Transmission and reflection of planetary and topographic Rossby waves in a two-layer ocean
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Transmission and reflection problems when “kissing≓ occurs among planetary and topographic Rossby waves in a two-layer ocean are studied. The slope parameterS(=dh2/dx, whereh2is the thickness of the lower layer) is assumed to have constant values in the regionsx≤ 0 andx≥L and to vary linearly with the increase ofx in the region0≤x≤L (refer to Fig. 2 in the text). Furthermore, a wave is entered fromx=−∞ and kissing is assumed to occur in the region (0<)xa≲x≲xb(<L).
It is found that a wave of the same type as the incident wave is mainly transmitted when the width of the region in which kissing occurs,Lkiss(=txb−xa), is smaller thanλkiss=2π/(¦K¦+Βy/2Ω), whereK is a representative wavenumber in the regionxa<x<xb, Βy is they-component of Β, and Ω is the frequency. WhenLkiss is larger thanλkiss, on the other hand, the main wave transmitted is of a different type to the incident wave. As an application, transmission and reflection problems of planetary Rossby waves are considered, and it is shown that when an external (internal) planetary Rossby wave is entered, an internal (external) one can be transmitted due to the effect of kissing.
KeywordsReflection Lower Layer Incident Wave Rossby Wave Slope parameterS
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