The Application of the Semigeostrophic Equations to the Frontal Instability Problem

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  • 1 AFGWC/WPA, Offuit AFB, Nebr. 68113
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Abstract

The stability of the classical Norwegian polar front model is reinvestigated, using a numerical technique to supplement the precise conclusions which are possible in the limiting case of zero density difference or zero wavenumber. Instead of using the primitive equations, a system of filtered momentum equations which neglects the substantial derivative of the ageostrophic put of the horizontal wind is used to test the applicability to meteorological problems. For Rossby numbers ≪0.4, the agreement between the primitive and the semigeostrophic equations is found to he good provided that the Richardson number is not ton small. Unstable waves are found only at Rossby numbers less than a critical value; large-scale shear instability exists at small Richardson number and quasigeostrophic baroclinic instability occurs at larger Richardson number.

Abstract

The stability of the classical Norwegian polar front model is reinvestigated, using a numerical technique to supplement the precise conclusions which are possible in the limiting case of zero density difference or zero wavenumber. Instead of using the primitive equations, a system of filtered momentum equations which neglects the substantial derivative of the ageostrophic put of the horizontal wind is used to test the applicability to meteorological problems. For Rossby numbers ≪0.4, the agreement between the primitive and the semigeostrophic equations is found to he good provided that the Richardson number is not ton small. Unstable waves are found only at Rossby numbers less than a critical value; large-scale shear instability exists at small Richardson number and quasigeostrophic baroclinic instability occurs at larger Richardson number.

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