Inertial Wave Beam Path in a Non-uniformly Rotating Cylinder with Sloping Ends

Abstract

The features of the inertial wave beam propagation in a librating cylindrical cavity with symmetrically inclined end-walls are experimentally studied. The geometry provides the existence of two flow regimes – inertial wave attractor and the case of symmetric beam reflection that is like the closed periodic orbit in a rotating spherical shell. Despite the visual similarity, the nature of the regimes is different. The first is due to the geometric focusing of the beams into the limit cycle after a series of reflections from sloping ends, and the second with the symmetry wave path for a given frequency and cavity geometry. Although the geometry of the problem is three-dimensional, these regimes are almost two-dimensional: the closed wave trajectory is trapping near the plane of the direction of the slope gradient of the ends. Also, we study the scaling laws for the width and amplitude of the oscillating shear layers in the axial section. At large amplitudes of the librational forcing, the global azimuthal vorticity grows in a quadratic manner, which indicates the development of a nonlinear regime of inertial waves. Fourier analysis shows that a spectrum, besides the fundamental frequency, contains two sets of closely spaced subharmonic frequencies that satisfy the triadic resonance condition.