GUIDE WAVE ANALYSIS AND FORECASTING - WMO

water boundary into shallow water. The changes in wave
direction thus obtained may focus energy in areas where
the rays converge, or defocus energy in areas where the
rays diverge. An example of a ray pattern in an area of
non-uniform depth is given in Figure 7.2.
From the energy balance (Equation 7.5) between
two adjacent wave rays, it is relatively simple to estimate
the wave height. If no generation or dissipation occurs
the wave height at a location 2 is computed from the
wave height at a location 1 with the energy balance
between two adjacent wave rays:
c g,1
H (7.8)
2 =
where the ray separations and the group speeds are ∆b1, ∆b2, and cg,1, cg,2, respectively.
∆b1 ⋅ ⋅H1 ,
∆b2 cg,2 (a)
depth
(b) (c)
wave rays
WAVES IN SHALLOW WATER 83
In areas with a very smooth bathometry, the
approach based on the local ray separation generally
presents no problem. However, in the case of an irregular
bathometry, the ray pattern may become chaotic (see
Figure 7.2 for example). In such cases a straightforward
transformation of local ray separation into local wave
heights, if at all possible, yields highly erratic values.
Quite often adjacent rays will cross and fundamental
problems arise. The ray separation becomes zero and the
wave height would be infinite (as diffraction effects are
ignored, see Section 7.4). A continuous line of such
crossing points (a caustic) can be created in classical
academic examples. A spatial averaging technique to
smooth such erratic results has been proposed by Bouws
and Battjes (1982). An alternative ray method which
avoids the problem of crossing wave rays is to backtrack
Figure 7.2 —
(a) The bathometry of the Haringvliet branch of the Rhine
estuary (the Netherlands), (b) The wave ray pattern for the
indicated harmonic wave entering the Haringvliet, and (c) The
significant wave height computed with the shallow water
spectral wave model SWAN (no triad interactions; Ris et al.,
1994) (courtesy Delft University of Technology)