Nonlinear regimes of inertial waves in a rotating spherical shell are experimentally investigated. Energy is injected into the system through the prograde circular oscillations of an inner core, along a trajectory with constant radius in the equatorial plane of the shell. Under these conditions, the basic wave motion is represented by either free spiral-shaped shear layers or spatial wave resonance. As the amplitude of the core oscillation increases, secondary waves with subharmonic frequencies that satisfy the temporal condition for triadic interactions are generated. There are three different patterns of significant spectral peaks in the azimuthal velocity spectrum: subharmonics with pairs of different frequencies (T), strictly parametric fluid oscillations (P), and subharmonics with pairs of different frequencies containing a slow (low-frequency) component (L). The coexistence of all regimes is manifested when the directly forced inertial waves experience a spatial resonance. The instabilities appear simultaneously in several zones of the spherical shell with different frequencies and wave numbers: short-wave subharmonics occur close to the cavity outer wall, while long-wave subharmonics appear near the rotation axis. Beyond the frequency range of the spatial inertial wave resonance, the P-type instability weakens, while the L-type (T-type) becomes dominant at high (low) forcing frequencies. The development of wave instability is accompanied by the generation of slow quasi-two-dimensional vortices effectively revealed in period-averaged flow patterns. The frequency of these vortices is proportional to the azimuthal wavenumber and depends on the magnitude of the zonal flow velocity.
Subbotin et al. (Fri,) studied this question.