Abstract
AbstractMotivated 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.
Highlights
Internal gravity waves (GWs) are an important mode of atmospheric dynamics, transporting energy and momentum over large distances from generation regions to regions of dissipation, thereby significantly influencing the atmospheric circulation, especially in the middle atmosphere (Fritts and Alexander, 2003; Kim et al, 2003; Plougonven and Zhang, 2014)
Being too small in scale to be fully resolvable by present-day weather forecast and climate codes, GWs constitute an important aspect of the parametrization problem in these models
Note that we restrict our analysis to the internal gravity wave evolution and neglect the vortical mode corresponding to the solution ωβ = 0
Summary
Internal gravity waves (GWs) are an important mode of atmospheric dynamics, transporting energy and momentum over large distances from generation regions to regions of dissipation, thereby significantly influencing the atmospheric circulation, especially in the middle atmosphere (Fritts and Alexander, 2003; Kim et al, 2003; Plougonven and Zhang, 2014). Wave-turbulence theory (Hasselmann, 1962; 1966; Caillol and Zeitlin, 2000; Nazarenko, 2011; Eden et al, 2019) is a well-established tool for studies of corresponding spectra, considering statistical ensembles of GW fields, which most often focus on resonant triad interactions In all of these the influence of mean-flow shear and varying stratification are neglected. Strongly sheared environments might suppress nonlinear interactions, while such interactions, as described by wave-turbulence theory, might be more effective in less-sheared locations of the atmosphere With this motivation in mind, the work reported here builds on the study of Grimshaw (1988), who proposed a WKBJ theory for wave–wave interactions modulated by a slowly varying background flow. We follow Grimshaw (1988) and Glebov et al (2005), and consider two distinct regimes: the linear offresonance solution, where the nonlinear triad terms can be neglected, and the weakly nonlinear near-resonance solution
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