Statistics of the Richardson number: Mixing models and finestructure

Abstract

Parameterization of the dissipation rate of turbulent kinetic energy (ε) in terms of Richardson number (Ri = N2/S2) is examined for a variety in internal wave environments. Previous work with these data suggests a scaling of ε ∼ E2N̄2 g(ω) to within a factor of 2, where E represents a low-wavenumber shear spectral density, N̄ the background buoyancy frequency, and g(ω) a dependence upon average wave frequency content. The alternative Richardson-number-based parameterization of Kunze et al. is also shown to collapse the dissipation data to within a factor of 2. On the basis of a number of theoretical Richardson number probability distributions, however, the nominal (E, N̄) scaling of the Kunze et al. model is determined to be E2N̄3. The difference between the nominal (N̄3) and observed (N̄2) scaling is hypothesized to be an effect of turbulent momentum and buoyancy fluxes on the internal wave shear and strain profiles associated with the shear instability. For a statistically homogeneous subset of the data, S2 and N2 are determined to be statistically dependent. It is proposed that the statistical dependence represents both the direct effects of turbulent momentum and buoyancy fluxes decreasing S2 and N2 within a mixing event and the indirect effect of internal waves interacting with permanent buoyancy perturbations resulting from mixing.