Some statistical and dynamical properties of turbulence in the oceanic pycnocline

Abstract

Statistics of turbulence length scales in individual mixing patches are used to describe the nature of mixing in the oceanic pycnocline near steep bottom topography. The majority of the observed mixing events can be explained with the conventional ideas of shear‐driven turbulence. The statistics of some large patches, however, deviate substantially from expected values, suggesting that there is at least one other significant source of turbulent kinetic energy besides small‐scale shear production. On the basis of inertial subrange energy arguments, it is proposed that the overturning seen in these events is a release of potential energy to kinetic energy which is consistent with advective instability in a finite‐amplitude internal wave field. We find that within large turbulent patches the turbulent kinetic energy dissipation rate εr averaged over a region of height r has a lognormal distribution consistent with Kolmogorov's third hypothesis, σ2ln(εr) = A + μ, ln (LP/r), where σ2ln(εr) is the variance of ln (εr); r satisfies LP ≫ r ≫ η; LP is the size of the mixing patch; η is the Kolmogorov scale; A depends on the large‐scale flow field; and μ is the intermittency coefficient, which is found to be approximately 0.4 in large patches. The variance of ln (εr) also depends on the Reynolds number and the characteristic length scales of the mixing patches.