Gravity wave breaking in two and three dimensions: 2. Three‐dimensional evolution and instability structure

Abstract

A companion paper by Andreassen et al. (this issue) introduced and used a nonlinear, compressible, spectral collocation code to address the relative evolutions of two‐dimensional motions obtained in two‐ and three‐dimensional simulations of gravity wave breaking. That study illustrated the effects of instability on the wave field and mean flow evolution and suggested that two‐dimensional models are unable to fully describe the physics of the wave breaking process. The present paper examines in detail the structure, evolution, and energetics of the three‐dimensional motions accounting for wave instability as well as their associated transports of momentum and heat. It is found that this instability comprises counterrotating vortices which evolve very rapidly within the convectively unstable region of a breaking wave. Instability scales are selected based on wave geometry and vortices are elongated in the streamwise direction (horizontal wavenumber in the spanwise direction) and result in the rapid collapse of superadiabatic regions within the wave field. The resulting spectra show clearly the transition from gravity wave forcing of harmonics of the incident wave to instability onset and evolution. Fluxes of momentum and heat by the instability reveal the manner in which the gravity wave amplitude is constrained and the influences of instability on the wave transports of these quantities. The breakdown of the instability structure and its evolution toward isotropic small‐scale structure is the subject of the companion paper by Isler et al. (this issue).

The structure of turbulence in the middle and lower atmosphere seen by and deduced from MF, HF and VHF radar, with special emphasis on small-scale features and anisotropy

“…Some of these deliberations have their origin in initial proposals by Bolgiano (1968) about the structure of the atmospheric turbulence (and especially with regard to the edges of the layers). We note that the recent modelling work using super computers (Fritts et al, 1994;Werne and Fritts, 1999;Gibson-Wilde et al, 2000) just confirm these principles which had been developed and have emerged from radar observations over the past decades. Figure 10 shows the expected structure across a turbulent layer in even greater detail.…”

Numerical simulation of pulsations in the bora wind

“…KHI takes over and leads the flow to the state of turbulence (e.g. Fritts et al, 1994;Isler et al, 1994). Thus, a combination of the first and third mechanisms is quite a possible scenario.…”

Long-period unstable gravity-waves and associated VHF radar echoes

“…Measurements with 2 or more pairs of symmetric beams in di erent azimuths could, therefore, be compared with model predictions of long-period wave instability (e.g. Andreassen et al, 1994;Fritts et al, 1994), and the associated vertical wave number spectrum might also be investigated. A radar system with a greater number of beam azimuth angles could show how the azimuth of largest power di erence varies as Fig.…”