26
and noting that U,V,Cly and a are known quantities; taking forward difference derivatives
in x and backward difference derivatives in y and solving for the wave height, H,j, at the
iyj grid yields
Hij =
(V+C,in g)g,,y_l (U+C, cot 9)Hi+1j
aY ~ aX
V+C4ini U+C, cot 9
(2.39)
ay a:' LJjj
The computation is a row by row iteration proceeding from large i (offshore in the
coordinate system of the above cited authors) to small i. During the computation of each
Hij the breaking height is also calculated and if Hij exceeds this value, then the breaking
wave height is used. Several breaking height indices are possible. Miche (1944) gave as the
theoretical limiting wave steepness the condition
^r- = .142tanh(fcj,h¡,)
Lb
(2.40)
where the b subscript indicates breaking conditions. Le Mhaut and Koh (1967) indicated
from experimental data that the limiting steepness is
^r- = .12tanh(fc¡,h,)
Lb
(2.41)
or
ff* = ^.12tanh(Jfc6fc6) (2.42)
Kb
This is the breaking height criterion used by Noda et al. (1974). Perhaps the simplest
breaking height criterion is the spilling breaker assumption
Hb = .78 hb (2.43)
which is used by Vemulakonda (1984) and Vemulakonda et al. (1985).
The scheme described above of determining the wave angle 6 from the irrotationality
of the wave number (2.33) and the dispersion relation (2.34) and the wave height from
the energy equation (2.35) has its limitations. Principally this scheme does not take into
account the effects of diffraction. This limitation is surmounted by use of a parabolic wave
equation. However this presents another problem in that the wave angle is not determined