3 BOUNDARY CONDITIONS
Along rigid, impermeable vertical walls, no flow normal to the surface gives
η / n = 0 . However, in general, the following partial reflection boundary condition
$
applies along coastlines or permeable structures
η
$
=αη
(9)
$
n
where α = α 1 + iα 2 is a complex coefficient . For simplicity, α is generally represented as
1- Kr
α = ik
(10)
1+ Kr
Along the open boundary where outgoing waves must propagate to infinity, the
Sommerfeld radiation condition applies
$
kr - ikηS → 0
lim
(11)
r
kr→ ∞
where ηS is the scattering wave potential. It is shown in Mei (1983) that the desired
$
scattered wave potential ηS , which is a solution of the mild-slope equation and satisfies
$
the radiation condition Equation 11, can be written as:
∞
ηS = ∑ H n (kr)(α n cos nθ + βn sin nθ)
(12)
$
n =0
9
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