The large-scale effects of flow over periodic mesoscale topography

Airflow over two-dimensional sinusoidal mesoscale topography is studied usi ng 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 func tion of mountain height, and predictions from such formulas are shown to ag ree well with model results. The vertical distribution of drag, due to grav ity 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 alway s accompanied by a layer of stagnant fluid in the valleys. Separate analyti c 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 hei ght between the two regimes is also argued analytically. A key difference from flow over isolated mountains is explained. This sugge sts that studies of flow over both isolated and periodic topography are nee ded in the development of orographic parameterizations for large-scale mode ls.