On the tidal motion around the earth complicated by the circular geometry of the ocean’s shape. (English) Zbl 0952.35101

Ibragimov, Ranis N.

Electron. J. Differ. Equ. 2000, Paper No. 35, 11 p. (2000).

Summary: We study the Cauchy-Poisson free boundary problem on the stationary motion of a perfect incompressible fluid circulating around the Earth. The main goal is to find the inverse conformal mapping of the unknown free boundary in the hodograph plane onto some fixed boundary in the physical domain. The approximate solution to the problem is obtained as an application of this method. We also study the behaviour of tidal waves around the Earth. It is shown that on a positively curved bottom the problem admits two different high-order systems of shallow water equations, while the classical problem for the flat bottom admits only one system.

MSC:

35Q35	PDEs in connection with fluid mechanics
86A05	Hydrology, hydrography, oceanography
76B07	Free-surface potential flows for incompressible inviscid fluids

Keywords:

Cauchy-Poisson free boundary problem; stationary motion of a perfect incompressible fluid; inverse conformal mapping; tidal waves; shallow water equations