Low-Frequency Oscillations in a Rotating Annulus with Topography

Abstract

Experiments were performed in a rotating, differentially heated annulus, with and without bottom topography of azimuthal wavenumber 2. Both water and a viscous glycerol-water mixture were used as a working fluid. In one series of experiments, measurements of azimuthal velocity u were carded out by Doppler-laser velocimetry at midradius and at ? and ? depth. In the other, temperature measurements were made by a set of thermistors at three different heights and three different radii. Results were analyzed by Fourier transformation, separately in space and in time, and in terms of complex empirical orthogonal functions (CEOFs). In the experiments with topography, a standing wave 2 is generated, with larger amplitude at the upper level and a tilted wave structure. The two leading CEOFs contain a very large fraction of the variance, and give an excellent picture of the spatial modulation of the traveling baroclinic waves. The dominant baroclinic wave has azimuthal wavenumber 4, 5 or 6, according to the nondimensional parameters of the given experiment, and pronounced sidebands due to the topography. The modulation of this wave is such that its largest amplitude occurs at the lower level upstream of the two topographic ridges. At the upper level, the modulation is weaker, with the maximum wave amplitude located downstream of the ridges. Partial decoupling of the two wave trains attached to the two ridges is evident in one experiment. Low-frequency vacillation of the entire flow pattern is apparent; this vacillation has a period of about 50 annulus rotations in the viscous mixture. The possible relevance of this topographically induced vacillation to the extratropical 30?60 day oscillation is discussed.