Vorticity Equation Terms for Extratropical Cyclones

Richard Grotjahn National Center for Atmospheric Research, Boulder, Colorado

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Abstract

All terms of the frictionless, nonlinear, vorticity equation are examined. Traditional scale analysis provides one of several justifications for using the quasigeostrophic (QG) system of equations to model extratropical cyclones. Analysts of observations have long known that some of the other terms (non-QG) are individually comparable to terms kept in quasigeostrophy. While the non-QG terms are not small, they are assumed to have a large degree of cancellation and so are still neglected in sum. The distributions, magnitudes, and possible cancellations of vorticity equation terms are examined. Analyzed data composites for 15 cases of mature, developing, extratropical cyclones are used.

These results lead us to conclude that several commonly neglected terms are neither especially small nor do they cancel. The way each term contributes to the redistribution, advection, of amplification of vorticity is discussed. In sum, cyclone growth is greater at all levels, especially at low levels, in the full set of terms compared to the QG terms.

Abstract

All terms of the frictionless, nonlinear, vorticity equation are examined. Traditional scale analysis provides one of several justifications for using the quasigeostrophic (QG) system of equations to model extratropical cyclones. Analysts of observations have long known that some of the other terms (non-QG) are individually comparable to terms kept in quasigeostrophy. While the non-QG terms are not small, they are assumed to have a large degree of cancellation and so are still neglected in sum. The distributions, magnitudes, and possible cancellations of vorticity equation terms are examined. Analyzed data composites for 15 cases of mature, developing, extratropical cyclones are used.

These results lead us to conclude that several commonly neglected terms are neither especially small nor do they cancel. The way each term contributes to the redistribution, advection, of amplification of vorticity is discussed. In sum, cyclone growth is greater at all levels, especially at low levels, in the full set of terms compared to the QG terms.

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