The Influence of Gravity Waves on the Slope of the Kinetic Energy Spectrum in Simulations of Idealized Midlatitude Cyclones

Abstract

The influence of gravity waves generated by surface stress and by topography on the atmospheric kinetic energy (KE) spectrum is examined using idealized simulations of a cyclone growing in baroclinically unstable shear flow. Even in the absence of topography, surface stress greatly enhances the generation of gravity waves in the vicinity of the cold front, and vertical energy fluxes associated with these waves produce a pronounced shallowing of the KE spectrum at mesoscale wavelengths relative to the corresponding free-slip case. The impact of a single isolated ridge is, however, much more pronounced than that of surface stress. When the mountain waves are well developed, they produce a wavenumber to the −5/3 spectrum in the lower stratosphere over a broad range of mesoscale wavelengths. In the midtroposphere, a smaller range of wavelengths also exhibits a −5/3 spectrum. When the mountain is 500 m high, the waves do not break, and their KE is entirely associated with the divergent component of the velocity field, which is almost constant with height. When the mountain is 2 km high, wave breaking creates potential vorticity, and the rotational component of the KE spectrum is also strongly energized by the waves. Analysis of the spectral KE budgets shows that the actual spectrum is the result of continually shifting balances of direct forcing from vertical energy flux divergence, conservative advective transport, and buoyancy flux. Nevertheless, there is one interesting example where the −5/3-sloped lower-stratospheric energy spectrum appears to be associated with a gravity-wave-induced upscale inertial cascade.

The Horizontal Spectrum of Vertical Velocities near the Tropopause from Global to Gravity Wave Scales

“…The kinetic relationship implies a connection between the spectral slope of the horizontal velocities and the vertical velocity spectrum at least for incompressible and horizontally isotropic divergent motions. Besides in the numerical results shown in section 3, this relationship can also be identified in w and divergence spectra derived from numerical simulations of baroclinically unstable shear flows (Menchaca and Durran 2019). This kinematic connection may cause a dynamic connection between vertical and horizontal motions and affect the transition scale L. The flatter spectrum at mesoscales may be a consequence of energy transfer from horizontal to vertical divergent motions.…”

Normal Mode Spectra of Idealized Baroclinic Waves

“…Rossby wave velocity divergence associated with meridionally varying Coriolis parameter is also missing in the f-plane setup considered here. In addition, physical mechanisms that are neglected here are known to amplify the DKE spectra, and will therefore have a similar effect on the AE: these include moist physics (Waite and Snyder 2013;Peng et al 2015a,b;Sun et al 2017) and topography and surface fluxes (Menchaca and Durran 2019). Indeed, normal mode spectra from reanalysis data show that the GE and AE spectra do indeed cross at length scales of a few hundred kilometers, leading to a more pronounced mesoscale spectrum that what was found here (Terasaki et al 2011;Zagar et al 2017).…”

“…In dry simulations, the amplitude of the DKE spectrum is not large enough to significantly modify the KE spectrum in the troposphere, but it does in the stratosphere, where the total kinetic energy shallows under the dominance of the DKE (Waite and Snyder 2009). The addition of moist physics (Waite and Snyder 2013;Peng et al 2015a,b) or topography and surface fluxes (Menchaca and Durran 2019) enhances the DKE spectrum and, as a result, the mesoscale KE spectrum.…”

Horizontal Wavenumber Spectra Across the Middle Atmosphere From Airborne Lidar Observations During the 2019 Southern Hemispheric SSW

“…The questions which dynamical mechanism underlies the mesoscale k −5/3 spectrum and whether there is a universal dynamical mechanism at all have still not been unequivocally answered, as studies suggest that the spectral energy is rather intermittent because of the intermittency of the dynamical processes, for example, convection or GWs (Menchaca & Durran, 2019; Selz et al., 2019). However, knowing and understanding the atmospheric spectra is of importance for NWP and atmospheric predictability (Charney, 1971), and for the development and application of GW parameterizations in all layers of the atmosphere (Harvey et al., 2022; Kim et al., 2003; Plougonven et al., 2020).…”