John H. Simpson

Tidal straining, density currents, and stirring in the control of estuarine stratification

Buoyancy input as fresh water exerts a stratifying influence in estuaries and adjacent coastal waters. Predicting the development and breakdown of such stratification is an inherently more difficult problem than that involved in the analogous case of stratification induced by surface heating because the buoyancy input originates at the lateral boundaries. In the approach adopted here, we have adapted the energy considerations used in the surface heating problem to describe the competition between the stabilizing effect of fresh water and the vertical mixing brought about by tidal and wind stirring. Freshwater input induces horizontal gradients which drive the estuarine circulation in which lighter fluid at the surface is moved seaward over heavier fluid moving landward below. This contribution to stratification is expected to vary in time as the level of turbulence varies over the tidal cycle. The density gradient also interacts directly with the vertical shear in the tidal current to induce a periodic input to stratification which is positive on the ebb phase of the tide. Comparison of this input with the available stirring energy leads to a simple criterion for the existence of strain-induced stratification. Observations in a region of Liverpool Bay satisfying this criterion confirm the occurrence of a strong semidiurnal variation in stratification with complete vertical mixing apparent around high water except at neap tides when more permanent stratification may develop. A simulation of the monthly cycle based on a model including straining, stirring, and the estuarine circulation is in qualitative agreement with the main features of the observations.

Models of stratification and frontal movement in shelf seas

Abstract The availability of turbulent kinetic energy from tidal flow in the shelf sea areas of the oceans is considered. This energy source, together with wind mixing and buoyancy input by surface heating, is incorporated in a constant efficiency model of the vertical mixing in the shelf seas. The relative importance of wind and tidal stirring is assessed on the basis of observed potential energy distributions. The results of satellite infrared (i.r.) imagery are used to describe the variability of frontal positions. After the removal of tidal advection, there is a residual r.m.s. displacement of ∼7 km that cannot be explained by springs-neaps adjustment or seasonal changes. The minimal springs-neaps movement observed (∼4 km) leads to a modified energy model in which a feedback component reduces the efficiency of mixing as stratification becomes established. Predictions by the variable efficiency model of the annual cycle of the potential energy V are compared with observations at locations experiencing widely different levels of tidal mixing.

Physical processes in the ROFI regime

Abstract The distinctive feature of all ROFI (Regions Of Freshwater Influence) systems is the input of significant amounts of buoyancy as freshwater from river sources. If the spatial scale is unrestricted by coastal topography and stirring is weak, this input tends to drive a coast-parallel flow in which the Coriolis force constrains a wedge of low density water against the coastal boundary. Without frictional effects, this flow is subject to baroclinic instability which induces large meanders and eddies in the flow but in, many ROFIs, the tidal flow induces frictional effects which stabilise the density driven flow. In the absence of the effects of rotation and stirring, the buoyancy input tends to induce stratification through an estuarine circulation in the direction of the gradient. When stirring is applied, by the action of wind, waves or tidal flow, the density current is suppressed but is rapidly re-established when stirring ceases, as in the Linden-Simpson (1988) laboratory tank experiments. In real ROFI systems, a combination of all these processes operates so that the structure of the water column and the flow is the result of a competition between the stratifying influence of buoyancy input and the net stirring effect of the wind, waves and the tides. This competition is more difficult to analyse than the heating-stirring competition, because freshwater buoyancy input is not spatially uniform but enters at discrete sources along the coast and its subsequent spreading has to be determined. While the springs-neaps cycle in tidal stirring imposes a regular fortnightly modulation on vertical mixing, the influence of the wind is irregular and depends, not just on the magnitude of the stress, but also on the direction in which it acts. In some exposed shallow water situations there may also be significant stirring due to waves generated by non-local winds. ROFI systems are further complicated by the action of tidal straining in which differential advection, due to vertical shear in the tide, interacts with the density gradient to generate fluctuations in vertical stability at the tidal frequency which, in some cases, are of sufficient amplitude to switch the water column between stable stratification and vertical density homogeneity each tidal cycle. This straining along with the other ROFI processes have been incorporated into a series of 1-D models to provide a more objective test of the hypotheses about the mechanisms involved. Comparison of model hindcasts with observations indicate that we now have a first-order understanding of the complex behaviour of ROFIs. On a global scale it is clear that ROFIs represent an important component of the shelf-sea environment of particular concern in relation to the impact of pollutant discharges. To date, most studies of ROFIs have concentrated on systems in temperate latitudes but attention needs to be focused on the very extensive ROFIs in tropical regions where most of the worlds river discharge enters the ocean. In monsoonal regions, these inputs exhibit strong seasonal modulation which may, in competition with tidal stirring, result in an annual cycle of stratification and the formation of fronts.

The Vertical Structure of Turbulent Dissipation in Shelf Seas

Abstract The free-fall FLY profiler has been used to determine the variation in energy dissipation ϵ in the water column over a tidal cycle at mixed and stratified sites in the Irish Sea. It was found that ϵ exhibits a strong M4 variation with a pronounced phase lag that increases with height above the bed. In mixed conditions this M4 signal, which extends throughout the water column, is reasonably well reproduced by turbulent closure models of the vertical exchange. In the summer stratified situation, the M4, signal in ϵ is confined to about 40 m above the seabed with phase delays of more than 4 h relative to the seabed. The lowest levels of dissipation (∼10−5 W m−3), measured in the pycnocline, are significantly above the system noise level and much higher than predicted by a model using the Mellor-Yamada level 2 closure scheme (MY2.0). However, when allowance is made for the diffusion of TKE, the model (MY2.2) simulates the depth-time distribution of dissipation in the stratified case satisfactorily if...

The Cycle of Turbulent Dissipation in the Presence of Tidal Straining

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 ( e) 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 m23) 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.

Reynolds Stress and Turbulent Energy Production in a Tidal Channel

Abstract A high-frequency (1.2 MHz) acoustic Doppler current profiler (ADCP) moored on the seabed has been used to observe the mean and turbulent flow components in a narrow tidally energetic channel over six tidal cycles at neap and spring tides. The Reynolds stress has been estimated from the difference in variance between the along-beam velocities of opposing acoustic beams with a correction for the sampling scheme and bin size. Shear stress was found to vary regularly with the predominantly semidiurnal tidal flow with the stresses on the spring ebb flow (up to 4.5 Pa) being generally greater than on the flood flow (<2 Pa) when the currents are weaker. The vertical structure approximated to linear stress profiles decreasing from maximum values near the bed to almost zero stresses just below the surface. The variation in the bed stress was well represented by a quadratic drag law, based on the depth-mean current, with an estimated drag coefficient of 2.6 ± 0.2 × 10−3. The production of turbulent kinetic...

Dynamics of tidal mixing fronts in the North Sea

Twenty years since the discovery of tidal mixing fronts there are still few convincing observations of the velocity field associated with these structures. Simple models of shelf sea fronts predict strong along-front jets, weaker convergent circulations and instabilities. During the North Sea Project a series of studies of the Flamborough frontal system has used a new approach based upon novel combinations of modern instrumentation (hf radar, acoustic Doppler current profiler, Decca-Argos drifting buoys and towed undulating ctd) and have provided one of the first directly observed pictures of shelf sea frontal circulation. Observational confirmation of jet-like along-front flow has been found together with evidence of cross-frontal convergence. A new generation of eddy-resolving models will help to focus the next phase of frontal circulation studies in relation to questions concerning baroclinic instability and eddy generation.

Effect of the Earth's rotation on the circulation in regions of freshwater influence

Recent surveys in various regions of freshwater influence have shown considerably different flow patterns in each region. An analytical model including viscous effects and the Earths rotation is proposed to examine the along-channel flow pattern and to explain the differences. Model results show that the flow pattern is strongly dependent on the Ekman number E. With a large Ekman number (E > 1) the system is governed by gravitational circulation, and thus horizontal density gradients in along-channel direction are important. The whole water column is in the Ekman layer and consequent jet inflow penetrates the surface over a deep depression if the bottom topography varies in a cross-channel direction. With an intermediate Ekman number (E ∼ 0.1) this jet inflow concentrates in the lower layer in which the viscosity still plays an important role. The flow in the upper layer is, on the other hand, determined by the geostrophic balance. The contribution by the geostrophic flow becomes larger so that the cross-channel density gradients are important when die Ekman number is small (E < 0.01). Since the Ekman layer is clung to the bottom, the jet inflow exists only in the thin bottom layer. The hydrographic and acoustic Doppler current profiler surveys were conducted in Ise Bay, Japan. Both the density structure and the flow pattern were different from those observed in many drowned river valleys. A strong jet inflow existed in the lower layer over the depression while the flow in the upper layer suggested anticyclonic circulation. The estimated Ekman number is 0.07 in the bay and thus the observed pattern is consistent with the model result when E = 0.1.

Residual and tidal flow at a tidal mixing front in the North Sea

Abstract A ship-mounted acoustic Doppler current profiler (ADCP) has been used to study the circulation in a frontal region of the North Sea, at the boundary between mixed and stratified water. The ship steamed backwards and forwards across a front on two sections for at least two tidal cycles to enable tidal and residual flows to be resolved. The residual flows parallel to the front are generally larger (by a factor of ∼3) than those perpendicular to it and exhibit significant structure. On a section near the Yorkshire coast, observations at neaps show that the flow is to the southeast with two regions where the flow is up to ∼6 cm s−1 separated by a zone of low flow. This structure is in qualitative agreement with the geostrophic flow based on the density field. At a section near the Dogger Bank there is evidence of a frontal jet, with currents reaching 15 cm s−1. However, the jet is not present all the time, and there are indications that it is stronger at springs and weaker at neaps. The cross-frontal residual current also is better defined at spring tides, with convergence at the surface and divergence near the bottom. The ADCP has enabled details of the tidal current profile to be elucidated. There are clear indications that the profile is influenced by the density structure. The tidal currents near the bottom lead those near the surface on both sides of the front, but on the stratified side this phase change is concentrated in a narrow band at the thermocline depth. On the mixed side, the phase change is spread more evenly over the water column. The tidal current vector rotates clockwise in the top 20 m and then anticlockwise in the rest of the water column, an effect known to be caused by bottom friction. A more subtle feature is the observed clockwise veering of the semi-major axis with depth from the surface.

The modification of tidal ellipses by stratification in the Rhine ROFI

We report on recent observations of the vertical structure of density and velocity profiles, using a bottom mounted ADCP, in the Rhine ROFI system in the North Sea which confirms previous indications that the presence of stratification modifies the vertical structure of the tidal ellipse characteristics. During periods of stratification, the ellipses change from degener- ate to a more circular pattern, with the surface ellipse rotating clockwise and the bottom ellipse rotating anticlockwise. The surface to bottom ellipticity difference ae is found to be closely related to a bulk Richardson number which incorporates both the stratification and a measure of the tidal shear. An explanation of the observed dependency of elliptieity on the density structure is offered in terms of the different thickness of the frictional layers for clockwise and anticlockwise motion in a rotating system. The changes in polarization of the flow are large enough to introduce a significant cross-shore velocity component which enhances the vertical shear in the tidal flow and is responsible for the strong semi-diurnal variation of stratification observed in this ROFI system.