Achatz, U. and Ribstein, B. and Senf, F. and Klein, R. The interaction between synopticscale balanced flow and a finiteamplitude mesoscale wave field throughout all atmospheric layers: weak and moderately strong stratification. Quarterly Journal of the Royal Meteorological Society . (In Press)

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Official URL: http://doi.wiley.com/10.1002/qj.2926
Abstract
The interaction between locally monochromatic finiteamplitude mesoscale waves, their nonlinearly induced higher harmonics, and a synopticscale flow is reconsidered, both in the tropospheric regime of weak stratification and in the stratospheric regime of moderately strong stratification. A review of the basic assumptions of quasigeostrophic theory on an fplane yields all synoptic scales in terms of a minimal number of natural variables, i.e. two out of the speed of sound, gravitational acceleration and Coriolis parameter. The wave scaling is defined so that all spatial and temporal scales are shorter by one order in the Rossby number, and by assuming their buoyancy field to be close to static instability. WKB theory is applied, with the Rossby number as scale separation parameter, combined with a systematic Rossbynumber expansion of all fields. Classic results for synopticscaleflow balances and inertiagravitywave (IGW) dynamics are recovered. These are supplemented by explicit expressions for the interaction between mesoscale geostrophic modes (GMs), a possibly somewhat overlooked agent of horizontal coupling in the atmosphere, and the synopticscale flow. It is shown that IGW higher harmonics are slaved to the basic IGW, and that their amplitude is one order of magnitude smaller than the basicwave amplitude. GM higher harmonics are not that weak and they are in intense nonlinear interaction between themselves and the basic GM. Compressible dynamics plays a significant role in the stratospheric stratification regime, where anelastic theory would yield insufficient results. Supplementing classic derivations, it is moreover shown that, in the absence of mesoscale waves, quasigeostrophic theory holds also in the stratospheric stratification regime.
Item Type:  Article 

Uncontrolled Keywords:  gravity waves; geostrophic flow; mesoscale; wave – mean flow interaction; parametrization; wave action; enstrophy 
Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group 
ID Code:  2014 
Deposited By:  Ulrike Eickers 
Deposited On:  30 Jan 2017 13:02 
Last Modified:  03 Mar 2017 14:42 
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