Journal ArticleDOI
On the instability of Helmholtz velocity profiles in stably stratified fluids when a lower boundary is present
TLDR
In this article, the stability of a Helmholtz velocity profile in a stably stratified fluid when a lower boundary is present is investigated and it is shown that the gravity wave instabilities result from the ability of an unstable shear layer to overreflect such waves (reflected amplitudes are greater than incident amplitudes).Abstract:
We investigate the stability of a Helmholtz velocity profile in a stably stratified fluid when a lower boundary is present. In addition to the traditional Kelvin-Helmholtz interfacial instability we find an infinitude of unstable internal gravity waves, the most unstable of which bear a close resemblance to disturbances observed in connection with clear air turbulence. It is shown that the gravity wave instabilities result from the ability of an unstable shear layer to overreflect such waves (reflected amplitudes are greater than incident amplitudes). Overreflection at the shear layer is constantly fed by total reflection from the lower boundary. The growth rate of gravity wave instabilities depends markedly on the distance between the shear layer and the ground. A mechanism is suggested whereby gravity wave instability can lead to long-lived almost neutral shear layers.read more
Citations
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Journal ArticleDOI
Turbulence and stress owing to gravity wave and tidal breakdown
TL;DR: In this article, the effects of mean winds and gravity waves on the mean momentum budget were investigated and it was shown that the existence of critical levels in the mesosphere significantly limits the ability of gravity waves to generate turbulence.
Journal ArticleDOI
Convective and dynamical instabilities due to gravity wave motions in the lower and middle atmosphere: Theory and observations
TL;DR: In this paper, the authors review the theory and the observational evidence for both types of instabilities in the lower and middle atmosphere and show that convective instabilities predominate for high-frequency wave motions.
Journal ArticleDOI
Solar tides as revealed by measurements of mesosphere temperature by the MLS experiment on UARS
Jeffrey M. Forbes,Dong Wu +1 more
TL;DR: In this article, temperatures between 25 and 86 km measured by the Microwave Limb Sounder (MLS) experiment on the Upper Atmosphere Research Satellite (UARS) are analyzed to delineate diurnal, semidiurnal, and terdiurnal tidal structures and stationary planetary waves.
Journal ArticleDOI
Review of wave-turbulence interactions in the stable atmospheric boundary layer
Jielun Sun,Carmen J. Nappo,Larry Mahrt,Danijel Belušić,Branko Grisogono,David R. Stauffer,Manuel Pulido,Chantal Staquet,Qingfang Jiang,Annick Pouquet,Carlos Yagüe,Boris Galperin,Ronald B. Smith,John Finnigan,Shane D. Mayor,Gunilla Svensson,Andrey A. Grachev,William Neff +17 more
TL;DR: In this article, a review of wave-turbulence interactions in stable atmospheric boundary layer (SABL) flows is presented, focusing on the nocturnal SABL.
Journal ArticleDOI
Instability of plane parallel shear flow (toward a mechanistic picture of how it works)
TL;DR: In this paper, the authors reviewed work done over the last twelve years on wave overreflection in shear flows, and on the development of a mechanical picture of how over-reflection and instability work.
References
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Journal ArticleDOI
Note on a paper of John W. Miles
TL;DR: In this article, the theorem X established by Miles in the preceding paper is given a simpler and more general proof, and further theoretical results concerning the stability of heterogeneous shear flows are also presented, in particular a demonstration that the complex wave velocity of any unstable mode must lie in a certain semicircle.
Journal ArticleDOI
The critical layer for internal gravity waves in a shear flow
TL;DR: In this paper, the effect of the Richardson number R on the propagation of gravity waves from the troposphere to the ionosphere is considered, and it is shown that if R is everywhere larger than 1/4, the waves are attenuated by a factor as they pass through a critical level at which U is equal to the horizontal phase speed, and momentum is transferred to the mean flow there.
Book
Numerical Methods That Work
TL;DR: Part I. Fundamental Methods: The calculation of functions, Roots of transcendental equations, and the care and treatment of singularities.
Journal ArticleDOI
Note on a heterogeneous shear flow
John W. Miles,Louis N. Howard +1 more
TL;DR: In this paper, it was shown that the principal branch of this eigenvalue equation yields one and only one unstable mode if and only if the wave-number lies in a band that decreases from Rayleigh's band to zero as the Richardson number increases from 0 to ¼.
Journal ArticleDOI
Reflexion and stability of waves in stably stratified fluids with shear flow: a numerical study
TL;DR: In this article, a numerical examination of the reflectivity of critical levels with low Richardson number to internal gravity waves propagating in stratified fluids with shear is made, and the normal mode instabilities of three simple models have also been computed.