Joint Centre for Mesoscale Meteorology (JCMM)

Consequences of the geostrophic momentum approximation on barotropic instability
by S Malardel, A J Thorpe and A Joly

A subsynoptic instability with dominant barotropic signature has been found to be a possible mechanism for the development of frontal waves.  Linear semi-geostrophic calculations of the growth rate of waves developing along a front exhibiting a low level vorticity band are here compared with the results of similar experiments made with a primitive equation model.  The growth rates of the subsynoptic instability are significantly underestimated by the semi-geostrophic system, a result which is the opposite of what has been found by previous semi-geostrophic/primitive equation comparisons in the case of baroclinic instability calculations.

Analytical solutions of the Rayleigh model of pure barotropic instability confirm this behaviour of the geostrophic momentum approximation (GMA) in the case of barotropic instability.  The inaccuracy of the equations with GMA is very sensitive to the basic wind shear amplitude.  Such sensitivity seems to be directly linked with the definition of the semi-geostrophic vorticity.

It should be noted however that the frontal wave instability is not filtered by the balanced system but rather it is described in a quantitatively inaccurate way.

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