Shear-gravity wave: Difference between revisions
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<div class="definition"><div class="short_definition">A combination of [[gravity waves]] and a [[Helmholtz wave]] on a [[surface of discontinuity]] of [[density]] and [[velocity]].</div><br/> <div class="paragraph">If the densities of the lower and upper layers respectively are ρ and ρ′ and the velocities ''U'' and ''U''′, the [[phase speed]] ''c'' of the shear–gravity wave is <div class="display-formula"><blockquote>[[File:ams2001glos-Se19.gif|link=|center|ams2001glos-Se19]]</blockquote></div> where ''g'' is the [[acceleration of gravity]] and ''L'' the [[wavelength]]. The motion is unstable if and only if the bracketed quantity is negative; the [[density]] difference thus contributes to [[stability]] and the velocity difference to [[instability]]. Applications have been made to atmospheric [[frontal surfaces]] and [[inversions]]; perhaps the most successful of these is to the phenomenon of [[billow clouds]]. Reasonable atmospheric values for the parameters yield stationary wavelengths of the order of 1 km.</div><br/> </div><div class="reference">Drazin, P. G., and W. H. Reid 1981. Hydrodynamic Stability. Cambridge University Press, . 14–22. </div><br/> | <div class="definition"><div class="short_definition">A combination of [[gravity waves]] and a [[Helmholtz wave]] on a [[surface of discontinuity|surface of discontinuity]] of [[density]] and [[velocity]].</div><br/> <div class="paragraph">If the densities of the lower and upper layers respectively are ρ and ρ′ and the velocities ''U'' and ''U''′, the [[phase speed]] ''c'' of the shear–gravity wave is <div class="display-formula"><blockquote>[[File:ams2001glos-Se19.gif|link=|center|ams2001glos-Se19]]</blockquote></div> where ''g'' is the [[acceleration of gravity]] and ''L'' the [[wavelength]]. The motion is unstable if and only if the bracketed quantity is negative; the [[density]] difference thus contributes to [[stability]] and the velocity difference to [[instability]]. Applications have been made to atmospheric [[frontal surfaces]] and [[inversions]]; perhaps the most successful of these is to the phenomenon of [[billow clouds]]. Reasonable atmospheric values for the parameters yield stationary wavelengths of the order of 1 km.</div><br/> </div><div class="reference">Drazin, P. G., and W. H. Reid 1981. Hydrodynamic Stability. Cambridge University Press, . 14–22. </div><br/> | ||
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Latest revision as of 16:52, 25 April 2012
shear–gravity wave
A combination of gravity waves and a Helmholtz wave on a surface of discontinuity of density and velocity.
If the densities of the lower and upper layers respectively are ρ and ρ′ and the velocities U and U′, the phase speed c of the shear–gravity wave is where g is the acceleration of gravity and L the wavelength. The motion is unstable if and only if the bracketed quantity is negative; the density difference thus contributes to stability and the velocity difference to instability. Applications have been made to atmospheric frontal surfaces and inversions; perhaps the most successful of these is to the phenomenon of billow clouds. Reasonable atmospheric values for the parameters yield stationary wavelengths of the order of 1 km.
Drazin, P. G., and W. H. Reid 1981. Hydrodynamic Stability. Cambridge University Press, . 14–22.
