Turbulent diffusion in a stratified fluid

Abstract

The behaviour of cylinders of fluid injected vertically downwards into a similar stationary fluid has been observed with particular reference to the effect of a stable density stratification in the stationary fluid upon the penetration and upon the mixing between the injected and ambient fluids.When the ambient fluid is of uniform density, it is found that the motion is approximately self-preserving, and that the energy decay rate per unit mass of moving fluid follows the same law as does the decay rate in a turbulent fluid.The observations demonstrate that the effect of the density stratification in the ambient fluid is principally upon the gross motion and only slightly upon the smaller scales of motion.Estimates are given of the maximum conversion of kinetic energy to potential energy, and of the ultimate loss of energy to buoyancy, as a function of a Richardson number determined from the initial conditions of volume, velocity, density gradient, density, and the acceleration of gravity.