Nonlinear advection schemes and energy cascade on semi-staggered grids.

Abstract

A common problem with nonlinear advection schemes is the false accumulation of energy at the smallest resolvable scales. In this paper, it is demonstrated that, in contrast to the staggered grid, the conservation of energy and enstrophy on the semi-staggered grids does not guarantee that the erroneous transport of energy from large to small scales will be effectively restricted. Using a new approach to the application of the Arakawa Jacobian, a scheme for a semi-staggered grid which exactly reflects the Arakawa theory for nondivergent flow is obtained for the first time. -from Author