Comparative terrestrial atmospheric circulation regimes in simplified global circulation models: II. energy budgets and spectral transfers

The energetics of possible global atmospheric circulation patterns in an Earth-like atmosphere are explored using a simplified GCM based on the University of Hamburg’s Portable University Model for the Atmosphere (designated here as PUMA-S), forced by linear relaxation towards a prescribed temperature field and subject to Rayleigh surface drag and hyperdiffusive dissipation. Results from a series of simulations, obtained by varying planetary rotation rate Ω with an imposed equator-to-pole temperature difference, were analysed to determine the structure and magnitude of the heat transport and other contributions to the energy budget for the time-averaged, equilibrated flow. These show clear trends with rotation rate, with the most intense Lorenz energy cycle for an Earth-sized planet occurring with a rotation rate around half that of the present day Earth (i.e. Ω* = Ω/ΩE = 1/2, where ΩE is the rotation rate of the Earth). KE and APE spectra, EK(n) and EA(n) (where n is total spherical wavenumber), also show clear trends with rotation rate, with n^-3 enstrophy-dominated spectra around Ω* = 1 and steeper (~ n^-5) slopes in the zonal mean flow with little evidence for the n^-5/3 spectrum anticipated for an inverse KE cascade. Instead, both KE and APE spectra become almost flat at scales larger than the internal Rossby radius, Ld, and exhibit near-equipartition at high wavenumbers. At Ω* << 1, the spectrum becomes dominated by KE with EK(n) ~ (2 - 3)EA(n) at most wavenumbers and a slope that tends towards n^-5/3 across most of the spectrum. Spectral flux calculations show that enstrophy and APE are almost always cascaded downscale, regardless of rotation rate. KE cascades are more complicated, however, with downscale transfers across almost all wavenumbers, dominated by horizontally divergent modes, for Ω* ≲ 1/4. At higher rotation rates, transfers of KE become increasingly dominated by rotational (horizontally non-divergent) components with strong upscale transfers (dominated by eddy-zonal flow interactions) for scales larger than Ld and weaker downscale transfers for scales smaller than Ld