Instability and breakdown of internal gravity waves. I. Linear stability analysis

Abstract

We have performed three-dimensional linear stability analysis, based on Floquet theory, to study the stability of finite amplitude internal gravity waves. This analysis has been used to compute instability growth rates over a range of wave amplitudes and propagation angles, especially waves above and below overturning amplitude, and identifies several new characteristics of wave instability. Computation of instability eigenfunctions has allowed us to analyze the energetics of the instability and to clarify the paths of energy transfer from the base wave to the instability. We find that the presence of wave overturning has no qualitative effect on the wave instability, except for the limiting case when the wavenumber vector is vertical. Instabilities which are nearly two-dimensional are closely related to second-order wave–wave interactions. But the three-dimensional instabilities, more prominent at higher wave amplitudes, may be caused by higher order resonance interactions. The energetics of the instabilities range from being shear driven to being driven by ‘‘density gradient’’ production (the potential energy analog of ‘‘shear’’ production); this characteristic is strongly dependent on wave propagation angle and the three-dimensionality of the instability.

Stratified Kolmogorov flow. Part 2

“…Staircases can then be predicted to occur; we examine the robustness of layering within this formulation. Our analysis is similar to that used to compute eddy diffusivities in homogeneous fluid (Gama, Vergolassa & Frisch 1994), and there are analogies with stability theories of Rossby waves (Lorenz 1972) and internal gravity waves (Drazin 1978;Kurgansky 1979Kurgansky , 1980Lombard & Riley 1996) which have applications to atmospheric dynamics and to oceanic mixing (Thorpe 1994).…”

Investigation of a mesospheric gravity wave ducting event using coordinated sodium lidar and Mesospheric Temperature Mapper measurements at ALOMAR, Norway (69°N)

“…GW instabilities are likewise challenging to identify and quantify because they are inherently nonlinear and multiscale, they display a wide range of possible instability structures, and observations typically lack the precision needed to enable a comprehensive description of GW and environmental parameters [see, e.g., Lombard and Riley, 1996;Sonmor and Klaassen, 1997;Fritts and Alexander, 2003;Fritts et al, 2009aFritts et al, , 2009bFritts et al, , 2013. Distinguishing between GWs that are vertically propagating and ducting events or mesospheric bores are challenging to characterize with confidence due to various remote and local potential sources and their expected sensitivity and responses to small-scale features in the environmental wind and temperature profiles [Chimonas and Hines, 1986;Fritts and Yuan, 1989;Pasko, 2003, 2008;Simkhada et al, 2009;Laughman et al, 2009Laughman et al, , 2011Walterscheid and Hickey, 2009;Snively et al, 2013].…”

The Deep Propagating Gravity Wave Experiment (DEEPWAVE): An Airborne and Ground-Based Exploration of Gravity Wave Propagation and Effects from Their Sources throughout the Lower and Middle Atmosphere

“…1) GW linear dynamics, propagation, conservation properties, and fluxes (Hines 1960;Eliassen and Palm 1961;Bretherton 1969a,b;Booker and Bretherton 1967;Gossard and Hooke 1975;Smith 1980;Nappo 2013); 2) GW sources, characteristics, and responses (Fritts 1984;Fritts and Alexander 2003); 3) GW refraction, mean flow interactions, and responses (Lindzen and Holton 1968;Holton 1982;Garcia and Solomon 1985;Haynes et al 1991;Sutherland 2010;Bühler 2014); 4) GW spectral properties, interactions, instabilities, and saturation (Yeh and Liu 1981;Smith et al 1987;Hines 1991;Lombard and Riley 1996;Sonmor and Klaassen 1997;Fritts et al 2009); and 5) GW parameterizations for NWP and climate models (Lindzen 1981;Holton 1982;McFarlane 1987;Warner and McIntyre 1996;Hines 1997a,b;Kim et al 2003;Fritts and Alexander 2003).…”