Stably stratified square cavity subjected to horizontal oscillations: responses to small amplitude forcing

A stably stratified fluid-filled two-dimensional square cavity is subjected to harmonic horizontal oscillations with frequencies less than the buoyancy frequency. The static linearly state, which an equilibrium of unforced system, not for any non-zero forcing amplitude. As viscous effects are reduced, horizontally forced flows computed from Navier–Stokes–Boussinesq equations tend have piecewise constant or linear vorticity within pattern characteristic lines originating corners cavity. These well described in inviscid limit by a perturbation analysis using amplitude as small parameter. At first order, this leads hyperbolic system subject boundary conditions and spatio-temporal symmetries associated forcing. Fredholm alternative determines type solutions system: either response uniquely determined forcing, it resonant corresponds intrinsic mode Both types responses investigated terms waveform function satisfying set functional related behaviour characteristics system. In particular, non-retracing (ergodic) may lead fractal responses. Models dissipation also formulated adjust model obtained nonlinear simulations.