Abstract
In this paper a set of new Reynolds averaged equations which contain both the dissipation and dispersion effects are derived by using Prandtl's mixing length theory. The dispersion effects. (b) The dispersion effects alone could result in the inverse energy cascade dispersion effects. (b) The dispersion effects alone could result in the inverse energy cascade which represents the eddies giving up kinetic energy to the mean flow in large-scale motion. The dispersion effects are also necessary for the eddies to gain kinetic energy from available potential energy. The necessary and sufficient conditions of an inverse energy cascade are given. (c) The dispersion effects are used to analyse atmospheric balance motions of the planetary boundary layer and produce a more satisfactory Ekman spiral fit to the observed wind hodograph.
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