Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 17 2 2010 10.5194/npg-17-201-2010 http://www.nonlin-processes-geophys.net/17/201/2010/ http://www.nonlin-processes-geophys.net/17/201/2010/npg-17-201-2010.html http://www.nonlin-processes-geophys.net/17/201/2010/npg-17-201-2010.pdf 201 210 2010-04-12 The effect of shear on the generation of gravity waves M. Humi mhumi@wpi.edu Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA 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. 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