Mean and Transient Spectral Energy and Enstrophy Budgets

Abstract

The scale-dependent behavior of atmospheric flow on the sphere is investigated in terms of the spectra and spectral budgets of enstrophy and kinetic and available potential energy. The decomposition into both the α = (n, m) and the more usual n-spectral forms is considered. Several novel spectral results are obtained. First, a direct test of the extent to which large-scale atmospheric flow satisfies the necessary and sufficient conditions for homogeneous and isotropic two-dimensional turbulent behavior is carried out by calculating ?spectral teleconnections? from data. The conditions are satisfied for the higher wavenumber transient component of the flow. Second, the spectral budget equations are extended to include the decomposition into time mean and transient components, a method that, although common and straightforward in real-space calculations, is novel in the spectral domain. The terms in these budgets are evaluated from data. Finally, the flow of energy and enstrophy through α-spectral space is displayed in terms of a novel ?spectral potential function,? which is related to spectral fluxes. The results give information about the scales and wavenumbers at which sources and sinks of the mean and transient components of energy and enstrophy are found and how these quantities are transferred between scales and converted from one form to another. The interaction between the high wavenumber homogeneous and isotropic transient components and the low wavenumber inhomogeneous and nonisotropic mean components is seen to be an essential aspect of the spectral budgets.