Numerical simulations of axisymmetric inertial waves in a rotating sphere by finite elements

Axisymmetric inertial waves of a viscous fluid that fill a perturbed rotating spherical container are numerically simulated by finite elements. A laminar flow of an incompressible viscous fluid of Newtonian type is assumed in the numerical simulations. A monolithic computational code is employed, which is based on stabilized finite elements by means of a Streamline Upwind Petrov Galerkin ( SUPG) and Pressure Stabilized Petrov Galerkin (PSPG) composed scheme. The Reynolds number is fixed as 50,000, while the ranges of the Rossby and Ekman numbers are 0.2 <= Ro <= 1 and 2 x 10(-5) <= Ek <= 10(-4), respectively. Some flow visualizations are performed. The pressure coefficient spectrum at the centre of the sphere is plotted as a function of the frequency ratio and some resonant frequencies are identified. The position of these resonant frequencies are in good agreement with previous experimental and analytical ones in the inviscid limit.