TY  - JOUR
A1  - Völker, Georg S.
A1  - Akylas, Triantaphyllos R.
A1  - Achatz, Ulrich
T1  - An application of WKBJ theory for triad interactions of internal gravity waves in varying background flows
T2  - Quarterly journal of the Royal Meteorological Society
N2  - 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.
KW  - internal gravity waves
KW  - parametrization
KW  - ray-tracing
KW  - triadic wave–wave interaction
KW  - wave modulation
Y1  - 2020
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/62164
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-621645
SN  - 1477-870X
N1  - 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
VL  - 147
IS  - art. 735
SP  - 1112
EP  - 1134
PB  - Wiley
CY  - Weinheim [u.a.]
ER  -