Abstract.Motions of the ocean and atmosphere are characterized by the large Reynolds and small Froud numbers. In order to describe these motions the Euler equations of ideal fluid are considered and the expansion in perturbation series is obtained using the dimensionless form depending on the Froud number. It is shown that expanding the dimensionless Euler momentum equation in the perturbation series it is defined only for the fluid in motion. The perturbation is singular and should include the zero order velocities in the perturbation series. In the C. Eckart notation motions of the atmosphere and oceans were considered as first or higher order perturbation terms which complicates definition of the first order energy equation. Taking into account singularity of the expansion the first order energy equation follows clearly from the applied perturbation method. The obtained equation has the form accepted by C. Eckart, although that in the perturbation series the first order velocities are of the zero order due to the singularity of the series.

Received: September 28, 2008

AMS Subject Classification: 76M45, 86A05, 86A10

Key Words and Phrases: Euler's hydrodynamic equations, Froud's number, singular perturbation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 1