GUIDE WAVE ANALYSIS AND FORECASTING - WMO

small enough that swell can survive over large distances.
Some interesting observations of the propagation of
swell were made by Snodgrass et al. (1966) when they
tracked waves right across the Pacific Ocean from the
Southern Ocean south of Australia and New Zealand to
the Aleutian Islands off Alaska.
The spectra of swell waves need not be narrow. For
points close to large generating areas, faster waves from
further back in the generating area may catch up
with slower waves from near the front. The result is a
relatively broad spectrum. The dimensions of the wavegenerating
area and the distance from it are therefore
also important in the type of swell spectrum which will
be observed.
In Chapter 4, more detail will be given on how to
determine the spectrum of wind waves and swell and on
how to apply the above ideas.
Other considerations in propagating waves are the
water depth and currents. It is not too difficult to adapt
the advection equation to take account of shoaling and
refraction. This is considered in Sections 7.2 and 7.3.
For operational modelling purposes, currents have often
been ignored. The influence of currents on waves
depends on local features of the current field and wave
propagation relative to the current direction. Although
current modulation of mean parameters may be negligible
in deep oceans, and even in shelf seas for ordinary
purposes, the modulation of spectral density in the highfrequency
range may be significant (see, for instance,
Tolman, 1990). Waves in these frequencies may even be
blocked or break when they propagate against a strong
current, as in an estuary. For general treatment of this
subject see Komen et al. (1994). The gain in wave forecast
quality by taking account of currents in a
forecasting model is not generally considered worth
while compared to other factors that increase computing
time (e.g. higher grid resolution). Good quality current
fields are also rarely available in larger ocean basins.
3.4 Dissipation
Wave energy can be dissipated by three different processes:
whitecapping, wave-bottom interaction and surf
breaking. Surf breaking only occurs in extremely shallow
water where depth and wave heights are of the
same order of magnitude (e.g. Battjes and Janssen,
Figure 3.4 —
The effect of dispersion on waves leaving
a fetch. The spectrum at the fetch
front is shown in both (a) and (b). The
first components to arrive at a point far
downstream constitute the shaded part
of the spectrum in (a). Higher frequencies
arrive later, by which time some of
the fastest waves (lowest frequencies)
have passed by as illustrated in (b)
E
WAVE GENERATION AND DECAY 39
1978). For shelf seas this mechanism is not relevant. A
number of mechanisms may be involved in the dissipation
of wave energy due to wave-bottom interactions. A
review of these mechanisms is given by Shemdin et al.
(1978), which includes bottom friction, percolation
(water flow in the sand and the sea-bed) and bottom
motion (movement of the sea-bed material itself). In
Sections 7.6 and 7.7, dissipation in shallow water will
be discussed more fully.
The primary mechanism of wave-energy dissipation
in deep and open oceans is whitecapping. As waves
grow, their steepness increases until a critical point when
they break (see Section 1.2.7). This process is highly
non-linear. It limits wave growth, with energy being lost
into underlying currents. This dissipation depends on the
existing energy in the waves and on the wave steepness,
and can be written:
S f E f
ds ( , θ) = – ψ( ) E( f,
θ)
,
f
(3.3)
where ψ(E) is a property of the integrated spectrum, E.
ψ may be formulated as a function of a wave steepness
parameter (ξ = Ef – 4 /g 2 , where f – is the mean frequency).
Forms for ψ have been suggested by Hasselmann (1974)
and Komen et al. (1984).
There are also the processes of micro-scale breaking
and parasitic capillary action through which wave
energy is lost. However, there is still much to learn about
dissipation and usually no attempt is made to distinguish
the dissipative processes. The formulation of S ds still
requires research.
Manual wave calculations do not need to pay
specific attention to dissipative processes. Generally,
the dissipation of wind waves is included implicitly in
the overall growth curves used. Swell does suffer a
little from dissipative processes, but this is minor. It is
observed that swell can travel over large distances.
Swell is mostly reduced by dispersion and angular
spreading.
3.5 Non-linear interactions
In our introduction we noted that simple sinusoidal
waves, or wave components, were linear waves. This is
an approximation. The governing equations admit more
(a) (b)
Frequency Frequency
2