Asymptotic theory of inertial convection in a rotating cylinder

Abstract

Inertial convection in a fluid contained in a rotating cylinder heated uniformly from below is investigated on the basis of the assumption that convection at leading order can be represented by a single or several inertial wave modes which propagate either in the prograde or retrograde direction. Buoyancy forces appear at the next order to drive inertial convection against the effect of viscous damping. Asymptotic expressions for inertial convection for four different combinations of the sidewall boundary condition are derived for a cylinder of arbitrary aspect ratio. New convection patterns in rotating cylinders are revealed by the asymptotic analysis. A fully numerical solution of the same problem is also carried out, demonstrating a quantitative agreement between the asymptotic and numerical analysis.