Fluid Mixing in Stratified Gravity Currents: The Prandtl Mixing Length

Abstract

Shear-induced vertical mixing in a stratified flow is a key ingredient of thermohaline circulation. We experimentally determine the vertical flux of momentum and density of a forced gravity current using high-resolution velocity and density measurements. A constant eddy-viscosity model provides a poor description of the physics of mixing, but a Prandtl mixing length model relating momentum and density fluxes to mean velocity and density gradients works well. For the average gradient Richardson number ${\mathrm{Ri}}_{g}\ensuremath{\approx}0.08$ and a Taylor Reynolds number ${\mathrm{Re}}_{\ensuremath{\lambda}}\ensuremath{\approx}100$, the mixing lengths are fairly constant, about the same magnitude, comparable to the turbulent shear length.