An approximate dispersion equation for atmosphere gravity waves

2011 ◽  
Vol 17 (1) ◽  
pp. 43-46 ◽  
Author(s):  
G.V. Lizunov ◽  
◽  
A.Yu. Leontiev ◽  
Keyword(s):  
Dispersion Equation ◽  
Gravity Waves

scholarly journals Analytical Approximations of Dispersion Relations for Internal Gravity Waves Equation with Shear Flows

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1865
Author(s):  
Vitaly Bulatov ◽  
Yury Vladimirov
Keyword(s):  
Bessel Function ◽  
Dispersion Equation ◽  
Gravity Waves ◽  
Shear Flows ◽  
Internal Gravity Waves ◽  
Stratified Medium ◽  
Buoyancy Frequency ◽  
Modified Bessel Function ◽  
Analytical Approximations ◽  
Background Shear

The problem of internal gravity waves fields in a stratified medium of finite depth is considered for model distributions of background shear currents. For the analytical solution of the problem, a constant distribution of the buoyancy frequency and various linear dependences of the background shear current on depth were used. The dispersion dependences are obtained, which are expressed in terms of the modified Bessel function of the imaginary index. Under the Miles–Howard stability condition and large Richardson numbers, the Debye asymptotics of the modified Bessel function of the imaginary index were used to construct analytical solutions. The dispersion equation is solved using the proposed analytical approximation. The properties of the dispersion equation are studied and the main analytical characteristics of the dispersion curves are investigated depending on the parameters of background shear flows.

Steady water waves with vorticity: an analysis of the dispersion equation

2014 ◽  
Vol 751 ◽  
Author(s):  
V. Kozlov ◽  
N. Kuznetsov ◽  
E. Lokharu
Keyword(s):  
Dispersion Equation ◽  
Gravity Waves ◽  
Water Waves ◽  
Liouville Problem ◽  
Finite Depth ◽  
Stokes Waves ◽  
General Dispersion ◽  
Sturm Liouville ◽  
Necessary And Sufficient ◽  
Appl Math

AbstractTwo-dimensional steady gravity waves with vorticity are considered on water of finite depth. The dispersion equation is analysed for general vorticity distributions, but under assumptions valid only for unidirectional shear flows. It is shown that for these flows (i) the general dispersion equation is equivalent to the Sturm–Liouville problem considered by Constantin & Strauss (Commun. Pure Appl. Math., vol. 57, 2004, pp. 481–527; Arch. Rat. Mech. Anal., vol. 202, 2011, pp. 133–175), (ii) the condition guaranteeing bifurcation of Stokes waves with constant wavelength is fulfilled. Moreover, a necessary and sufficient condition that the Sturm–Liouville problem mentioned in (i) has an eigenvalue is obtained.

Model of the internal gravity waves excited by lithospheric greenhouse effect gases

2001 ◽  
Vol 7 (2s) ◽  
pp. 26-33 ◽  
Author(s):  
O.E. Gotynyan ◽  
◽  
V.N. Ivchenko ◽  
Yu.G. Rapoport ◽  
◽  
...  
Keyword(s):  
Gravity Waves ◽  
Greenhouse Effect ◽  
Internal Gravity Waves

Height of the penetration into the ionosphere for internal atmosphere gravity waves

2014 ◽  
Vol 20 (4(89)) ◽  
pp. 31-41 ◽  
Author(s):  
G.V. Lizunov ◽  
◽  
A.Y. Leontiev ◽  
Keyword(s):  
Gravity Waves
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