Statistics of Richardson Number and Instability in Oceanic Internal Waves

The probability density function (pdf) of Richardson number in a Gaussian internal-wave field is derived. It is found to compare well with available data. The pdf depends on only parameter λ, the rms stain in the field, which is very weakly dependent on depth if at all. The probability Ri<0.25 is a very sensitive function of λ, which is about λ≈0.5 in the ocean. Numerical simulations of vertical profiles Ri(z) are calculated based on a set of stochastic differential equations. The statistics of the vertical distributions of regions where Ri<0.25 is investigated and a simplified mixing model based on the stochastic differential equations is derived. We conclude that shear instability is a significant factor in the dissipation of internal waves.