Experimental and numerical studies of ordered and chaotic dynamics in rotating stratified fluids are proposed. Numerical computations and laboratory experiments will further clarify the role of sidewall boundaries and boundary layer separation in observations of two-layer baroclinic chaos. Direct retrieval of Poincare sections of fluid column motions will allow a comparison of LaGrangian mixing in the laboratory with that predicted by models. For example, mixed wave states, or vacillatory states may generate localized (in space) chaotic particle dynamics that can be predicted by applying Melnikov's method to the governing Hamiltonian dynamical system for parcel motion. The effects of weak to moderate "seasonal" forcing will be studied both in laboratory and in fully resolved two-layer models, with the goal of verifying the robustness of previous results which showed a dramatic destabilization and loss of predictability in low order models that include such forcing. A focus of the proposed research is the application of recent ideas from dynamical systems to both experimental and numerical data on baroclinic flows. These techniques include singular value decomposition, linear and nonlinear prediction, and principle orthogonal decomposition. We hope to generate cleaner pictures (e.g. Poincare sections and return maps) of the deterministic part of the data, along with better estimates of dimension, Lyapunov exponents, and other qualitative signatures of nonlinear baroclinic flow. Low-order descriptions of the fractal dynamics observed in high resolution numerical solutions of the quasi-geostrophic partial differential equations will be sought.
