Transmission and reflection problems when “kissing” occurs among planetary and topographic Rossby waves in a two-layer ocean are studied. The slope parameter
S (=
dh2/
dx, where
h2 is the thickness of the lower layer) is assumed to have constant values in the regions
x≤0 and
x≥
L and to vary linearly with the increase of
x in the region 0≤
x≤L (refer to Fig. 2 in the text). Furthermore, a wave is entered from
x=-∞ and kissing is assumed to occur in the region (0<)
xα≤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, L
kiss (=
xb-
xa), is smaller than λ
kiss=2π/(|
K|+βν/2ω), where
K is a representative wavenumber in the region
xa<
x<
xb, βν is the γ-component of β, and ω is the frequency. When Lkiss is larger than 2kiss, 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.
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