Subgrid scale closure for the Burgers equation based on stochastic mode reduction

Applying a systematic stochastic mode reduction strategy (Majda et al 2003), a local closure for the subgrid scale dynamics in the Burgers equation is constructed. Using an energy and momentum conserving finite difference discretization and introducing a fine and a coarse grid, the model variables are split into fast and slow modes. This is a different approach compared to previous studies, where the separation between the modes is done by truncation in EOF or Fourier space. Also, for the first time the nonlinear dynamics of the fast modes is parameterized as an oscillating Ohrnstein-Uhlenbeck (OU) process, instead of a simply damped OU process. The model performs well in reproducing the variance and the autocorrelation function of the full model. Switching from the damped OU process to the oscillating OU process further improves the impact of the derived closure.