Some properties of horizontally homogeneous, statistically steady turbulence in a stratified fluid

Abstract

The paper contains a description of research closely connected to an experimental investigation of turbulent, stratified, shearing flow.

The experiment is one of the simplest in which three basic properties of a turbulent flow — stratification, energy dissipation and shear — are present, and we hope that a good understanding of this experiment will lead to useful information about turbulent processes in the atmosphere and oceans and other density-stratified fluid systems.

The experiment is characterized by the overall Richardson number Ri* based on the density and velocity variations across the depthH of the channel. The typical density profile contains layers of ‘homogeneous’ fluid separated by thin layers across which the density and velocity change abruptly. For Ri*>2.5, approximately, there are two ‘homogeneous’ layers at top and bottom separated by a stable layer. In some undetermined range below 2.5 and greater than 1, three `homogeneous' layers and two ‘stable’ layers appear.

When Ri*>2.5 and there is one ‘stable’ layer in the middle, the thickness of the density variation δ is less than that of the linear velocity variation,L, but δ does not vary with Ri*, and L varies as Ri*^−1/2. The result is that thegradient Richardson number in the ‘stable’ layer is always of order one for values of Ri* up to 60 or so. An investigation of the relative importance of buoyancy and inertia indicates that they are of the same order in both the ‘stable’ and the ‘homogeneous’ layers.

Buoyancy flux has been measured and a non-dimensional form was found to be proportional to Ri*⁻¹. Momentum flux has not yet been measured, but reasonable assumptions suggest that it is proportional to Ri*^−1/2.

Finally, an attempt was made to compare a theory of turbulence in stratified shearing flow to some observations of the experiment. Several comparisons indicated agreement with observations and independent reasoning.