Calculations of nonlinear interaction of available potential energy, kinetic energy, enstrophy, and potential enstrophy have been carried out in the domain of wave numbers. The processes of interest are the interactions among waves, the interactions between a given wave and the zonal average, and interactions due to the beta effect for (potential) enstrophy. Results are presented for a three‐month (February through April 1963) period. It is found that available potential energy is cascaded from small to large wave numbers, while kinetic energy is cascaded from intermediate wave numbers to both small and large wave numbers: the greater amounts go to the small wave numbers. Enstrophy and potential enstrophy are cascaded from small to large wave numbers with relatively little accumulation in the middle range (8≤m≤11, where m is the wave number). Verification of the existence of an inertial subrange is inconclusive, although power spectrum analyses of enstrophy and potential enstrophy yield a −1 power law, combined with a −3 slope for the associated kinetic energy spectrum. A value of 2.5×104 m2 sec−1 is obstained for the coefficient of eddy viscosity by means of Leith's formulation, while the value of the cut‐off wavelength for the −3 range is approximately 420 km by means of the formulation by Kraichnan.
The evidence from observational calculations and a numerical simulation experiment point to the dominance of the baroclinic process over the non‐linear cascade of kinetic energy in the spectral range 7 ≤ m ≤ 15 in atmospheric flow (m is the wavenumber). It is therefore suggested that the power law governing this portion of the kinetic energy spectrum be derived using Ci, the imaginary part of the phase speed commonly used in studies of baroclinic instability. Evidence is presented to support this view.
The development of turbulence is studied numerically through the use of a simplified two-level quasi-geostrophic model. The domain occupied by the fluid has 64 x 64 grid points in the horizontal and obeys cyclic boundary conditions in the x-and y-directions. The turbulence is generated by a heating function composed of the 2-dimensional fourier components having the larger wave number, m = 8. Three cases are investigated for two values of H, the amplitude of the heating function and two values of Y , the coefficient of eddy viscosity. Quasistationary spectra are obtained in each case. The slopes of the spectra for 8 G m < 16 on a log-log graph vary from -1.7 to -3.4 depending on Y and H. The nonlinear cascade of available potential energy is found to be toward larger wavenumbers. The nonlinear cascade of kinetic energy is from components for which 8 < m Q 14, mainly toward 1 G m 4 7, the larger scales. The gains for m > 14 resulting from the cascade is relatively small. These transfers are in qualitative agreement with atmospheric observations. Gains of enstrophy are observed to be fairly constant for 14
The evidence from observational calculations and a numerical simulation experiment point to the dominance of the baroclinic process over the non-linear cascade of kinetic energy in the spectral range 7 $ m $ 15 in atmospheric flow (m is the wavenumber). It is therefore suggested that the power law governing this portion of the kinetic energy spectrum be derived using C,, the imaginary part of the phase speed commonly used in studies of baroclinic instability, Evidence is presented t o support this view.
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