ESS228
Prof. Jin-Yi Yu
Shallow-Water Equation on an Equatorial b-Plane
Linearized shallow-water
equations
Assume wave-form solutions
Dispersion relationship for
equatorial waves
Only these waves that satisfy the
condition that
the wave amplitudes decay far
from the equator (where the
beta-plane approximation
becomes invalid.)
This
cubic dispersion equation permit three groups of equatorially
trapped waves:
The index n corresponds to the number of nodes in the meridional velocity
profile in the domain |y| <
∞.
(1)Eastward-moving gravity waves
(2)Westward-moving gravity waves
(3)Westward-moving Rossby waves
Only if this constant equal
to an odd integer that the boundary condition (v=o at y= 0 ) can be
satisfied.
