Induced Flow due to Wavy Motion of a Wall I. The Case of Small and Moderately Large Reynolds Numbers

Abstract

A two-dimensional viscous flow induced by sinusoidal wavy motion of an infinite wall is considered for Reynolds numbers which are of the order of magnitude both less and greater than unity. It is found that the induced mean steady flow is proportional to the ratio 4π²a²⁄L²(a⁄L<<1), where a and L are the amplitude and the wavelength of the wavy wall, respectively. It is also found that the steady flow velocity approaches to a constant value in the form of damped oscillation with respect to the distance from the wall.