Scaling laws and phase transitions of atmospheric macroturbulence

Theory and simulations show that the supercriticality, a measure of the slope of isentropes and of the nonlinearity of eddy-eddy interactions in atmospheric macroturbulence, cannot increase beyond a critical value at which eddy-eddy interactions are weakly nonlinear. This was found to be true over eight decades of eddy energies in simulations with an idealized GCM (see poster submission). An implication of this result is that scaling laws for baroclinic eddy fluxes, for example, of heat and momentum, can be derived as functions of mean fields and of the supercriticality.

Eddy fluxes exhibit phase transitions with changes in scaling laws depending on whether the flow is subcritical or at saturated supercriticality. The phases are distinguished according to whether the thermal stratification of the atmosphere is maintained primarily by radiation and convection or whether it is modified by baroclinic eddies. In both phases, weakly nonlinear theories give scaling laws for baroclinic eddy fluxes that are consistent with simulations. Eddy fluxes of surface potential temperature, for example, depend more strongly on surface potential temperature gradients for subcritical flows, i.e., when the baroclinicity is low. This implies that in a low-baroclinicity climate, there is a stronger stabilizing feedback on temperature gradients than in a climate of higher baroclinicity, in which the dependence of surface potential temperature fluxes on gradients is weaker.

Implications of the results for climate sensitivity and potential generalizations of the arguments to moist atmospheres will be discussed.