Superharmonic and triadic resonances in a horizontally oscillated stably stratified square cavity

Abstract

The response to harmonic horizontal oscillations of a stably stratified fluid-filled two-dimensional square container is examined as the forcing amplitude is increased. For the studied forcing frequency, the response flow at very small forcing amplitudes is a synchronous periodic flow with piecewise-constant vorticity in regions delineated by the characteristics emanating from the corners of the container, regularized by viscosity. The second temporal harmonic of the forced response flow resonantly excites an intrinsic mode of the stratified container, whose magnitude grows as the square of the forcing amplitude. Above a critical forcing amplitude, a sequence of pairs of other container modes are excited via triadic resonances with the second-harmonic-driven mode. The flows are computed from the Navier–Stokes–Boussinesq equations and the ensuing dynamics is analysed using Fourier techniques, providing a comprehensive picture of the transition to internal wave turbulence.