Nonlinear regimes of inertial wave attractors generated by a precessing lid: Zonal flows and Rossby waves

Abstract

Fluid flow excited by inertial waves in a rotating annulus with a trapezoidal cross section is experimentally investigated. The forcing is introduced by the precession of a flat annular lid bounding the cavity. Such a setup allows to investigate interactions between inertial waves and zonal flows in the presence of equivalent topographic beta-effect, and its dynamic behavior under weak and strong forcing is experimentally studied for the first time. Due to the specific dispersion relation of inertial waves, a cavity shape supports wave attractors that appear only for retrograde lid precession. At a relatively low wave intensity, a zonal flow is generated in the vicinity of a “virtual” axial cylinder, the radius of which coincides with the radius of the focusing reflection from the conical bottom. A succession of non-linear regimes is observed as forcing increases, starting with a clearly identifiable case of triadic resonance. Further, the frequency spectrum is progressively enriched by emergence of additional discrete components, gradually reaching the state of “overheated” wave turbulence with a significant continuous background of the frequency spectrum. Finally, a strong low-frequency component develops in the frequency spectrum, and the continuous background of the spectrum decreases dramatically. The low-frequency component corresponds to azimuthally periodic structures identified as Rossby waves. In the case of strong forcing, a long-term variability of zonal-flow velocity at the timescale of tens of forcing periods is observed, which is likely a consequence of the interaction of azimuthal structures corresponding to a rich wave number set.