Repository: Freie Universität Berlin, Math Department

On the application of WKB theory for the simulation of the weakly nonlinear dynamics of gravity waves

Muraschko, J and Fruman, M. D. and Achatz, U. and Hickel, S. and Toledo, Y. (2014) On the application of WKB theory for the simulation of the weakly nonlinear dynamics of gravity waves. Quarterly Journal of the Royal Meteorological Society .

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The dynamics of internal gravity waves is modelled using WKB theory in position-wavenumber phase space. A transport equation for the phase-space wave-action density is derived for describing one-dimensional wave fields in a background with height-dependent stratification and height- and timedependent horizontal-mean horizontal wind, where the mean wind is coupled to the waves through the divergence of the mean vertical flux of horizontal momentum associated with the waves. The phase-space approach bypasses the caustics problemthat occurs inWKB ray-tracingmodels when the wavenumber becomes a multivalued function of position, such as in the case of a wave packet encountering a reflecting jet or in the presence of a time-dependent background flow. Two numerical models were developed to solve the coupled equations for the wave-action density and horizontal mean wind: an Eulerian model using a finite-volumemethod, and a Lagrangian “phase-space ray tracer” that transports wave-action density along phase-space paths determined by the classical WKB ray equations for position and wavenumber. The models are used to simulate the upward propagation of a Gaussian wave packet through a variable stratification, a wind jet, and the mean flow induced by the waves. Results from the WKB models are in good agreement with simulations using a weakly nonlinear wave-resolving model as well as with a fully nonlinear large-eddy-simulation model. The work is a step toward more realistic parameterizations of atmospheric gravity waves in weather and climate models.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:1431
Deposited By: Ulrike Eickers
Deposited On:01 Aug 2014 09:54
Last Modified:01 Aug 2014 10:12

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