Repository: Freie Universität Berlin, Math Department

Modulational stability of nonlinear saturated gravity waves

Schlutow, M. (2019) Modulational stability of nonlinear saturated gravity waves. Journal of the Atmospheric Sciences .

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Stationary gravity waves, such as mountain lee waves, are effectively described by Grimshaw’s dissipative modulation equations even in high altitudes where they become nonlinear due to their large amplitudes. In this theoretical study, a wave-Reynolds number is introduced to characterize general solutions to these modulation equations. This nondimensional number relates the vertical linear group velocity with wavenumber, pressure scale height and kinematic molecular/eddy viscosity. It is demonstrated by analytic and numerical methods that Lindzen-type waves in the saturation region, i.e. where the wave-Reynolds number is of order unity, destabilize by transient perturbations. It is proposed that this mechanism may be a generator for secondary waves due to direct wave-mean-flow interaction. By assumption the primary waves are exactly such that altitudinal amplitude growth and viscous damping are balanced and by that the amplitude is maximized. Implications of these results on the relation between mean-flow acceleration and wave breaking heights are discussed.

Item Type:Article
Additional Information:Early Online Release-Posted online on 19 Aug 2019
Subjects:Mathematical and Computer Sciences
Mathematical and Computer Sciences > Mathematics
Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:2364
Deposited By: Ulrike Eickers
Deposited On:20 Aug 2019 12:37
Last Modified:27 Sep 2019 11:53

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