Georgia Institute of Technology College of Sciences

Backscatter is the process of energy transfer from small to large scales in turbulence; it is crucially important in the inverse energy cascades of two-dimensional and quasi-geostrophic turbulence, where the net transfer of energy is from small to large scales. A numerical scheme for stochastic backscatter in the two-dimensional and quasi-geostrophic inverse kinetic energy cascades is developed and analyzed. Its essential properties include a local formulation amenable to implementation in finite difference codes and non-periodic domains, smooth behavior at the coarse grid scale, and realistic temporal correlations, which allows detailed numerical analysis, focusing on the spatial and temporal correlation structure of the modeled backscatter. The method is demonstrated in an idealized setting of quasi-geostrophic turbulence using a low-order finite difference code, where it produces a good approximation to the results of a spectral code with more than 5 times higher nominal resolution. This is joint work with I. Grooms and A. J. Majda