The Inertial Wave Frequency Spectrum in a Cylindrically Confined, Inviscid, Incompressible Two Component Liquid

摘要

A theoretical and experimental study is made of the phenomenon indicated in the title. It is shown that for inertial waves, just as for gravity waves, there are discontinuities in the tangential particle velocities at the interface in a real, two-component liquid, a fact implying the existence of a vortex sheet. For the case where the two liquids completely fill the cylinder, other results are obtained that are analogous to those for gravity waves. In particular, if the liquids are nearly of the same density, there are two sets of frequencies, one set characterizing oscillations of the liquid mass as a whole, the other set characterizing very low frequency oscillations at the interface. For the case in which the two liquids have markedly different densities, there are again two sets of frequencies, one set characterizing oscillations of the inner liquid as though the outer liquid were a solid mass, the other set characterizing oscillations of the outer liquid as though the inner were absent. (Author)