Prediction Errors Associated with Sparse Grid Estimates of Flows over Hills

Abstract

Numerical simulations of geophysical flows have to be done on very sparse grids. Nevertheless, flows over moderately sloped hills can be predicted quite accurately as long as the near ground vertical resolution is reasonably dense. Recirculation flows behind steeper hills are associated with slow convergence towards grid independent integrations, but even then moderately stratified flows of this type can be predicted usefully accurately. For better horizontal grids than about half the hill-height Δx 1/H ≈ 0.5 or so, separation and recirculating domains are predicted with an error factor comparable to 0.3. The characteristic wavelength of lee waves is predicted more accurately while the lee wave amplitude and the maximum turbulence intensity in recirculating domains are underestimated by factors comparable to 0.3. Strongly stratified flows may be associated with hydraulic transitions and even this is predicted on quite coarse grids, up to say Δx 1/H ≈ 0.5. However, the details of such flows turn out to be predicted with considerable errors also on high-resolution grids. Inaccurate modelling of stratified turbulence is a main contributor to this error.