An application of WKBJ theory for triad interactions of internal gravity waves in varying background flows

  • Motivated by the question of whether and how wave–wave interactions should be implemented into atmospheric gravity-wave parametrizations, the modulation of triadic gravity-wave interactions by a slowly varying and vertically sheared mean flow is considered for a non-rotating Boussinesq fluid with constant stratification. An analysis using a multiple-scale WKBJ (Wentzel–Kramers–Brillouin–Jeffreys) expansion identifies two distinct scaling regimes, a linear off-resonance regime, and a nonlinear near-resonance regime. Simplifying the near-resonance interaction equations allows for the construction of a parametrization for the triadic energy exchange which has been implemented into a one-dimensional WKBJ ray-tracing code. Theory and numerical implementation are validated for test cases where two wave trains generate a third wave train while spectrally passing through resonance. In various settings, of interacting vertical wavenumbers, mean-flow shear, and initial wave amplitudes, the WKBJ simulations are generally in good agreement with wave-resolving simulations. Both stronger mean-flow shear and smaller wave amplitudes suppress the energy exchange among a resonantly interacting triad. Experiments with mean-flow shear as strong as in the vicinity of atmospheric jets suggest that internal gravity-wave dynamics are dominated in such regions by wave modulation. However, triadic gravity-wave interactions are likely to be relevant in weakly sheared regions of the atmosphere.

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Author:Georg S. Völker, Triantaphyllos R. Akylas, Ulrich Achatz
Parent Title (English):Quarterly journal of the Royal Meteorological Society
Place of publication:Weinheim [u.a.]
Document Type:Article
Date of Publication (online):2020/12/16
Date of first Publication:2020/12/16
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2021/11/03
Tag:internal gravity waves; parametrization; ray-tracing; triadic wave–wave interaction; wave modulation
Issue:art. 735
Page Number:23
First Page:1112
Last Page:1134
German Research Foundation (DFG) US National Science Foundation. Grant Numbers: AC 71/8-2, AC 71/9-2, AC 71/10-2, AC 71/11-2, AC 71/12-2 and BO 5071/1-2, 631 DMS-1512925
Institutes:Geowissenschaften / Geographie
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 55 Geowissenschaften, Geologie / 550 Geowissenschaften
Licence (German):License LogoCreative Commons - Namensnennung 4.0