The structure of non-linear processes

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Quinet, A. (2011)

The spectral energetics of a two-layer quasi-geostrophic model of the kind of Lorenz (1960b) is presented. The model has the channel geometry and is subject to friction and heating. It is found that the barotropic transfers between three spectral components of the kinetic energy are governed by a conservation law similar to Fjörtoft's (1953): the kinetic energy flows from the intermediate scale towards the two extreme scales or conversely. The baroclinic transfers between three spectral components of the available potential energy involve three individual conservative processes, relating two scales of motion only, so that a given scale may feed one of the two others and be fed by the third. The structure of the baroclinic conversions between available potential energy and kinetic energy is formally similar to the structure of transfers between different spectral components of the available potential energy. For each set of non-linearly associated scales, the baroclinic production of kinetic energy is controlled by a function of the individual conversion rates, the weighting coefficients depending upon the static stability and the wave numbers of the associated scales. Obviously, all the transfer and conversion rates are function of the geometry of the system.DOI: 10.1111/j.2153-3490.1973.tb00638.x
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