Three-Dimensional Structure of Forced Gravity Waves and Lee Waves

R. D. Sharman National Center for Atmospheric Research,* Boulder, Colorado

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M. G. Wurtele Department of Atmospheric Sciences, University of California, Los Angeles, Los Angeles, and Center for Meteorology, University of California, Berkeley, Berkeley, California

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Abstract

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.

Corresponding author address: Dr. Robert Sharman, NCAR/RAP, P.O. Box 3000, Boulder, CO 80307-3000. Email: sharman@ucar.edu

Abstract

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.

Corresponding author address: Dr. Robert Sharman, NCAR/RAP, P.O. Box 3000, Boulder, CO 80307-3000. Email: sharman@ucar.edu

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