Measurements and analysis of the turbulent Schmidt number in density stratified turbulence

Abstract

Results are reported of measurements of the turbulent Schmidt number Sc t in a stably stratified water tunnel experiment. Sc t values varied with two parameters: Richardson number, Ri, and ratio of time scales, T*, of eddy turnover and eddy advection from the source of turbulence generation. For large values (T* ∼ 10) values of Sc t approach those of neutral stratification (Sc t ≈ 1). In contrast for small values (T* ∼ 1) values of Sc t increase with Ri. The variation of Sc t with T* explains the large scatter of Sc t values observed in atmospheric and oceanic data sets as a range of values of T* occur at any given Ri. The dependence of Sc t values on advective processes upstream of the measurement location complicates the development of an algebraic formulation of Sc t = f (Ri, T*) from single point dynamical balances for use in turbulence closure models. Observations of values of T* ∼ O(1) for strong stratification argues against the existence of a critical Richardson number at which turbulence collapses to laminar flow.