×

Natural oscillations of a rotating spherical fluid layer of variable depth. (English. Russian original) Zbl 1215.76109

Fluid Dyn. 45, No. 1, 121-125 (2010); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza 2010, No. 1, 137-142 (2010).
Summary: Small harmonic oscillations of the free surface of a thin fluid layer covering a rotating sphere are considered. The fluid is in the central field of sphere gravity and is exposed to the centrifugal and Coriolis forces. It is assumed that the fluid layer depth is independent of the longitude. In this formulation the problem is governed by a differential equation with singular coefficients that generalizes the Laplace tidal equation. The method of local separation of singularities is applied to integrate this equation. The solutions obtained are compared with the corresponding modes of the Laplace tidal equation, that is, the solutions of the problem for a fluid layer of constant depth.

MSC:

76U05 General theory of rotating fluids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] P.H. Le Blond and L.A. Mysak, Waves in the Ocean, Elsevier, Amsterdam (1978).
[2] J. Kroll and P.P. Niiler, ”The Transmission and Decay of Barotropic Topographic Rossby Waves Incident on a Continental Shelf,” J. Phys. Oceanogr. 6, 432 (1976).
[3] P.B. Rhines, ”Slow Oscillations in an Ocean of Varying Depth. Part 1. Abrupt Topography,” J. Fluid Mech. 37, 161 (1969). · Zbl 0175.52803
[4] M.I. Ivanov, ”Nonaxisymmetric Solutions of Laplace’s Tidal Equation and Rossby Waves.” Fluid Dynamics 42, No. 4, 644 (2007). · Zbl 1354.76034
[5] M.I. Ivanov, ”Horizontal Structure of Atmospheric Tidal Oscillations,” Fluid Dynamics 43, No. 3, 447 (2008). · Zbl 1210.76200
[6] M.I. Ivanov, ”Wave Motions of Fluids in Complicated Domains with Account for Rotation,” Cand. Sci. (Phys.-Math.) Dissertation, Russian Academy of Sciences, Institute for Problems in Mechanics, Moscow (2008).
[7] G.R. Goldsborough, ”The Tides in Oceans on a Rotating Globe. Part 1,” Proc. Roy. Soc. London. Ser. A. 117, 692 (1928). · JFM 54.1015.01
[8] C. Eckart, Hydrodynamics of Oceans and Atmospheres, Pergamon Press, New York (1960). · Zbl 0204.24906
[9] H. Lamb, Hydromechanics, Cambridge Univ. Press, Cambridge (1932).
[10] L.N. Sretenskii, Dynamic Theory of Tides [in Russian], Nauka, Moscow (1987).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.