Multistablity Effects in Internal Wave Modes and Wave Attractor Regimes in Stratified Fluids

Unlike many classical wave phenomena in fluid dynamics, internal and inertial waves exhibit unique behaviour that challenges conventional modal descriptions. In typical closed hydrodynamical systems, the dynamics are often described in terms of global modes - solutions that satisfy boundary conditions and oscillate harmonically in time, such as Fourier modes in rectangular domains. However, internal and inertial waves defy this framework. These waves preserve a constant angle with respect to gravity (for internal waves) or the rotation axis (for inertial waves) upon reflection at boundaries. This constraint leads to striking consequences for both their linear and nonlinear dynamics. In stratified or rotating fluids, wave beams tend to focus and form persistent patterns known as wave attractors, rather than standing global modes. Such wave attractors may dominate energy pathways, particularly in complex geometries with pronounced slopes to the anisotropy direction. The dynamical impact of internal and inertial waves is far from negligible: they are capable of transporting significant kinetic energy over vast distances in the ocean interior. In the deep ocean, their vertical amplitudes can reach several hundred metres, underscoring their crucial role in large scale oceanic processes. Rectangular tanks aligned with gravity and/or rotation therefore represent an exceptional, yet highly important, case. Our work focuses on two aspects of internal wave dynamics in this context. First, we investigate the influence of the aspect ratio on the transition to turbulence and mixing for structurally stable wave attractors. Second, we examine the interplay between wave - attractor regimes and modal structures in the vicinity of rectangular geometries. Surprisingly, a conventional rectangular geometry may exhibit much more complex regimes with multistability, than those observed for simple wave attractors. We demonstrate competition between different triadic instability pairs, leading to multistability and a nearly uniform picket -fence spectrum, which is markedly different from the spectrum resulting from cascades of triadic instabilities driven by large aspect ratio wave attractors.