The numerical calculation of rotating fluid flows at low Rossby numbers

Abstract

In this paper some numerical methods which can be used to calculate flows in a rapidly rotating fluid are described. The flows considered are those w~,thin a closed cylindrical container, rotatln 9 about an axis which is aligned with the sidewalls, when there is a slow motion superposed upon the rigid rotation of the fluid, so that the Rossby number Re is small. In addition, the Ekman number E Is considered to be small so that viscous diffusion is confined to thin layers in the fluid (Greenspan, 1968). The flows calculated are those in the geostrophlc region of the fluid where the m~tion is depth-lndependent andthe governing equations are two-dimensional. However, between the geostrophlc flow and the walls of the container there are ageostrophlc layers of two types; by analysing these layers theoretically, appropriate boundary conditions on the geostrophlc flow can be calculated. The primary motlvatlen behind the study of these flows Is to model the effects observed in experiments performed on fluids in cylindrical containers under almost rigid rotation. For this reason both the geometry and parameter regimes examined will correspond to those usually used in laboratory studies; in particular the range of Rossby numbers considered includes those values for which inertial effects are significant.