Gravity‐wave drag on two mountains

The generation of linear internal gravity waves by the flow over two idealized mountains, whose summits are aligned in the same direction as the mean wind, is studied. In particular, the sensitivity of the wave drag to the downwind distance between the mountains is examined by using a three‐dimensional numerical model based on the linearized steady‐state Boussinesq equations of motion. Both two‐ and three‐dimensional orography is considered. When the upstream conditions are such that the wind and buoyancy‐frequency do not vary with height, and the mountains are wide enough for non‐hydrostatic effects to be unimportant, the model predicts the same drag dependence on two‐dimensional ridge spacing as was derived analytically by Grisogono et al. The corresponding three‐dimensional numerical result predicted by the model is qualitatively very similar to the two‐dimensional result. When the mountains are narrow and the waves are non‐hydrostatic the drag dependence on mountain spacing is more complicated; maxima and minima in the drag can occur when the distance between the two mountains is such that waves generated by the mountain furthest upstream are in phase (maxima in the drag), or out of phase (minima in the drag), with the waves generated by the downstream mountain. It is shown that this is an important effect when the waves are trapped by upstream profiles whose wind speed varies with height.