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Abstract The flux Richardson numberR_f, also called the mixing efficiency of stratified turbulence, is important in determining geophysical flow phenomena such as ocean circulation and air‐sea transports. MeasuringR_fin the field is usually difficult, thus parameterization ofR_fbased on readily observed properties is essential. Here, estimates ofR_fin a strongly turbulent, sediment‐stratified estuarine flow are obtained from measurements of covariance‐derived turbulent buoyancy fluxes (B) and spectrally fitted values of the dissipation rate of turbulent kinetic energy (ε). We test scalings forR_fin terms of the buoyancy Reynolds number (Re_b), the gradient Richardson number (Ri), and turbulent Froude number (Fr_t). Neither theRe_b‐based nor theRi‐based scheme is able to describe the observed variations inR_f, but theFr_t‐based parameterization works well. These findings support further use of theFr_t‐ based parameterization in turbulent oceanic and estuarine environments. 

Studies of Kelvin–Helmholtz (KH) instability have typically modelled the initial flow as an isolated shear layer. In geophysical cases, however, the instability often occurs near boundaries and may therefore be influenced by boundary proximity effects. Ensembles of direct numerical simulations are conducted to understand the effect of boundary proximity on the evolution of the instability and the resulting turbulence. Ensemble averages are used to reduce sensitivity to small variations in initial conditions. Both the transition to turbulence and the resulting turbulent mixing are modified when the shear layer is near a boundary: the time scales for the onset of instability and turbulence are longer, and the height of the KH billow is reduced. Subharmonic instability is suppressed by the boundary because phase lock is prevented due to the diverging phase speeds of the KH and subharmonic modes. In addition, the disruptive influence of three-dimensional secondary instabilities on pairing is more profound as the two events coincide more closely. When the shear layer is far from the boundary, the shear-aligned convective instability is dominant; however, secondary central-core instability takes over when the shear layer is close to the boundary, providing an alternate route for the transition to turbulence. Both the efficiency of the resulting mixing and the turbulent diffusivity are dramatically reduced by boundary proximity effects. 

Abstract We test the hypothesis that internal waves observed in flow over forest canopies are generated by Kelvin–Helmholtz instability. The waves were observed at night, under stably stratified and weak wind conditions, with a horizontally scanning aerosol lidar and an instrumented tower. The lidar images are used to determine the salient wavelength and phase propagation velocity of each episode. Time series data measured at the tower are then used to form vertical profiles of background velocity and buoyancy just before each observed wave event. The profiles are input to the Taylor–Goldstein equation to predict the phase velocity, wavelength and period of the fastest-growing linear instability, and the results compared with the lidar observations. The observed wavelengths tend to be longer than predicted by the Taylor–Goldstein theory, typically by a factor of two. That discrepancy is removed when the theory is extended to account for the effects of ambient, small-scale turbulence. 

In a stably stratified shear layer, multiple competing instabilities produce sensitivity to small changes in initial conditions, popularly called the butterfly effect (as a flapping wing may alter the weather). Three ensembles of 15 simulated mixing events, identical but for small perturbations to the initial state, are used to explore differences in the route to turbulence, the maximum turbulence level and the total amount and efficiency of mixing accomplished by each event. Comparisons show that a small change in the initial state alters the strength and timing of the primary Kelvin–Helmholtz instability, the subharmonic pairing instability and the various three-dimensional secondary instabilities that lead to turbulence. The effect is greatest in, but not limited to, the parameter regime where pairing and the three-dimensional secondary instabilities are in strong competition. Pairing may be accelerated or prevented; maximum turbulence kinetic energy may vary by up to a factor of 4.6, flux Richardson number by 12 %–15 % and net mixing by a factor of 2. 

Abstract This study presents field observations of fluid mud and the flow instabilities that result from the interaction between mud-induced density stratification and current shear. Data collected by shipborne and bottom-mounted instruments in a hyperturbid estuarine tidal channel reveal the details of turbulent sheared layers in the fluid mud that persist throughout the tidal cycle. Shear instabilities form during periods of intense shear and strong mud-induced stratification, particularly with gradient Richardson number smaller than or fluctuating around the critical value of 0.25. Turbulent mixing plays a significant role in the vertical entrainment of fine sediment over the tidal cycle. The vertical extent of the billows identified seen in the acoustic images is the basis for two useful parameterizations. First, the aspect ratio (billow height/wavelength) is indicative of the initial Richardson number that characterizes the shear flow from which the billows grew. Second, we describe a scaling for the turbulent dissipation rate ε that holds for both observed and simulated Kelvin–Helmholtz billows. Estimates for the present observations imply, however, that billows growing on a lutocline obey an altered scaling whose origin remains to be explained. 

The mixing efficiency of stratified turbulence in geophysical fluids has been the subject of considerable controversy. A simple parameterization, devised decades ago when empirical knowledge was scarce, has held up remarkably well. The parameterization rests on the assumption that the flux coefficient Γ has the uniform value 0.2. This note provides a physical explanation for Γ = 0.2 in terms of the “marginal instability” property of forced stratified shear flows, and also sketches a path toward improving on that simple picture by examining cases where it fails.