The large-scale effects of flow over periodic mesoscale topography

Airflow over two-dimensional sinusoidal mesoscale topography is studied using simulations from a numerical model, with an eye toward quantification of the net effect on the large-scale flow. Analytic formulas are derived for the amount of form drag, that is, the total slowdown of the flow, as a function of mountain height, and predictions from such formulas are shown to agree well with model results. The vertical distribution of drag, due to gravity wave breaking at various altitudes, is briefly discussed. The flow is divided into two regimes: a "linear" regime for small mountain heights, and a "blocked" regime for taller mountains. The latter is always accompanied by a layer of stagnant fluid in the valleys. Separate analytic arguments are used in each regime, and together they provide a prediction of form drag over a wide range of parameter space. The cutoff mountain height between the two regimes is also argued analytically. A key difference from flow over isolated mountains is explained. This suggests that studies of flow over both isolated and periodic topography are needed in the development of orographic parameterizations for large-scale models.