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

Integrated Publishing, Inc. |