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Perturbation series of the Euler hydrodynamic equations at small Froud's number

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, apart that in the perturbation series the first order velocities are of the zero order due to the singularity of the series.

Euler's hydrodynamic equations ; Froud's number ; Sigular perturbations

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