Systematic analysis of inertial wave patterns in spherical shell

Inertial waves for an incompressible fluid inside a spherical shell are investigated. Inertial waves have an important role for the motion in the liquid outer core of the earth, the atmosphere and the oceans. Different inertial modes are excited as the modulation frequency is varied. The inertial waves propagating from inner sphere have inclined characteristics throughout the shell and are reflected back from the outer sphere. For larger forcing amplitudes and smaller libration frequencies, the inertial waves become unstable and can be stated as turbulent. The angle of propagation of waves with respect to axis of rotation is dependent on libration frequency. A layer is present at the tangent of inner sphere's equator and parallel to the axis of rotation called as Stewartson layer and its thickness and properties are dependent on libration frequency and amplitude. Zonal flow becomes unstable for larger amplitudes. Good agreement is found when the experimental results are compared with theory.