Microstructure Fluxes across Density Surfaces

Abstract

When averaging the equations of motion, thermodynamics, and scalar conservation over turbulent fluctuations, we perform the process in several stages. First, an average is taken over the microscopic scales of turbulence, including the centimeter-scale band in which the dissipation of kinetic energy and temperature or density variance occurs. The eddy-correlation fluxes that arise in this stage are called microstructure fluxes. Next, the equations are transformed into coordinates relative to the microscopically averaged isopycnals. Finally, an average is taken, relative to these isopycnals, over macroscopic scales of eddy variability, which may include the mesoscale band of planetary motions. Average transport terms, analogous to conventional Reynolds transports in fixed-depth averages, arise also from the macroscopic eddies. This is not so for density, for which no counterparts of macroscopic Reynolds transports exist on constant density surfaces. Only microstructure flux divergence, which is synonymous with diapycnal velocity, contributes to the density balance. Under the assumption that microstructure density variance production is in equilibrium with its molecular dissipation, the microstructure density flux has the form of the molecular flux of heat down the vertical mean gradient, amplified by the Cox number. Munk's abyssal recipe for the vertical velocity/diffusivity ratio can now be reinterpreted as the diapycnal velocity/diffusivity ratio.