Scaling Laws and Regime Transitions of Macroturbulence in Dry Atmospheres

In simulations of a wide range of circulations with an idealized general circulation model, clear scaling laws of dry atmospheric macroturbulence emerge that are consistent with nonlinear eddy–eddy interactions being weak. The simulations span several decades of eddy energies and include Earth-like circulations and circulations with multiple jets and belts of surface westerlies in each hemisphere. In the simulations, the eddy available potential energy and the barotropic and baroclinic eddy kinetic energy scale linearly with each other, with the ratio of the baroclinic eddy kinetic energy to the barotropic eddy kinetic energy and eddy available potential energy decreasing with increasing planetary radius and rotation rate. Mean values of the meridional eddy flux of surface potential temperature and of the vertically integrated convergence of the meridional eddy flux of zonal momentum generally scale with functions of the eddy energies and the energy-containing eddy length scale, with a few exceptions in simulations with statically near-neutral or neutral extratropical thermal stratifications. Eddy energies scale with the mean available potential energy and with a function of the supercriticality, a measure of the near-surface slope of isentropes. Strongly baroclinic circulations form an extended regime in which eddy energies scale linearly with the mean available potential energy. Mean values of the eddy flux of surface potential temperature and of the vertically integrated eddy momentum flux convergence scale similarly with the mean available potential energy and other mean fields. The scaling laws for the dependence of eddy fields on mean fields exhibit a regime transition between a regime in which the extratropical thermal stratification and tropopause height are controlled by radiation and convection and a regime in which baroclinic entropy fluxes modify the extratropical thermal stratification and tropopause height. At the regime transition, for example, the dependence of the eddy flux of surface potential temperature and the dependence of the vertically integrated eddy momentum flux convergence on mean fields changes—a result with implications for climate stability and for the general circulation of an atmosphere, including its tropical Hadley circulation.