Energy transfer from large to small scale is a critical issue in the dynamics of ocean and atmosphere, and also an important fundamental question. Owing to density-stratification and rotation, ocean and atmosphere support internal and inertial waves which are known to propagate in form of oblique beams. Dispersion properties of these waves lead to strong variation of beam width upon reflection at a sloping boundary. In confined fluid domains, successive reflections may lead to formation of a closed trajectory, an internal wave attractor. Thus, the energy input at a global scale can be strongly concentrated on a closed loop of finite width, implying nonlinear instabilities very likely to occur. They arise indeed in form of parametric subharmonic instability which generates secondary waves having smaller scale than the width of the wave beams of the attractor. This two-step mechanism has been revealed experimentally by the applicant of this project during a short visit to the host organization. It was observed also that at large amplitude of input perturbation a patchwork structure of internal wave field is formed which hardly bears a resemblance to a classic pattern of a wave attractor. Observations of patchwork structures in ocean were recently reported in the literature.
The scientific goal is to investigate this mechanism with an emphasis on issues important for interpretation of oceanographic data: What is the influence of the scale effects? How does the threshold amplitude needed to destabilize an attractor depend on the Reynolds number? How does the Reynolds number affect the spatial scale of secondary waves? Does the type of instability change (locally?) with amplitude of oscillations? How is formed the patchwork structure of the wave field? What are the energy contents of different components of the wave field? Are the key mechanisms similar in stratified and rotating fluids? We are aiming to answer these questions by launching a broad experimental campaign.
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