Yakun Guo

On the breaking of internal solitary waves at a ridge

An experimental laboratory study has been carried out to investigate the propagation of an internal solitary wave of depression and its distortion by a bottom ridge in a two-layer stratified fluid system. Wave profiles, density fields and velocity fields have been measured at three reference locations, namely upstream, downstream and over the ridge. Experiments have been performed with wave amplitudes in the range 0.2– 1.9 times the depth of the upper layer, and a ratio between the lower and the upper layer in the range 3.0–8.5. The ridge slope was varied from 0.1 to 0.33 and the maximum ridge height was two-thirds of the thicker fluid layer. Over the ridge, the flow has been classified into: (i) cases when the bottom ridge has little influence on the propagation and spatial structure of the internal solitary wave, (ii) cases where the internal solitary wave is significantly distorted by the blocking effect of the ridge (though no wave breaking occurs), and (iii) cases for which the internal solitary wave is broken as it encounters and passes over the bottom ridge. A detailed description of the processes leading to wave breaking is given. Breaking has been found to take place when the fluid velocity in the lower layer exceeds 0.7 of a local nonlinear wave speed, defined at the top of the ridge. The breaking condition is also expressed in terms of the amplitude of the incident wave, the layer thickness ratio and the relative height of the ridge. The wave breaking can be determined from the input parameters of the experiment. The transmitted waves have been found to always consist of a leading pulse (solitary wave) followed by a dispersive wavetrain. The (solitary) wave amplitude is significantly reduced only when breaking takes place at the ridge. Internal waves of mode two are generated in cases with strong breaking.

Laboratory model studies of flushing of trapped salt water from a blocked tidal estuary

Results are presented from a series of laboratory model studies of the flushing of saline water from a partially- or fully-closed estuary. Experiments have been carried out to determine quantitatively the response of the trapped saline volume to fresh water Hushing discharges Q for different values of the estuary bed slope a and the density difference (Δρ)0 between the saline and fresh water. The trapped saline water forms a wedge within the estuary and for maintained steady discharges, flow visualisation and density profile data confirm that its response to the imposition of the freshwater purging flow occurs in two stages, namely (i) an initial phase characterised by intense shear-induced mixing at the nose of the wedge and (ii) a relatively quiescent second phase where the mixing is significantly reduced and the wedge is forced relatively slowly down and along the bed slope. Scalings based upon simple energy balance considerations are shown to be successful in (i) describing the time-dependent wedge behaviour and (ii) quantifying the proportion of input kinetic energy converted into increasing the potential energy of the wedge/river system. Measurements show that the asymptotic value of the energy conversion factor increases with increasing value of the river Froude number Fr 0 at small values of Fr 0, thereafter reaching a maximum value and a gradual decrease at the highest values of Fr 0. Dimensional analysis considerations indicate that the normalised, time-dependent wedge position (x w)3 (g′)0/q 2 can be represented empirically by a power-law relationship of the form (x w)3 [(g′)0/q 2]⅓ = C {(t)[(g′)0 2/q]⅓} n where the proportionality coefficient C is a function of both Fr 0 and the slope angle a and the exponent n has a value of 0.24. Successful attempts are made to relate the model data to existing field observations from a microtidal estuary. Experiments with multiple, intermittent periodic flushing flows confirm the importance of the starting phase of each flushing event for the timedependent behaviour of the saline wedge after reaching equilibrium in the intervals between such events. For the parameter ranges investigated and for otherwise-identical external conditions, no significant differences are found in the position of the wedge between cases of sequential multiple flushing flows and steady single discharges of the same total duration.

Laboratory model studies of Mediterranean outflow adjustment in the Gulf of Cadiz

Results are presented from a series of laboratory modelling studies carried out as part of the international multidisciplinary project CANIGO. The focus of interest has been the phenomenon of flow adjustment within the Gulf of Cadiz of the Mediterranean outflow plume, modelled by a turbulent, negatively-buoyant jet discharging into a rotating stratified reservoir scaled to the idealised topography of the Gulf. The results show that the fully developed flow pattern that forms close to the entrance to the Gulf consists of a relatively intense jet that divides when it encounters the southern Iberian coastal boundary; part of the jet is deflected westwards to form a boundary current at intermediate depth along the coastline and part is deflected eastwards and back towards the Strait to form a closed weak circulation near the diverging right wall of the Gulf. Within this closed circulation (the typical horizontal dimensions of which scale with the source Froude number when normalised with the inertial radius), small-scale eddy features are embedded. The degree of entrainment into the descending turbulent jet is seen to be determined primarily by the receiving water Froude number (and is relatively insensitive to the Burger and Rossby numbers of the flow), resulting in the formation of a boundary current of intermediate density that follows the Iberian coastal boundary with a typical velocity determined primarily by the effective driving head at the source and weakly by the Burger number of the flow.

Topographic and stratification effects on shelf edge flows

Results are presented from two sets of laboratory model experiments on the effects of an isolated seamount upon the flow of an intermediate-water slope current along a continental shelf. The experimental results for initial ambient conditions of respectively two-layer and linearly stratified fluids show that the structure of such a boundary current depends primarily on the values of the appropriate set of dimensionless dynamical parameters (namely the Burger (Bu), Ekman (Ek) and Rossby (Ro) numbers), as well as the dimensionless lateral separation of the seamount and shelf and the proportional height of the seamount relative to the distance from the bottom at which the intermediate-water flows. Comparisons of the present results with those from a previous two-layer fluid study with no obstacle present reveals that the presence of the obstacle does not alter significantly the stability of the current even when situated close to the shelf. However, for such configurations, the density, velocity and vorticity fields in the local zone of interaction between the current and the obstacle are distorted significantly by the presence of the obstacle, provided that the summit of the obstacle penetrates the level of current flow. Measurements of density, velocity and vorticity fields show no significant dependence of the flow interaction upon the detailed bathymetry of the shelf-slope. For stable intermediate-water slope currents, the nature of the interaction with the obstacle is determined primarily by (i) the lateral separation of the obstacle and the shelf edge and (ii) the Ro of the flow. For sufficiently low values of the former and high values of the latter, the interaction results in a splitting of the incident flow around the obstacle, with cyclonic and anticyclonic eddy pairs being generated in the lee. Geostrophic equilibrium is seen to be maintained in the current, even in the near wake of the obstacle. For cases in which the summit of the seamount is below the initially-undisturbed intermediate water level, no Taylor column-like division of the slope current occurs and no significant distortion of the current structure (velocity and density) occurs for the parameter ranges investigated. For linearly stratified cases, measurements show that no significant local elevation or depression of the density interfaces is observed in the interaction zone. The distributions of the local buoyancy frequencies calculated from the density profiles reveal that the minimum value of the frequency upstream of the obstacle is smaller than that downstream, indicating that the flow interactions generate local mixing downstream, with consequent erosion of the density interfaces.

Boundary currents over shelf and slope topography

Abstract Laboratory experiments are presented from a modelling investigation into the influence of shelf and slope topography on f-plane surface and intermediate flows along ocean boundaries. The surface flows are formed from an upstream source by the release of fresh water into a rotating tank containing salt water, while for the intermediate-water counterpart flows, neutrally-buoyant fluid was released from a submerged source into stably-stratified (two-layer) and quiescent receiving waters in solid body rotation. It is shown that the stability of these buoyancy-driven currents can be described satisfactorily by a combination of the dimensionless parameters Bu=N2/f2, Ek=2ν/fD02 and Ro=U0/fL0, where N and f are the buoyancy and Coriolis frequencies respectively, D0, L0 and U0 are the initial depth, width and velocity of the currents, respectively, and ν is the kinematic viscosity of the fluid. Furthermore, comparison with physical models of surface and intermediate flows along a vertical wall and over a flat bottom reveals that the stability regimes are not significantly altered by the presence of shelf topography. Variation of the depth of the surface flows with respect to the total fluid depth above the underlying shelf is shown to have a significant effect on the velocity and density structure of these flows. When the depth and width ratios are small, the surface flow is not affected by the varying topography. However, when the current occupies a considerable height above the shelf and is at least as wide as the shelf, upper layer fluid is transported offshore through the bottom Ekman layer, where it is arrested above the sloping bottom. At this location, a deepening of the upper layer develops due to potential vorticity conservation of the lower layer, accompanied by a local alongshore velocity maximum. This shelf break front prevents significant offshore transport of upper layer fluid far beyond the shelf break, even in cases where the flow is unstable. Comparison of the intermediate currents with dynamically-similar currents above a flat bottom does not reveal a stabilising effect of the slope. For unstable intermediate currents, offshore transport is not prohibited (as it is shown to be for surface currents over narrow shelves, due to the presence of the slope), and large scale instability patterns can extend over great distances from the slope. It is shown that the geostrophic nature of these currents is destroyed close to the sloping bottom. Here, the upper and lower density interfaces, denoting the vertical extents of the intermediate current, tilt sharply downwards.

The salt wedge position in a bar-blocked estuary subject to pulsed inflows

A series of laboratory experiments were carried out to investigate the response of a bar-blocked, saltwedge estuary to the imposition of both steady freshwater inflows and transient inflows that simulate storm events in the catchment area or the regular water releases from upstream reservoirs. The trapped salt water forms a wedge within the estuary, which migrates downstream under the influence of the freshwater inflow. The experiments show that the wedge migration occurs in two stages, namely (i) an initial phase characterized by intense shear-induced mixing at the nose of the wedge, followed by (ii) a relatively quiescent phase with significantly reduced mixing in which the wedge migrates more slowly downstream. Provided that the transition time t T between these two regimes satisfies t T >g′h 4 L/q 3 α, as was the case for all our experiments and is likely to be the case for most estuaries, then the transition occurs at time t T =1.2(gα 3 L 6 /g′ 3 q 2 ) 1/6 , where g′=gΔρ/ρ0 is the reduced gravity, g the acceleration due to gravity, Δρ the density excess of the saline water over the density ρ 0 of the freshwater, q the river inflow rate per unit width, and L and α are the length and bottom slope of the estuary, respectively. A simple model, based on conversion of the kinetic energy of the freshwater inflow into potential energy to mix the salt layer, was developed to predict the displacement xw over time t of the saltwedge nose from its initial position. For continuous inflows subject to t T , the model predicts the saltwedge displacement as x w /h=1.1 (t/τ) 1/3 , where the normalizing length and time scales are h=(q 2 /g) 1/3 and τ=g′α 2 h4L/q 3 , respectively. For continuous inflows subject to t>tT, the model predicts the displacement as xw/h=0.45N1/6(t/τ)1/6/α, where N=q 2 /g′h 2 L is a non-dimensional number for the problem. This model shows very good agreement with the experiments. For repeated, pulsed discharges subject to t T , the saltwedge displacement is given by (xw/h)3−(x0/h)(xw/h)2=1.3t/τ, where x 0 is the initial displacement following one discharge event but prior to the next event. For pulsed discharges subject to t>t T , the displacement is given by (xw/h) 6 −(x0/h)(xw/h) 5 =0.008N(t/τ)/α 6 . This model shows very good agreement with the experiments for the initial discharge event but does systematically underestimate the wedge position for the subsequent pulses. However, the positional error is less than 15%.

Laboratory modelling experiments on the flow generated by the tidal motion of a stratified ocean over a continental shelf

Abstract Laboratory model experiments have been conducted to investigate the interaction of a tidally forced stratified flow with a continental shelf. Results collected from a wide range of parametric experiments covering sub-, critical and super-critical tidal forcing are presented to show that the resulting flow regimes can be classified conveniently by the dimensionless parameters Fr=Usb/cw and μ=ω2/N02α, where Usb is the maximum velocity at the shelf break of slope angle α, cw is the long-wave speed of the lowest internal mode, ω is the frequency of the forcing and N0 is the buoyancy frequency of the initial undisturbed flow. Three distinct and characteristic flow regimes are observed, namely (i) shelf break eddies, (ii) intense downslope jets associated with offshore filamentary transport and (iii) pure up- and down-slope oscillatory jet flow, the occurrence of each of which is well-determined within Fr:μ parameter space. Measurements show a monotonic increase in eddy size (normalised by the amplitude A of the tidal forcing) with increasing Fr, while the thickness of the up- and downslope jet is shown to scale with A and to have no significant dependence on Fr. Measurements of the perturbation density field show significant intra-cycle variability in the local mixing and overturning parameters such as the buoyancy anomaly g′(zi), the available potential energy function ξ and the r.m.s. density ρr.m.s., with evidence of weak mixing and overturning (but significant internal wave activity) at slack tide conditions. Maximum values of both ξ and ρr.m.s. within a cycle show monotonic increases with increasing Fr and a strong dependence upon α and offshore location. Overall qualitative agreement with aspects of related numerical model results of Xing and Davies (J. Phys. Oceanogr. 27 (1997) 2100) and Holloway and Barnes (Cont. Shelf Res. 18 (1998) 31) is shown to be encouraging.

The Flow Generated in a Stratified Fluid by the Motion of a Flat Horizontal Disk

The response of a stratified fluid to the imposition of a surface stress has long been a topic of interest in geophysical fluid dynamics because of the relevance of the problem to mixing and overturning in large lakes, reservoirs and ocean basins. In the first definitive laboratory investigations (e.g Kato and Phillips, 1969; Kantha et al., 1977; Scranton and Lindberg, 1983) in this area, a linearly-stratified fluid contained in an annular tank was subjected to a constant surface stress imposed by the motion of a rotating screen and the process of entrainment was thereby initiated. As a result, a so-called mixed layer was generated, the thickness of which grew with time at a rate dependent upon the appropriate Richardson number of the established flow. In the annular geometry, the presence of secondary flows ensured that the development of the mixed layer was three-dimensional. Further experiments have been carried out by many authors since the above investigations and the reader is referred specifically to the recent article by Fernando (1991) for a comprehensive record and review of the resulting data