Experiments on entrainment in an annulus with and without velocity gradient across the density interface

Abstract

The entrainment process in a two layer density stratified fluid column was studied experimentally by imposing external shear stress on one or both layers. The experiments have been conducted in an annular tank containing two water layers of different salt concentration and the shear stress was applied by means of rotating screens. The following quantities were measured: the screen velocity (which was kept constant during each experiment), the stress at the upper screen, and vertical profiles of circumferential velocity and density at different radial locations.

When equal stress was imposed at the surface of the upper layer and at the bottom of the lower layer, entrainment took place from the two sides of the density interface at equal rate so that the interface was stationary in the central position between the two screens and there was no velocity gradient across the interface. The dependence of the entrainment coefficient on Richardson number obtained in these experiments was similar in form to that obtained in the shear-free experiments with an oscillating grid (e.g. Nokes 1988).

When a shear stress was applied at the upper surface only, the upper layer depth increased with time and a velocity gradient existed at the interface. The influence of the interfacial velocity gradient on the entrainment rate was studied by comparing the rates obtained with and without this velocity gradient. The entrainment rates were approximately the same for high values of the Richardson number while at low Richardson number the entrainment rate was much larger when a velocity gradient existed across the interface.

The main results of this work are as follows:

• (i) Despite the curved geometry of the annular system, the dependence of the entrainment coefficient on Richardson number for shear-free interface experiments was found to be similar in form to that obtained for oscillating grid experiments.

• (ii) The entrainment across the interface is due to turbulent energy generated at some distance from the interface by an external source (i.e. shear stress induced by a screen) and due to turbulence produced locally at the interface by a velocity gradient. The relative contribution of each turbulence source to the total entrainment was found to depend on the stability of the interface.