PV dynamics: The role of small‐scale turbulence, submesoscales and mesoscales

The diabatic and frictional components of the PV fluxes J in the Haynes-McIntyre conservation law have been studied with physical arguments, scaling laws and numerical simulations. We suggest a procedure that expresses J in terms of buoyancy and momentum fluxes by small-scale turbulence SS, submesoscales SM and mesoscales M. We employ the latest parameterizations of these processes and derive analytic expressions of the diabatic and frictional J fluxes for arbitrary wind stresses; we then consider the case of an Ekman flow. Small-scale turbulence: at z50, down and up-front winds contribute equally to the frictional component of J while the diabatic component is much larger than that of mesoscales. Submesoscales: the geostrophic contributions to both diabatic and frictional J have the same sign while the wind contributions have opposite signs. Their magnitude depends on the SM kinetic energy which is derived in terms of large-scale parameters. Comparison with numerical simulations is limited since the ones available resolve M but not SM. They concluded that the field patterns of the J fluxes are very similar to those obtained without resolving M, in agreement with the present analysis; a second conclusion that the diabatic component of J is an order of magnitude larger than the frictional one, is also in accordance with present results. When wind stresses are accounted for, down-front winds lower PV and up-front winds increase it. The changes in Hoskins' criterion for the onset of symmetric instabilities are discussed.