Wind input term
Surf breaking
Whitecapping
Bottom friction
Output of source terms
Source terms in SWAN
For detailed information about the source terms the reader is referred to the background documentation by Delft University of Technology. This documentation also shows which alternative formulations for a certain source term are available. References to relevant literature can be found in the list of references of the SWAN home page of Delft University.Wind input term
The wind source term consists of a linear and an exponential part.
The linear term is dominant only in the first stage of growth; very soon the
exponential term will dominate.
The linear term is necessary if one starts with a completely flat surface (zero
wave energy) in a closed basin. In such circumstances the user must enable the
linear growth in the wind source term using the option AGROW in the command GEN3.
Usually only the exponential term is used. The strength of this source term for one
spectral bin is
equal to a factor times the energy density of that bin; the factor depends on the
frequency of the bin, the angle between the wind direction and the direction of the bin
and the ratio of the wind velocity and the phase velocity of the bin.
Surf breaking
When a certain wave height over depth ratio is exceeded waves will break.
Traditionally wave breaking was introduced in wave models by means of a maximum
wave height.
The formulation in Swan is different: the dissipation due to breaking depends
on the ratio between wave height and depth; when this ratio exceeds (roughly) 0.5
the dissipation increases rapidly.
The dissipation is proportional to the energy density and a coefficient dependent
on the wave height to depth ratio. A consequence is that the spectral shape
and the average wave period do not change as a result of breaking dissipation.
Whitecapping
The default formulation of whitecapping in Swan is similar.
The dissipation is proportional to the energy density and a coefficient dependent
on the overall steepness of the wave field (i.e. wave height to wave length ratio).
A consequence is that the spectral shape
and the average wave period do not change as a result of whitecapping dissipation.
Also a swell field will be dissipated in the presence of a steep wind sea which
is probably unphysical.
Whitecapping is essential if there is wind input. The wind input alone tends to
make the wave height grow indefinitely; whitecapping limits the wave height.
The quadruplet interactions cause the average period to increase gradually.
Bottom friction
Dissipation due to bottom friction results from the near-bottom orbital velocity
and the shear stress on the bottom. Both tend to 0 if the ratio of the wave length
and the depth becomes small. Therefore low frequencies are more strongly dissipated
than high frequencies.
The bottom shear stress obviously is dependent on the properties of the bottom
(roughness etc.) but the default formulation of bottom friction in Swan does not
show any dependency on bottom properties.
Since bottom properties may vary over the area so that often a variable friction
coefficient is usefull. The two other formulations have the possibility to enter
a variable friction coefficient.
However, before the optimal friction formulation is chosen the user should determine
whether friction is relevant in the model.
Exercise: compare the results of two computations in the Haringvliet area, one with
and one without bottom friction. All other data should be the same.
Output of source terms
Values of some of the source terms as computed in a Swan run can be shown by Swan.
Among the output quantities in Swan you will find:
DISSIP: the sum of the dissipation terms,
DISSURF: surf breaking dissipation,
DISBOT: bottom friction dissipation,
DISWCAP: whitecapping dissipation.
In addition the quantity Qb (fraction of breaking waves) a parameter in the surf breaking
term is available in Swan.
Numerical values of these terms can be written in a table or in block output.
Plots of each of these terms can also be obtained using the PLOTGEO command (SWAN-DHH).
The above source terms are all integrated over the spectrum. If the user wants to
know the spectral distribution of source terms the command TEST enables him
to get these for a limited number of test points; see the option S2D in this command.
The output of the source terms (and some other data) are made for every iteration.
Quantities in the S2D file are:
Swind: wind source term,
Swcap: whitecapping dissipation,
Sfric: bottom friction dissipation,
Ssurf: surf breaking dissipation,
Snl3: triad interactions,
Snl4: quadruplet interactions.
The output for test points is in a numerical format. Visualisation is possible
with the post-processing software OPGraph.
An example (quadruplet interaction term) is shown on this page.
Exercise: determine the relative importance for each dissipation term for some
different points in the Haringvliet area, one at 20 m depth,one at 5 m depth and
one at 1 m depth.
