MICROSTRUCTURE FLUXES ACROSS DENSITY SURFACES

When averaging the equations of motion, thermodynamics, and scalar con servation over turbulent fluctuations, we perform the process in sever al stages. First, an average is taken over the microscopic scales of t urbulence, including the centimeter-scale band in which the dissipatio n of kinetic energy and temperature or density variance occurs. The ed dy-correlation fluxes that arise in this stage are called microstructu re fluxes. Next, the equations are transformed into coordinates relati ve to the microscopically averaged isopycnals. Finally, an average is taken, relative to these isopycnals, over macroscopic scales of eddy v ariability, which may include the mesoscale band of planetary motions. Average transport terms, analogous to conventional Reynolds transport s in fixed-depth averages, arise also from the macroscopic eddies. Thi s is not so for density, for which no counterparts of macroscopic Reyn olds transports exist on constant density surfaces. Only microstructur e flux divergence, which is synonymous with diapycnal velocity, contri butes to the density balance. Under the assumption that microstructure density variance production is in equilibrium with its molecular diss ipation, the microstructure density flux has the form of the molecular flux of heat down the vertical mean gradient, amplified by the Cox nu mber. Munk's abyssal recipe for the vertical velocity/diffusivity rati o can now be reinterpreted as the diapycnal velocity/diffusivity ratio .