The horizontal energy spectra and cascade processes in rotating stratified turbulence

Yuji Kitmura* and Yoshihisa Matsuda** * Division of Earth and Planetary Sciences, Graduate School of Science, Kyoto University, Kyoto, Japan. ** Department of Astronomy and Earth Science, Tokyo Gakugei University, Tokyo, Japan.

The atmospheric energy spectrum over the range from a few kilometers to synoptic scale has been determined from wind and temperature measurements by commercial airplanes in the upper troposphere. The spectrum as a function of horizontal wavenumber k_H, has been found to follow a -3 power law in the horizontal wavelength range from about 1000 to 3000 km, and a -5/3 power law for wavelength shorter than 400--500 km Nastrom et al., 1984; Nastrom and Gage, 1985).

In this study, numerical experiments of rotating stratified turbulence are conducted with a high-resolution nonhydrostatic Boussinesq model over the range from a few kilometer to the synoptic scale to investigate the horizontal energy spectrum observed in the atmosphere. The slope of the energy spectrum excited by the synoptic scale of forcing with planetary rotation is close to -3 in the synoptic scales and -5/3 in the mesoscales, as observed in the troposphere. While the vortical modes are predominant in the -3 spectral range, magnitude of the divergent modes is greater than that of the vortical ones in the -5/3 range even if the external forcing includes only the geostrophic modes. The wavelength at which the spectral transition takes place is characterized by the scale in which the rotational and divergent energy are comparable and depends on the planetary rotation rate. The downscale energy cascade associated with the divergent modes plays an important role in the formation of the mesoscale k_H^{-5/3} spectrum.