Articles | Volume 17, issue 2
Nonlin. Processes Geophys., 17, 201–210, 2010
https://doi.org/10.5194/npg-17-201-2010
Nonlin. Processes Geophys., 17, 201–210, 2010
https://doi.org/10.5194/npg-17-201-2010

  12 Apr 2010

12 Apr 2010

The effect of shear on the generation of gravity waves

M. Humi M. Humi
  • Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA

Abstract. Previous research regarding the solutions of Long's equation always presumed that the flow far upstream is without shear. In this paper we derive the proper form of this equation when shear is present. We then apply a sequence of transformations to this equation which make it possible to linearize it while preserving its physical contents. We then derive conditions under which the solutions of this linear equation admit the existence (or creation) of gravity waves. We present also a solution of this model equation when the presence of shear in the overall flow is "small".