Laboratory experiments on stably stratified grid turbulence have suggested that turbulent diffusivity $\kappa_\rho$ can be expressed in terms of a turbulence activity parameter $\epsilon/\nu N^2$, with different power-law relations appropriate for different levels of $\epsilon/\nu N^2$. To further examine the applicability of these findings to both a wider range of the turbulence intensity parameter $\epsilon/\nu N^2$ and different forcing mechanisms, DNS data of homogeneous sheared stratified turbulence generated by Shih et al. (2000) and Venayagamoorthy et al. (2003) are analysed in this study. Both scalar eddy diffusivity $\kappa_\rho$ and eddy viscosity $\kappa_\nu$ are found to be well-correlated with $\epsilon/\nu N^2$, and three distinct regimes of behaviour depending on the value of $\epsilon/\nu N^2$ are apparent. In the diffusive regime $D$, corresponding to low values of $\epsilon/\nu N^2$ and decaying turbulence, the total diffusivity reverts to the molecular value; in the intermediate regime $I$, corresponding to $7 \,{<} \epsilon/\nu N^2 \,{<}\, 100$ and stationary turbulence, diffusivity exhibits a linear relationship with $\epsilon/\nu N^2$, as predicted by Osborn (1980); finally, in the energetic regime $E$, corresponding to higher values of $\epsilon/\nu N^2$ and growing turbulence, the diffusivity scales with $(\epsilon/\nu N^2)^{1/2}$. The dependence of the flux Richardson number $R_f$ on $\thing$ explains the shift in power law between regimes $I$ and $E$. Estimates for the overturning length scale and velocity scales are found for the various $\epsilon/\nu N^2$ regimes. It is noted that $\epsilon/\nu N^2 \,{\sim}\, \hbox{\it Re}/\hbox{\it Ri}\,{\sim}\,\hbox{\it ReFr}^2$, suggesting that such Reynolds–Richardson number or Reynolds–Froude number aggregates are more descriptive of stratified turbulent flow conditions than the conventional reliance on Richardson number alone.

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Abstract.The shoaling and breaking of an internal solitary wave of depression on a uniform slope were studied experimentally. The waves were generated with as large an amplitude as possible while minimizing mixing at the generation site, thus maximizing the amount of energy propagating onto the slope in the experiment. Various bottom slopes, fluid layer thickness ratios, and density ratios were investigated. The mechanism leading to breaking was examined with flow visualization and particle image velocimetry. Since the layer thickness ratio primarily controls the length (Lw) of the solitary wave (for a given amplitude a), it is found that the ratio of Lw and the characteristic length of the slope Ls determines the amount of energy reflected from the slope. The •nixing efficiency of the breaking event, defined as the ratio of the increase of potential energy divided by the amount of wave energy lost at the slope, peaks at a maximum of 25% when Lw/Ls = 0.5, with a decrease in efficiency for points on either side of this peak value.

We examine observations of turbulence in the geophysical environment, primarily from oceans but also from lakes, in light of theory and experimental studies undertaken in the laboratory and with numerical simulation. Our focus is on turbulence in density-stratified environments and on the irreversible fluxes of tracers that actively contribute to the density field. Our understanding to date has come from focusing on physical problems characterized by high Reynolds number flows with no spatial or temporal variability, and we examine the applicability of these results to the natural or geophysical-scale problems. We conclude that our sampling and interpretation of the results remain a first-order issue, and despite decades of ship-based observations we do not begin to approach a reliable sampling of the overall turbulent structure of the ocean interior.

Mechanisms for the degeneration of large-scale interfacial gravity waves are identified for lakes in which the effects of the Earth's rotation can be neglected. By assuming a simple two-layer model and comparing the timescales over which each of these degeneration mechanisms act, regimes are defined in which particular processes are expected to dominate. The boundaries of these regimes are expressed in terms of two lengthscale ratios: the ratio of the amplitude of the initial wave to the depth of the thermocline, and the ratio of the depth of the thermocline to the overall depth of the lake. Comparison of the predictions of this timescale analysis with the results from both laboratory experiments and field observations confirms its applicability. The results suggest that, for small to medium sized lakes subject to a relatively uniform windstress, an important mechanism for the degeneration of large-scale internal waves is the generation of solitons by nonlinear steepening. Since solitons are likely to break at the sloping boundaries, leading to localized turbulent mixing and enhanced dissipation, the transfer of energy from an initial basin-scale seiche to shorter solitons has important implications for the lake ecology.

In a laboratory study, we quantified the temporal energy flux associated with the degeneration of basin-scale internal waves in closed basins. The system is two-layer stratified and subjected to a single forcing event creating available potential energy at time zero. A downscale energy transfer was observed from the wind-forced basin-scale motions to the turbulent motions, where energy was lost due to high-frequency internal wave breaking along sloping topography. Under moderate forcing conditions, steepening of nonlinear basin-scale wave components was found to produce a high-frequency solitary wave packet that contained as much as 20% of the available potential energy introduced by the initial condition. The characteristic lengthscale of a particular solitary wave was less than the characteristic slope length, leading to wave breaking along the sloping boundary. The ratio of the steepening timescale required for the evolution of the solitary waves to the travel time until the waves shoaled controlled their development and degeneration within the domain. The energy loss along the slope, the mixing efficiency, and the breaker type were modeled using appropriate forms of an internal Iribarren number, defined as the ratio of the boundary slope to the wave slope (amplitude/wavelength). This parameter allows generalization to the oceanographic context. Analysis of field data shows the portion of the internal wave spectrum for lakes, between motions at the basin and buoyancy scales, to be composed of progressive waves: both weakly nonlinear waves (sinusoidal profile with frequencies near 10 Ϫ4 Hz) and strongly nonlinear waves (hyperbolic-secant-squared profile with frequencies near 10 Ϫ3 Hz). The results suggest that a periodically forced system may sustain a quasi-steady flux of 20% of the potential energy introduced by the surface wind stress to the benthic boundary layer at the depth of the pycnocline.

A basic framework characterising the interaction between aquatic flows and permeable sediment beds is presented here. Through the permeability Reynolds number (Re K = √ Ku * /ν, where K is the sediment permeability, u * is the shear velocity and ν is the fluid viscosity), the framework unifies two classical flow typologies, namely impermeable boundary layer flows (Re K 1) and highly permeable canopy flows (Re K 1). Within this range, the sediment-water interface (SWI) is identified as a transitional region, with Re K in aquatic systems typically O(0.001-10). As the sediments obstruct conventional measurement techniques, experimental observations of interfacial hydrodynamics remain extremely rare. The use of refractive index matching here allows measurement of the mean and turbulent flow across the SWI and thus direct validation of the proposed framework. This study demonstrates a strong relationship between the structure of the mean and turbulent flow at the SWI and Re K . Hydrodynamic characteristics, such as the interfacial turbulent shear stress, velocity, turbulence intensities and turbulence anisotropy tend towards those observed in flows over impermeable boundaries as Re K → 0 and towards those seen in flows over highly permeable boundaries as Re K → ∞. A value of Re K ≈ 1-2 is seen to be an important threshold, above which the turbulent stress starts to dominate the fluid shear stress at the SWI, the penetration depths of turbulence and the mean flow into the sediment bed are comparable and similarity relationships developed for highly permeable boundaries hold. These results are used to provide a new perspective on the development of interfacial transport models at the SWI.

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