AN EXPERIMENTAL INVESTIGATION OF THE INSTABILITY OF A SHEAR-FLOW WITH MULTILAYERED DENSITY STRATIFICATION

The evolution of stratified shear flows with multilayer density distributions is discussed briefly from a theoretical perspective, generalizing the results of Caulfield [J. Fluid Mech. 258, 255 (1994)] to allow for asymmetry. Three distinct types of instability are predicted to occur according to linear theory. In the laboratory, we measure the density profile and the velocity profile continuously, and so are able to identify the flow characteristics that are applicable when each of the different instabilities grow. Knowledge of the bulk Richardson number is insufficient to predict the observed properties of the instabilities of the flow. The parameter that is most determinant of the selection of a particular type of instability is found to be the ratio R of the depth of the intermediate density layer to the depth over which the velocity varies, though any asymmetry in the flow (either in the velocity or density fields) also plays a role. If R is close to 1, and hence the layer of intermediate density occupies a significant portion of the shear layer, overturnings appear in the intermediate layer, which are long lived, and strongly two dimensional. These overturnings are the three layer stratified generalization of the Kelvin-Helmholtz instability first discussed by Taylor [Proc. R. Soc. London Ser. A 132, 499 (1931)]. Such modes inefficiently mix the background flow, and the major mixing mechanisms are found to consist of overturnings in the lower fluid layer (and, to a lesser extent, the upper layer). These overturnings are clearly manifestations of an (asymmetric) three layer generalization of the Holmboe [Geophys. Publ. 24, 67 (1962)] instability. In general, all three instabilities can be observed simultaneously at markedly different wavelengths and phase speeds for extended periods of time, even though linear theory may predict significantly different growth rates. (C) 1995 American Institute of Physics.