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

Ishlinsky Institute for Problems in Mechanics RAS, 101-1, Pr. Vernadskogo, 119526 Moscow, Russia
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Symmetry 2020, 12(11), 1865; https://doi.org/10.3390/sym12111865
Received: 5 September 2020 / Revised: 9 November 2020 / Accepted: 10 November 2020 / Published: 13 November 2020
(This article belongs to the Special Issue Wave Processes in Fluids with Symmetric Density Stratification)
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. View Full-Text
Keywords: internal gravity waves; stratified medium; shear flows; dispersion relations internal gravity waves; stratified medium; shear flows; dispersion relations
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MDPI and ACS Style

Bulatov, V.; Vladimirov, Y. Analytical Approximations of Dispersion Relations for Internal Gravity Waves Equation with Shear Flows. Symmetry 2020, 12, 1865. https://doi.org/10.3390/sym12111865

AMA Style

Bulatov V, Vladimirov Y. Analytical Approximations of Dispersion Relations for Internal Gravity Waves Equation with Shear Flows. Symmetry. 2020; 12(11):1865. https://doi.org/10.3390/sym12111865

Chicago/Turabian Style

Bulatov, Vitaly, and Yury Vladimirov. 2020. "Analytical Approximations of Dispersion Relations for Internal Gravity Waves Equation with Shear Flows" Symmetry 12, no. 11: 1865. https://doi.org/10.3390/sym12111865

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