Wentzel-Kramers-Brillouin solutions to an equation of internal gravity waves in a stratified medium with slowly varying shear flows. (English. Russian original) Zbl 1509.76019
J. Appl. Mech. Tech. Phys. 63, No. 3, 392-399 (2022); translation from Prikl. Mekh. Tekh. Fiz. 63, No. 3, 25-33 (2022).
The study deals with internal gravity waves in a stratified medium and in the presence of background shear ocean flows. The linear equation for small perturbations of the vertical component of the velocity field, assuming constant Brunt-Väisälä frequency and one-dimensional background flow, is subjected to modal decomposition. This leads to a spectral boundary value problem.
Approximate formulas for eigenfunctions and dispersion curves for this spectral boundary value problem are derived assuming that the background shear flow is slowly varying, by means of the WKB approximation. The situation differs in the absence or presence of turning points corresponding to singularities of the underlying ODE. In the latter case the asymptotic behavior of the Airy functions is found necessary close to an (approximate) analytical solution for the dispersion relation.
These approximate formulas are tested numerically in the case of a multidirectional shear flow for which no turning point arises, and in the case of a unidirectional shear flow with turning points.
Approximate formulas for eigenfunctions and dispersion curves for this spectral boundary value problem are derived assuming that the background shear flow is slowly varying, by means of the WKB approximation. The situation differs in the absence or presence of turning points corresponding to singularities of the underlying ODE. In the latter case the asymptotic behavior of the Airy functions is found necessary close to an (approximate) analytical solution for the dispersion relation.
These approximate formulas are tested numerically in the case of a multidirectional shear flow for which no turning point arises, and in the case of a unidirectional shear flow with turning points.
Reviewer: Vincent Duchêne (Rennes)
MSC:
| 76B55 | Internal waves for incompressible inviscid fluids |
| 76B70 | Stratification effects in inviscid fluids |
| 86A05 | Hydrology, hydrography, oceanography |
Keywords:
buoyancy frequency; Airy function; perturbation method; eigenfunction; dispersion curve; spectral boundary value problemReferences:
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