| Abstract: |
| In this talk, we revisit the problem of emergence of fast gravity-wave oscillations in rotating, stratified flow using a reduced Primitive Equation model introduced by Lorenz in 1980. It will be shown that fast oscillations can develop brutally once a critical Rossby number is crossed. This is in contradistinction with fast oscillations emerging according to an exponential smallness scenario reported in previous studies on other related models. The consequences of this dynamical transition on the closure problem based on slow variables will be discussed. In that respect, we introduce a novel variational perspective on the closure problem exploiting manifolds. This framework allows for a unification of previous concepts such as the slow manifold or other concepts of ``fuzzy'' manifold. It allows furthermore for a rigorous identification of an optimal limiting object for the averaging of fast oscillations, namely the optimal parameterizing manifold (PM). Candidates of good approximation of this optimal PM will be presented, and the approach will be numerically illustrated. This is joint work with Mickael D. Chekroun (UCLA) and James C. McWilliams (UCLA).
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