An experimental study of the spin-up of a thermally stratified rotating fluid

A simple model of the spin-up of a continuously thermally stratified rotating fluid is examined experimentally. The geometry of the system consists of a right circular cylinder bounded on the top and bottom by perpendicular planes. The cylinder contains a linearly stratified fluid, initially rotating in solid body rotation with an angular velocity ω(1-∊). At time t = 0, the rotation rate of the boundary is changed to ω. The adjustment of the fluid to the new angular velocity, described by Walin and others for the case of nonconducting walls, is here expanded to treat the case of a partially conducting side boundary. Laboratory experiments testing the validity of the linear theory are discussed. The external rotational Froude number is very small, the Rossby number is 0(E ½), and the stratification parameter B = N/2ω is 0(1). The side wall conditions are shown to be effectively insulating in the framework of the expanded theory. While experiments confirm the qualitative aspects of the theory, namely spin-up in a time scale of 0(E -½ω−1), measurement of the time dependent density field indicates that the first modal spin-up time is significantly shorter than predicted. Several possible causes for this observed difference between theory and experiment are discussed. While a direct comparison is impossible, the observed faster spin-up appears to be consistent with the experimental results of Buzyna and Veronis. The observed laboratory density field is also compared for one experiment with the results of the numerical model for stratified spin-up developed by Barcilon, Lau, Piacsek and Warn-Varnas (see accompanying paper).