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

Abstract

Laboratory and numerical experiments have been conducted to study the secular spin-up of both a homogeneous and a thermally stratified rotating fluid in a right cylinder. In these experiments, the angular velocity of the container increases linearly in time from some initial rotation rate at t = 0. A simple quasi-geostrophic model is developed to describe the adjustment of the fluid over the characteristic spin-up time scale to the constant angular acceleration of the basin. Good agreement is found between the observed interior temperature and azimuthal velocity fields and the theory in both the homogeneous and stratified secular experiments. This result is in contrast to the much faster adjustment observed in stratified instantaneous spin-up experiments reported earlier. The main difference between these experimental cases is the inability of secular forcing to excite energetic inertial–gravity-wave transients during the initial phases of secular spin-up. Thus, the asymptotic theory which has filtered out these initial higher-frequency transients is accurate even though the inertial period is not much smaller than the characteristic spin-up time scale.