Nonlinear azimuthal waves in a centrifuge

Abstract

Azimuthal wave motions in a liquid which partially fills a cylinder (centrifuge) rapidly rotating about a horizontal axis are discussed in this paper. Under the action of centrifugal force the liquid is pressed to the wall of the cylinder and moves together with it about the central air core. The vibrations of the free surface which arise are called centrifugal waves [1]. The difficulties of their theoretical investigation are related to the nonlinearity both of the basic equations and also of the boundary condition for the pressure on the free surface; therefore they have previously been studied only by linear methods [1, 2]. Nonlinear azimuthal waves in a centrifuge with an infinite radius of the rotating cylinder are analytically described below. The waves found are an analog of Gerstner trochoidal waves on a cylindrical surface. An approximate solution for a centrifuge with a finite outer radius is constructed by matching the waves obtained to the known linear ones.