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Geometric and Multiscale Methods for Geophysical Fluid Dynamics
Flows in the atmosphere and ocean exhibit complex multi-scale dynamics that present a challenge both for analytical and numerical methods. To a high degree of approximation, the large scale flows of these systems can be considered inviscid, and the underlying Hamiltonian structure of the equations can be exploited, for example to develop simplified models that retain the structure of conservation laws and symmetries of the full systems. The Hamiltonian approach in analytical modeling was pioneered by Salmon, Holm, Shepherd and developed further by others. Recent times have also seen successes in the use of Hamiltonian methods in the numerical modeling of geophysical fluids. Nevertheless, the Hamiltonian formulation is incomplete for realistic modeling. Due to the cascade of energy to small scales, the Hamiltonian picture must be supplemented by a parameterization of subscale processes. The influence of internal/gravity waves on large scale motions represents conservative, meso-scale behavior. At the micro-scale, turbulent diffusion must be modeled in a way that respects the balance of energy and does not prohibit upscale cascades. Promising in this regard are stochastic methods. A practical synthesis of these modeling techniques can only be reached through active dialog with scientists from meteorological centers.
This workshop will provide a discussion forum for scientists working on geometric (i.e. variational/Hamiltonian) analytical and numerical methods for geophysical fluid dynamics, scientists working on parameterization of meso-scale (i.e. internal/gravity waves) and micro-scale (i.e. stochastic turbulence) effects, and scientists working on applications in meteorology and climate simulations.
At present, we are approaching a conflux of these research areas, where one can begin to envision a new breed of prediction tools, in which Hamiltonian-based large scale dynamics, with excellent energy balance, correct reduced dynamics in asymptotic parameter regimes, and superior statistical spectra, are coupled to advanced parameterization models of meso-scale wave effects and micro-scale stochastic turbulence.