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

Jorge D'Elia, Noberto Nigro, Mario Alberto Storti


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 × 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.
[To appear in International Journal of Computational Fluid Dynamics.Author Posting. (c) Taylor & Francis, 2007. ]

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