Turbulent Diffusion in a Stratified Fluid

Abstract

Abstract This paper examines the dynamical effects on a particle drifting in a homogeneous field of turbulence, stationary and uniform except for a constant vertical density gradient. The ordinary “mechanical” impulses due to random normal pressures and shear stresses are assumed to have the same statistical properties as in the absence of density stratification. The buoyancy forces arising from the displacement of the particle are, on the other hand, seen to be more nearly “organized” forces and their presence in the equations of motion modifies Lagrangian velocity autocorrelations significantly. The results show that under unstable stratification the velocity history of a diffusing particle is not stationary to second order, the variance increasing exponentially with time. When the stratification is stable, on the other hand, the standard deviation of vertical displacement tends asymptotically to a constant value. These results are in qualitative agreement with observations of the Prairie Grass project ...