Reflection and transmission of normally incident internal waves propagating across a geostrophic front, like the Kuroshio or Gulf Stream, are investigated using a modified linear internal wave equation. A transformation from depth to buoyancy coordinates converts the equation to a canonical partial differential equation, sharing properties with conventional internal wave theory in the absence of a front. The equation type is determined by a parameter D, which is a function of horizontal and vertical gradients of buoyancy, the intrinsic frequency of the wave, and the effective inertial frequency, which incorporates the horizontal shear of background geostrophic flow. In the Northern Hemisphere, positive vorticity of the front may produce D# 0, that is, a ''forbidden zone,'' in which wave solutions are not permitted. Thus,D50 is a virtual boundary that causes wave reflection and refraction, although waves may tunnel through forbidden zones that are weak or narrow. The slope of the surface and bottom boundaries in buoyancy coordinates (or the slope of the virtual boundary if a forbidden zone is present) determine wave reflection and transmission. The reflection coefficient for normally incident internal waves depends on rotation, isopycnal slope, topographic slope, and incident mode number. The scattering rate to high vertical modes allows a bulk estimate of the mixing rate, although the impact of internal wave-driven mixing on the geostrophic front is neglected.
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Acknowledgments. We thank two anonymous reviewers for their helpful comments. QL is supported by NSFC-41576008 and LTO1503. XM is supported by the National Basic Research Program of China (973 Program, 2014CB745002). SC is supported by NSFC-41430964 and Key Research Program of Frontier Sciences, CAS(QYZDJ-SSW-DQC034). Numerical computation is supported by Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund under Grant U1501501.
- Internal waves