The Relationship between Horizontal and Vertical Velocity Wavenumber Spectra in Global Storm-Resolving Simulations

Abstract

Abstract Several studies have reported vertical kinetic energy spectra almost white in horizontal wavenumber space with evidence of two maxima at synoptic scales and mesoscales, leaving the explanation of these maxima open. Processes known to influence the shape of the horizontal kinetic energy spectra include the superposition of quasi-linear inertia–gravity waves (IGWs), quasigeostrophic turbulence, and moist convection. In contrast, vertical kinetic energy has been discussed much less, as measuring vertical velocity remains challenging. This study compares the horizontal and vertical kinetic energy spectra and their relationships in global storm-resolving simulations from the DYAMOND experiment. The consistency of these relationships with linear IGW theory is tested by diagnosing horizontal wind fluctuations associated with IGW modes. Furthermore, it is shown that hydrostatic IGW polarization relations provide a quantitative prediction of the spectral slopes of vertical kinetic energy at large scales and mesoscales, where the intrinsic frequencies are inferred from the linearized vorticity equation. Our results suggest that IGW modes dominate the vertical kinetic energy spectra at most horizontal scales, whereas an incompressible, isotropic scaling of the continuity equation captures the relationship between horizontal and vertical kinetic energy spectra at small scales.