Estimation of Nonlinear Energy Transfer Spectra by the Cross-Spectral Method

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Abstract
Spectral formulas are derived to compute nonlinear energy transfer spectra by use of the cross-spectral technique. Nonlinear product terms are calculated directly from dependent variables without using the conventional interaction Fourier coefficients. The proposed method of computation is simpler than the conventional method and is applicable not only to wavenumber spectra but also to frequency or wavenumber-frequency spectra. Nonlinear aliasing errors associated with this approach can be either neglected or completely eliminated by Fourier interpolation. An example of the application of this method to atmospheric waves is given. Abstract Spectral formulas are derived to compute nonlinear energy transfer spectra by use of the cross-spectral technique. Nonlinear product terms are calculated directly from dependent variables without using the conventional interaction Fourier coefficients. The proposed method of computation is simpler than the conventional method and is applicable not only to wavenumber spectra but also to frequency or wavenumber-frequency spectra. Nonlinear aliasing errors associated with this approach can be either neglected or completely eliminated by Fourier interpolation. An example of the application of this method to atmospheric waves is given.

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