The problem of a two-dimensional cavity flow of an ideal fluid with small unsteady disturbances in a gravity free field is considered. By regarding the unsteady motion as a small perturbation of an established steady cavity flow, a fundamental formulation of the problem is presented. It is shown that the unsteady disturbance generates a surface wave propagating downstream along the free cavity boundary, much in the same way as the ...
A simple, but crude, analysis shows among other things that the radius at which the disturbance velocity is a maximum is roughly that at which the velocity of the Poiseuille flow is equal to the frequency, f, times the disturbance wavelength. Eigenfunctions are found precisely for the two limiting cases in which, as f a to the 2nd power/v tends to infinity, the disturbance becomes confined to a thin layer ...
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(PERTURBATION THEORY
