We study a Hamiltonian toy model for a Lagrangian fluid parcel in the semi-geostrophic limit which exhibits slow and fast dynamics. We first reinject unresolved fast dynamics into the deterministic equation through a stochastic parametrization that respects the conservation of the energy of the deterministic system. In a second step we use stochastic singular perturbation theory to derive an effective reduced stochastic differential equation for the slow dynamics. We verify the results in numerical simulations.

Additional Metadata
Keywords Homogenization, Multi-scale systems, Stochastic parametrizations
THEME Other (theme 6)
Publisher Elsevier
Journal Physica - D, Nonlinear Phenomena
Project Thermostat closures for inviscid fluids
Note doi:10.1016/j.physd.2013.03.010
Citation
Frank, J.E, & Gottwald, G.A. (2013). Stochastic homogenization for an energy conserving multi-scale toy model of the atmosphere. Physica - D, Nonlinear Phenomena, 254, 45–56.