Axisymmetric inertial oscillations of a fluid in a rotating spherical container

Abstract

This paper describes an experiment performed with a fluid-filled sphere whose rotation speed about a fixed axis was forcibly varied in a slight but sinusoidal manner about a non-zero mean value. The object of this experiment was both to excite axisymmetric inertial eigen-oscillations within the relatively low viscosity fluid through the mild pumping action of the oscillatory Ekman boundary layer near the wall, and to measure and compare with theory some of the properties of such modes.Seven distinct fluid resonances were detected via pressure measurements made along the axis for various ratios of the excitation to the mean rotation frequency. For the three most pronounced of those modes, the observed frequency ratios agree within ½ of 1% with the corresponding ratios predicted from linear, small viscosity theory. The response amplitudes at the various resonances and the rates of decay upon switching off the excitation also compare favourably with theory, although the observed amplitudes are systematically lower and the decays more rapid by a few per cent to several tens of per cent.The theory referred to above is largely that of Greenspan (1964, 1968). It is in part rederived here from energy considerations.