Interactions between Mesoscale and Submesoscale Gravity Waves and Their Efficient Representation in Mesoscale-Resolving Models

Abstract

As present weather forecast codes and increasingly many atmospheric climate models resolve at least part of the mesoscale flow, and hence also internal gravity waves (GWs), it is natural to ask whether even in such configurations subgrid-scale GWs might impact the resolved flow and how their effect could be taken into account. This motivates a theoretical and numerical investigation of the interactions between unresolved submesoscale and resolved mesoscale GWs, using Boussinesq dynamics for simplicity. By scaling arguments, first a subset of submesoscale GWs that can indeed influence the dynamics of mesoscale GWs is identified. Therein, hydrostatic GWs with wavelengths corresponding to the largest unresolved scales of present-day limited-area weather forecast models are an interesting example. A large-amplitude WKB theory, allowing for a mesoscale unbalanced flow, is then formulated, based on multiscale asymptotic analysis utilizing a proper scale-separation parameter. Purely vertical propagation of submesoscale GWs is found to be most important, implying inter alia that the resolved flow is only affected by the vertical flux convergence of submesoscale horizontal momentum at leading order. In turn, submesoscale GWs are refracted by mesoscale vertical wind shear while conserving their wave-action density. An efficient numerical implementation of the theory uses a phase-space ray tracer, thus handling the frequent appearance of caustics. The WKB approach and its numerical implementation are validated successfully against submesoscale-resolving simulations of the resonant radiation of mesoscale inertia GWs by a horizontally as well as vertically confined submesoscale GW packet.

Flows induced by Coriolis-influenced vertically propagating two-dimensional internal gravity wave packets

“…In this case, the total induced flow, which is dominated by u ev , is characterised by horizontal disturbances that decay to the left and right of the wavepacket as well as above and below. The enhanced lateral confinement of the induced flow due to rotation was also noted in the simulations of Wilhelm et al 20 .…”

“…The predicted streamfunction associated with the induced flow was computed in a domain with double the vertical and horizontal extent of that used in the simulations. The corresponding fields for spanwise vorticity, spanwise velocity and buoyancy were computed in Fourier space using ζ = −∇ 2 ψ, (19) and (20), respectively. The corresponding fields in Fourier space arê ζ = (κ 2 + µ 2 )ψ,v = −µ 0ψ andb = (N 2 /c gz )(κ/µ)ψ.…”

Efficient Modeling of the Interaction of Mesoscale Gravity Waves with Unbalanced Large-Scale Flows: Pseudomomentum-Flux Convergence versus Direct Approach

“…The numerical implementation of the transient interaction processes between IGW and large-scale flow is achieved by coupling the Multi-Scale Gravity-Wave Model (MS-GWaM), a Lagrangian phase-space WKB ray tracer, to the PincFloit code in a coarseresolution setting. MS-GWaM is based on the methods described by Muraschko et al (2015), Bölöni et al (2016), and Wilhelm et al (2018). It predicts the spectral distribution of wave action by a phase-space waveaction density N so that wave-action density and energy density are…”

“…Whenever the local wave amplitudes are large enough to make the wave field statically unstable, a turbulent viscosity is switched on that reduces the wave amplitudes within one time step to the saturation level. More details on the methods used by MS-GWaM can be found in Muraschko et al (2015), Bölöni et al (2016), and Wilhelm et al (2018).…”

“…The issue of caustics occurs when by wave-mean flow interactions a wave field loses its initial locally monochromatic character (Tabaei and Akylas 2007;Rieper et al 2013a). Based on the spectral approach, a prognostic Lagrangian WKB GW ray-tracing model has been implemented, using a multidimensional phase space spanned by physical space and the wavenumber space, and it has been successfully validated against wave-resolving large-eddy simulation (LES) data in different idealized settings, including one-dimensional (1D) vertically propagating idealized wave packets with variable vertical wavenumbers in a nonrotating Boussinesq atmosphere (Muraschko et al 2015), 1D wave packets propagating in a nonrotating compressible atmosphere (Bölöni et al 2016), and twodimensional (2D) wave packets of parameterized submesoscale GWs interacting with resolved mesoscale GWs in a rotating Boussinesq atmosphere (Wilhelm et al 2018). In addition, this approach has also been used to study the interaction between GWs and solar tides (Ribstein et al 2015;Ribstein and Achatz 2016).…”