stratification occurring around low water when the bed to surface temperature difference is ∼1°C and the salinity difference exceeds 0.5. The salinity difference is therefore the major contributor to stratification, as we would expect from the relative horizontal gradients of temperature and salinity.

The east–west component of the flow is dominated by the tide, with near-surface currents exceeding 0.7 m s−1 at maximum flood. Comparison with the cycle of sea surface elevation indicates that the tide is close to a pure standing wave, with high and low waters corresponding to the slack waters between the onshore and offshore flows. The vertical shear in the tidal currents is evident in Fig. 3c where it can be seen that the maximum currents observed near the surface are approximately twice those near the bed. The tide exhibits some asymmetry with a shorter, stronger flood (∼5 h 40 min, maximum surface speed >0.7 m s−1), and a weaker, longer ebb (∼6 h 45 min, maximum speed ∼0.6 m s−1). The north–south component (Fig. 3d) of the flow is generally much weaker except for a period before and during low water when a baroclinic circulation in the υ component is evident, with northward velocities of ∼0.3 m s−1 near the surface and southerly velocities of ∼0.2 m s−1 near the seabed. The flow pattern therefore switches from being predominantly unidirectional and barotropic around high water to having a significant transverse baroclinic circulation around low water. Tidal analysis of the flow reveals a 10° phase advance (20 min lead) in the tidal flow between the bottom ADCP bin (∼1.5 mab) and 10 meters above bottom.

The profiles of the rate of dissipation of turbulent kinetic energy ϵ have been compiled into an image plot, with density contours overlain (Fig. 4). The evolution of the vertical structure of ϵ exhibits strong quarter diurnal and semidiurnal cycles, which are consistent between the two tidal periods of observations. In the bottom 10 m of the water column there is a pronounced quarter-diurnal cycling between peak dissipations of ∼10−2 W m−3 close to the bed, corresponding to the maximum ebb and flood of the tide, and decreasing to ∼10−3 W m−3 at low water and about 10−4 W m−3 at high water. This difference in ϵ at low water and high water slack is apparently related to the fact that at low water there is a significant north–south baroclinic flow that is absent at high water when both components of flow are close to zero. Above a height of 15 mab, the variation in the ϵ has a predominant semidiurnal period with the lowest observed values <10−5 W m−3 observed around low water, and the highest dissipations reaching ∼3 × 10−3 W m−3 during the hour before high water.

There is, thus, a marked difference between the ebb and flood regimes. During the ebb, as the water column becomes stratified, the high dissipation region is confined to the lower half of the water column. By contrast, during the flood, high dissipation extends further up the water column and reaches to the upper limit of our observations (5 m below surface) just before high water. Two particularly interesting features in the ϵ observations are, first, that, during the initial few hours of the ebb, strong turbulence is confined to the lower layer of the still well-mixed water column. The second point is that, during the late part of the flood of both the tidal cycles sampled, enhanced dissipation persist longer in the upper part of the well-mixed water column than in the lower part, a result that cannot be attributable to near-bed-generated turbulence.

To illustrate the two regimes in more detail, individual profiles of water column structure, flow, and ϵ representative of the two regimes are presented in Fig. 5. The profile shown in Fig. 5a was taken toward the end of the ebb phase of the tide when stratification is close to a maximum, with a bed-to-surface difference in density of ∼0.6 kg m−3. At this time, the u velocity was flowing offshore at all depths and increasing with height from a near-bed velocity of 0.15 to 0.55 m s−1 at a height of 27 mab. The υ velocity profile exhibits significant shear in which there is a southerly flow of ∼0.15 m s−1 in the lower layer (below 15 mab) of the water column and a northerly flow of ∼0.1 m s−1 in the upper part of the water column. There is an almost well-mixed lower layer, extending up to ∼12 mab, within which there is relatively large dissipation (∼5 × 10−4 W m−3). Further up the water column where the density gradient is stronger dissipation was generally lower (<10−5 W m−3). The Ozmidov scale, which gives an estimate of the vertical scale at which the turbulence is affected by buoyancy forces (Peters 1997) is calculated (L0ϵ1/2N−3/2) to be ∼1 m in the well-mixed layer near the seabed and between 10 and 20 cm in the upper part of the water column.

The contrasting profile of Fig. 5b was taken ∼45 minutes before high water. At this time the water column is almost completely mixed, with very weak stratification and a number of small-scale instabilities in the density profile. The flow is predominantly in the east–west direction with current speeds of ∼0.3 m s−1 in the lower part of the water column increasing almost uniformly between 17 and 32 mab to 0.6 m s−1. Flow in the north–south direction is weak at all depths, with a slight southerly flow near the surface and a northerly flow near the bed. The ϵ profile is remarkably uniform over the water column with a value of ϵ = 5 × 10−4 W m−3 extending to the upper limit of our observations. Estimates of the Ozmidov scale decrease from ∼2 m near the seabed to ∼30 cm in the upper portion of the water column.

b. Turbulent indicators from the ADCP

Further, independent evidence for the occurrence of enhanced turbulent activity in the later stages of the flood comes from our measurements of the vertical and error velocities from the ADCP. The ensemble-averaged vertical velocity w is calculated as the mean of the four individual beam estimates, while the ensemble-averaged error velocity e is the mean difference from pairs of opposing beams, that is,
i1520-0485-31-8-2458-e9
where w1w4 are the ensemble averaged estimates of the vertical velocity for each of the beams. The long-term mean vertical velocity should be close to zero but fluctuations in w provide an index of turbulent activity. In addition the error velocity e gives an estimate of the spatial variability of the vertical velocity across the spread of the beams. As the transducers in the ADCP unit are mounted at a 20° angle to the vertical, the distance between the two beams of a beam pair will increase from 1.5 m at a height of 2 m above the transducers to 15 m at a height of 20 m above the transducers. Therefore e will give an indication of the loss of coherence between the beams and so provide qualitative information on the scales of the turbulent motions involved.

Figure 6 shows the vertical speed |w| and |e| derived from the 1-min mean values recorded by the ADCP for a number of bins spanning most of the water column. For much of the time series, the speed |w| at all levels is of order 0.005 m s−1, which is close to the noise level of the ADCP system. However, for the period between t = 187.05 d and t = 187.25 d, |w| increases substantially at all levels with values up to 0.025 m s−1. The modulus of the error velocity |e| (Fig. 6b) exhibits a comparable coincident increase in the upper bins where |e| > 0.05 m s−1 in contrast to the lowest bins where the increase is minimal.

This enhanced vertical motion, evident in both |w| and |e|, is coincident with the period, during the later part of the flood tide and extending 1 h into the ebb, when high values of ϵ extend up through the water column to the surface (see Fig. 3). A corresponding coincidence of enhanced vertical motion and high ϵ is also apparent at the end of the previous flood (prior to t = 186.7 d). The increase in |e|, evident higher up the water column, is in contrast to that in w, which is rather stronger lower down in the water column. Our interpretation is that the motions observed by the two beam pairs are becoming increasingly incoherent with height, which suggests that the horizontal length scale of the turbulent processes is less than the spread of the ADCP beams (18 m at 25 mab). Both w and e were found to have near-zero skewness.

6. Synthesis

The operation of the tidal straining process and its impact on the cycle of the rate of dissipation of turbulent kinetic energy are summarized in Fig. 7. The observed flow along the direction of the density gradient (E–W) is shown (7a) from near-surface and near-bed ADCP bins. The corresponding estimate of the change in the water column potential energy anomaly due to straining, calculated from the ADCP data using Eq. (2), is given in Fig. 7b. The straining term indicates the periods when the interaction between the current shear and horizontal density gradient destabilizes the water column (the term is negative) and when it contributes to the stratification (positive). The shear becomes destabilizing at the same time as the flood tide begins throughout the water column and remains destabilizing throughout the flood, and for approximately 1 h 10 min after the tide has begun to ebb at 5 mab. At 25 mab the tide begins to ebb 25 min later and this increasing phase lag in the tidal flow, with height, is sufficient to explain the continuance of the destabilizing shear into the ebb phase of the tide.

Advection by the M2 tidal flow is primarily responsible for the cycle of mean salinity (Fig. 7c), while the velocity shear interacts with the density gradient to promote or erode stratification. The level of stratification is represented (Fig. 7d) as the difference in salinity ΔS between the heights of 25 and 5 m above bed or, more fully, as the potential energy anomaly ϕ (Fig. 7f). The timing of the onset of stratification coincides with the current shear becoming stabilizing as is evident in both the tidal cycles sampled. There is tendency for the salinity difference and ϕ to dip somewhat following the maximum ebb current when vertical mixing is strong. The vertical turbulent buoyancy flux B (Fig. 7e) is estimated using
i1520-0485-31-8-2458-e10
where Kρ is the eddy diffusivity estimated from the observed dissipation and buoyancy frequency (N) using Kρ = 0.2ϵN−2 (Osborne 1980). The results show a large vertical buoyancy flux [∼1.0–1.5 (× 10−4 W m−3)] during the later part of the ebb tide of both of the tidal cycles sampled. The vertical flux falls off and the stratification (Fig. 7d) rises slightly around low water slack, then decreases rapidly and reaches a vertically well-mixed state some time after the shear in the current becomes destabilizing (Fig. 7b).

To facilitate comparison with the stratification cycle, we have separated the dissipation rates into near-surface (averaging between a height of 15 mab and 5 m below the surface; Fig. 7h) and near-bed (averaging between 0.15 and 15 mab, Fig. 7i) segments. The near-bed values show a quarter-diurnal signal with maximum values corresponding approximately to the maximum flood and ebb currents. The highest near-bed dissipation occurred during the flood phase of the tidal cycle, when the averaged dissipation was approximately twice that observed during the ebb, and which is qualitatively consistent with the larger tidal currents observed during the flood.

Comparing the time derivative of ϕ with the average dissipation (Fig. 7g), we see that sharp drop in stratification at the start of the flood coincides with large increases in dissipation occurring first in the lower layers and extending soon afterward up to the surface layers. After mixing is essentially complete, at around maximum flood, dissipation continues at a high level throughout the water column. During this period, the straining process is acting to destabilize the water column when there is no stratification to erode. As stratification breaks down, the boundary layer will thicken thus increasing the penetration of turbulence generated by the boundary shear flow. Once vertical homogeneity is achieved dissipation will be further enhanced by the potential energy available from the straining process, which acts to produce density instabilities in the water column, thus leading to convective motions. It is this convective input that we hypothesize is responsible for the remarkable upward extent of high levels of turbulent dissipation during the latter part of the flood (Fig. 5b).

7. Discussion

We have observed two consistent tidal cycles of dissipation and vertical structure in the Liverpool Bay ROFI system that demonstrate substantial differences from previous observations of the cycle of ϵ in the absence of significant horizontal gradients. The measurements reported in Simpson et al. (1996), in almost horizontally uniform conditions, indicate that dissipation exhibits a predominant quarter-diurnal variation, strongest near the bed and extending upward with an increasing phase lag (Simpson et al. 2000). In highly energetic situations the boundary layer and the quarter-diurnal variation reach to the surface while, in seasonally stratified situations, the quarter-diurnal signal is confined to the bottom boundary layer.

In our ROFI observations, ϵ again has a strong quarter-diurnal component near the bed but, further up the water column, there is a large asymmetry between flood and ebb with high dissipation prevailing throughout the water column during the latter part of flood. The high dissipations persist for approximately 1 h longer in the upper part of the water column than in the lower part, suggesting that turbulence has not originated from the bottom boundary layer. This period of intense dissipation and mixing has no counterpart on the ebb when the water column becomes stratified through the straining mechanism and dissipation levels in the upper half of the water column remain very low, even during the first few hours of the ebb when there is strong dissipation in the lower part of the well-mixed water column. As a consequence the variation in the dissipation in the upper layers is predominantly at the semidiurnal frequency.

Toward the end of the flood when the water column is already mixed, tidal straining is working to generate instability as heavier water is forced over lighter water below. Our inference of the role of convective forcing at this time is based on three independent pieces of coincident evidence;

  1. First, the combination of strong vertical shear in the tidal flow with the E–W density gradient ensure that the straining mechanism will provide an energy source in a water column that is already homogeneous in the vertical as demonstrated in Fig. 7b.
  2. Second, relatively high, uniform values of ϵ are observed, together with instabilities in the finescale temperature, throughout the water column (Fig. 5b). This is in contrast to the situation where turbulence is forced by boundary stresses and ϵ levels fall off rapidly in approximate accord with the law of the wall (Fig. 5a). The contrast is evident in Fig. 4 as the confinement of the high dissipation to the bottom 5–10 m of the water column during the early part of the ebb, despite the fact that the water column is well mixed, and the persistence of high dissipations further up the water column, for ∼1 h longer than nearer the seabed, toward the end of the flood tide.
  3. Third, the marked increase in vertical and error velocities only occurs during the flood phase of the tide and is directly associated with the period when high dissipations are observed to extend through the water column. That the vertical velocity variation decreases and error velocity increases with height implies that the vertical velocity estimate from each of the ADCP beam pairs is becoming increasingly incoherent with height as the ADCP beams spread.

Comparable observations of dissipation in an estuarine environment, as opposed to a ROFI, have been reported by Peters (1997) and Peters and Bokhorst (2000). In the Hudson Estuary they found a periodic switching between a stratified water column during the ebb phase of a spring tide, and full mixing during the flood (Figs. 5e–h of Peters and Bokhorst 2000). The density gradient and spring tidal currents they report fulfill the criteria for the occurrence of SIPS [Eq. (8)]. The evolution of dissipation shows a quarter-diurnal variation in ϵ through much of the water column. As in Liverpool Bay there is a contrast between the flood and the ebb phases of the tide, with ϵ generally smaller and with little variation near the surface during the ebb, and near-surface values increasing by an order of magnitude during maximum flood. The higher ϵ values during the flood are consistent with the larger flood tidal currents. There is, however, no evidence of a period of relatively uniform dissipation through the water column or of the high values of ϵ in the upper part of the water column toward the end of the flood, which we have observed in Liverpool Bay.

The high turbulent buoyancy flux during the ebb phase of the tide (Fig. 7e) emphasize the importance of vertical mixing at this time. As a consequence of this mixing the SIPS cycle is inelastic and results in the offshore transport of freshwater. It is therefore critical that models of circulation in coastal seas simulate vertical mixing accurately in order that they are able correctly predict the dispersion of river water in the coastal sea. Their ability to reproduce the observed evolution ϵ will provide a critical test of the vertical exchange schemes to be included in these models.

Acknowledgments

Ray Wilton (UWB) provided invaluable technical support. Our thanks go also to the crew of the RV Prince Madog for their assistance in making the measurements reported here. Dr. Jonathan Sharples (SOC) is thanked for the loan of the ADCP. Tom Rippeth is in receipt of the Natural Environmental Research Council Research Fellowship. The data collection and analysis were supported by the EU MAST III PROVESS project (Contract MAS3-CT97-0159) and Natural Environment Research Council Grant GR3/11829. We would also like to thank two anonymous reviewers for raising a number of useful suggestions, which led to the improvement of this paper.

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Fig. 1.
Fig. 1.

Irish Sea Location map showing the position at which the time series was collected, (LB2) (*) and the positions of the CTD stations (+)

Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2458:TCOTDI>2.0.CO;2

Fig. 2.
Fig. 2.

The water column structure running west–northwest from the mouth of the river Mersey to the north of Anglesey and across the western Irish Sea front. The arrow indicates the position of station LB2. The three sections are (a) temperature (°C), (b) salinity (psu), and (c) σT (kg m−3)

Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2458:TCOTDI>2.0.CO;2

Fig. 3.
Fig. 3.

Evolution of the water column and current structure at LB2 for a 24-h period on 5 and 6 of Jul 1999. (a) Temperature (°C) and (b) salinity measured by profiling with the FLY profiler and CTD; (c) u velocity and (d) υ velocity components (m s−1) measured using the seabed-mounted ADCP

Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2458:TCOTDI>2.0.CO;2

Fig. 4.
Fig. 4.

Evolution of the density structure [given as σT (kg m−3) and calculated from the temperature and salinity as shown in Figs. 3a and 3b] is overlain on top of a plot of the evolution of the rate of dissipation of turbulent kinetic energy (log10 − W m−3) measured using the FLY profiler at station LB2

Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2458:TCOTDI>2.0.CO;2

Fig. 5.
Fig. 5.

Individual profiles of temperature (°C), σT (kg m−3), ϵ (W m−3), and the u and υ velocity components (m s−1): (a) taken 1 h before the local low water and (b) taken 45 min before high water. The temperature profile has a vertical resolution of ∼4 cm

Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2458:TCOTDI>2.0.CO;2

Fig. 6.
Fig. 6.

Vertical and error velocity estimates made using the ADCP. The modulus of 1-min ensemble values of (a) vertical velocity and (b) error velocity for the depth bins centered at 23.5, 19.5, 15.5, 10.5, and 6.5 mab, respectively, above the seabed

Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2458:TCOTDI>2.0.CO;2

Fig. 7.
Fig. 7.

Summary plot: (a) the U velocity component measured in the upper (25 mab; solid line) and lower layers (5 mab; dashed line), (b) rate of change of ϕ due to straining estimated from the vertical shear in the u velocity, as measured by the ADCP [Eq. (2)], (c) the difference in salinity between 2 mab and just below the surface, (d) depth-averaged salinity, (e) vertical turbulent buoyancy flux [Eq. (10)], (f) hourly mean ϕ value calculated from the profiles of temperature and salinity made using FLY [Eq. (1)], (g) hourly mean ∂ϕ/∂t estimated from the values of ϕ given in (e), (h) vertically averaged rate of dissipation over between 15 mab and 5 m below the sea surface (near-surface region), and (i) vertically averaged rate of dissipation between the heights of 0.15 and 15 mab (near-bed region)

Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2458:TCOTDI>2.0.CO;2

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