TURBULENCE IN STRATIFIED SHEAR FLOWS - IMPLICATIONS FOR INTERPRETING SHEAR-INDUCED MIXING IN THE OCEAN

Direct numerical simulations of the time evolution of homogeneous stab ly stratified turbulent shear flows have been performed for several Ri chardson numbers Ri and Reynolds numbers R(lambda). The results show e xcellent agreement with length scale models developed from laboratory experiments to characterize oceanic turbulence. When the Richardson nu mber Ri is less than the stationary value Ri(s), the turbulence intens ity grows at all scales: the growth rate is a function of Ri. The size of the vertical density inversions also increases. When Ri greater-th an-or-equal-to Ri(s) the largest turbulent eddies become vertically co nstrained by buoyancy when the Ellison (turbulence) scale L(E) and the Ozmidov (buoyancy) scale L(O) are equal. At this point, the mixing is most efficient and the flux Richardson number or mixing efficiency is R(f) almost-equal-to 0.20 for the stationary Richardson number Ri(s) = 0.21. The vertical mass flux becomes countergradient when epsilon al most-equal-to 19nuN2, and vertical density overturns are suppressed in less than half of a Brunt-Vaisala period. The results of the simulati ons have also been recast in terms of the hydrodynamic phase diagram i ntroduced for fossil turbulence models. In this framework, buoyancy co ntrol of the energy-containing scales begins when epsilon almost-equal -to 4DCN2. This value is in good agreement with indirect laboratory ob servations and field observations. Careful examination of the individu al components of the velocity and scalar dissipation tensors reveals t hat, for fully developed, stably stratified shear flows, these tensors are far from isotropic. implying that the isotropic formulas often us ed to calculate the dissipation rates epsilon and chi in the oceanic t hermocline could underestimate these rates by factors of 2 to 4. Final ly, the validity of the steady-state models used to estimate vertical eddy diffusivities in the thermocline is discussed.