Three-dimensional structure of forced gravity waves and lee waves

The three-dimensional structure of lee waves is investigated using a combination of linear analysis and numerical simulation. The forcings are represented by flow over a single wave (monochromatic) in the along-stream direction but of limited extent in the cross-stream direction, and by flow over isolated obstacles. The flow structures considered are of constant static stability, and zero, positive, and negative basic-flow shears. Both nonhydrostatic and hydrostatic regimes are studied. Particular emphasis is placed on 1) the cross-stream structure of the waves, 2) the transition from three-dimensional to two-dimensional flow as the breadth of the obstacle is increased, 3) the criteria for three-dimensional nonhydrostatic to hydrostatic transitions, and 4) the effect of obstacle breadth-to-length aspect ratio on the wave drag for this linear system. It is shown that these aspects can in part be understood by relating the gravity waves produced by narrow-breadth obstacles to the "St. Andrew's Cross" for hydrostatic and nonhydrostatic uniform flow and for hydrostatic shear flow.