Abstract : 2G.10
The effect of the Earth’s rotation on the linear gravity wave drag of a sheared flow past a circular mountain

Miguel Teixeira, Pedro M A Miranda, Rita Cardoso
CGUL, IDL, University of Lisbon

The effect of wind shear on gravity wave drag (GWD) has been the object of recent linear theoretical studies. One of them, developed by Teixeira and Miranda (2006), provides closed-form analytical GWD formulas for hydrostatic non-rotating flow over elliptical mountains, extending analogous results for flow over circular and 2D mountains. These formulas are easily implemented in GWD parametrization schemes. For mountains with widths of 10km to 100km, which are inadequately resolved in many global models, the effects the Earth’s rotation on the GWD are likely to become important. The present study extends the model of Teixeira et al. (2004) for GWD in flow past a circular mountain to a case with rotation. Since the effects of rotation are scale-dependent, the GWD now depends on the shape of the orography, and the drag expressions calculated are not analytical, but must be evaluated numerically. Several unexpected results are found. For a linear wind profile, the GWD decreases as the Richardson number (Ri) decreases when there is no rotation, but this dependency is reversed at some value of the Rossby number (Ro). For lower Ro, the GWD increases as Ri decreases. For a wind that turns with height maintaining its magnitude, the drag always increases as Ri decreases, but its variation becomes faster as Ro becomes smaller. In both cases, whereas the maximum of the GWD with no shear occurs for infinite Ro, as Ri decreases this maximum shifts towards lower Ro. On the other hand, the drag at low Ro is enhanced by a considerable factor as Ri decreases. These results suggest that the effects of shear on the variation of the GWD are essentially positive, which may have important consequences for the globally integrated effects of the drag. These linear results are beginning to be tested with numerical simulations, which will also be used to investigate nonlinear effects.