Flow over two-dimensional sinusoidal topography is studied using simulations from a nonhydrostatic anelastic numerical model. Analytic formulae are derived for the amount of form drag as a function of mountain height, mountain horizontal lengthscale, flow velocity, and Brunt-Vaisala frequency. Predictions from such formulae are shown to agree well with model results over a wide range of parameter space.
The flow is divided into two regimes: a ``linear'' regime for small mountain heights, and a ``blocked'' regime for taller mountains. In the first, the form drag is equal to that calculated from linear theory; in the second, a layer of stagnant flow exists in the valleys and the form drag does not match the linear prediction. The cut-off between these two regimes is argued theoretically, varying only slightly with horizontal mountain lengthscale.
It is found that the blocked layer adjusts so that the effective height of the mountain, i.e. the height above the blocked layer, is roughly the same over an order of magnitude of peak-to-valley heights h_max. This reduces the quadratic dependence of the form drag on h_max (valid in the linear regime) to a linear dependence, which is derived theoretically. This contrasts with results for flow about isolated mountains, wherein one finds that the drag greatly exceeds the linear value for tall mountains. Explanations for this difference are given.
The drag due to gravity wave breaking is also analyzed, and some rules of thumb as to its behavior vs. horizontal and vertical mountain scale are developed. It is found that gravity wave breaking exists at lower hill heights than the formation of a blocked layer.
Implications on orographic parameterications in GCMs are discussed.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics