An experimental investigation of turbulent stratified shearing flow

Abstract

Some experiments are described in which steady-state shearing flows are developed in stratified brine solutions contained in a cyclically continuous tank of rectangular cross-section. Over the range of overall Richardson numbers studied, the results suggest that whenever turbulent layers are present on either side of a region of fluid with a gravitationally stable density gradient, they cause erosion of this region to occur. The erosion leads to the formation of two homogeneous layers separated by a thin layer of strong density and velocity gradients. The gradient Richardson number, computed by using the velocity and density gradients in this transition layer, tends to have a value of order one.If we define an overall Richardson number Ri* by averaging the velocity and density gradients over the entire depth of fluid in the tank, we find that the non- dimensional buoyancy flux, Q, is functionally related to Ri* by an equation of the form Q = C1(Ri*)−1 where C1 is a constant, approximately, and Ri* ranges in value between one and thirty.To check the effect of a large variation of the molecular diffusivity coefficient on flow conditions, we ran a limited number of experiments with thermally stratified fluid. Over a restricted range, 1·0 < Ri* < 5·0, velocity profiles very similar to those measured in the brine-stratified experiments at like values of Ri* were obtained. This suggests that the coefficient of molecular diffusion is not an important parameter in either type of experiment.Other experiments, made in the same apparatus, describe the entrainment by a turbulent, homogeneous layer of an initially quiescent layer of fluid with a linear density gradient. The depth of the turbulent layer, D, increases with time, t, according to the relation. \[ D^3\propto t. \] This result is consistent with that found by Kato & Phillips (1969), although the turbulent layer in the present experiment is generated in a different manner.