Transitional phenomena and the development of turbulence in stratified fluids: A review

Abstract

The processes which lead to vertical mixing in stratified fluids operate in a multiparameter space, much of which has not been explored theoretically or in laboratory experiments. This review focuses on the transitional phenomena which precede, and may eventually lead to, the broadband spectra associated with turbulent flow. Conditions of static instability are known to be produced in wave-wave, wave-current, and wave-boundary interactions, but little is known of the subsequent stages of transition. Whilst there has been considerable progress in describing transition in Rayleigh-B•nard and Taylor-Couette flows, that in Kelvin-Helmholtz instability is relatively unexplored, and in consequence, our knowledge of energy exchange and of density and momentum fluxes is extremely sparse. Attention is drawn here to the flow disturbance caused by sidewalls in laboratory experiments, and some recently discovered examples of transitional phenomena in Kelvin-Helmholtz instability are described. More information is available about fluxes in double-diffusive convection, but here too the transitional processes are as yet poorly known.Applying this information to the natural environment (and emphasis is given to the oceans) poses the fundamental difficulty of estimating the probability of conditions favoring the development of any particular kind of instability.Knowledge of transition in conditions in which the background field varies in space and time is deficient.

The baroclinic secondary instability of the two-dimensional shear layer

“…This secondary instability, emerging at the stagnation points of the vortical braids between the main Kelvin-Helmholtz structures was also suggested by Corcos and Sherman 7 and earlier hinted by Thorpe. 8 The study of such secondary instabilities is crucial as, according to Thorpe,9 it could be one of the mechanisms that triggers turbulence in geophysical shear layers. The braids, subjected to baroclinic vorticity production, are continuously stretched, experiencing a strain rate roughly proportional to the circulation around the cores, see Corcos and Sherman.…”

Time‐dependent mixing in stratified Kelvin‐Helmholtz billows: Experimental observations

“…It is well-known [Drazin and Reid, 1981] that under certain circumstances, such flows are susceptible to a beautiful instability, where the initial strip of vorticity in the shear layer rolls up into a quasi-periodic array of elliptical vortices, commonly referred to as Kelvin-Helmholtz (KH) billows. The properties of stratified KH billows have been widely studied in the laboratory [Thorpe, 1987;Fernando, 1991] and numerically [Peltier and Caulfield, 2003]. Of particular interest are the characteristics of the irreversible mixing associated with billows, since for flows with sufficiently high Reynolds numbers Re = Ud/n (where the fluid's kinematic viscosity is n, and U and d are the characteristic velocity and length scales of the shear layer respectively) KH billows trigger turbulence.…”

“…[5] Therefore, we have conducted a sequence of experiments using the technique developed by Thorpe (see Thorpe [1987] for a detailed review), whereby a stable stratification of miscible fluids is created in a tank that can be tilted to an arbitrary (though typically small) angle q. The stratification consists of fresh water of density r 0 and brine of density r 1 , r 1 > r 0 .…”

Temperature sheets and aspect sensitive radar echoes

“…Thorpe, 1987;Smyth and Moum, 2000). However, the strong gradient is necessarily associated with a strong mixing region which occurs nearby at the same altitude.…”