Axisymmetric compressible flow in a rotating cylinder with axial convection

The steady compressible flow of an ideal gas in a rotating annulus with thermally conducting walls is considered for small Rossby number ∊ and Ekman number E and moderate rotational Mach numbers M. Attention is focused on nonlinear effects which show up when σ and eM²are not small (σ= ε/HE^1/2, H is the dimensionless height of the container). These effects are not properly predicted by the classical linear perturbation analysis, and are treated here by quasi-linear extensions. The extra work required by these extensions is only the numerical solution of one ordinary differential equation for the pressure. Numerical solutions of the full Navier—Stokes equations in the nonlinear range are presented, and the validity of the present approach is confirmed.