## The influence of lateral boundariesin a Swan model

The boundary condition on the lateral boundaries of a computational grid is often completely unknown. For each lateral boundary there is a region of influence of roughly triangular shape (see the figure); the top angle of this triangle depends on the average direction of the incoming wave field (indicated by the white arrow) and the directional spread of the incoming wave field. The incoming wave field is a wind sea with $cos4$ distribution.
The region of influence has no hard borders; there is a gradual decrease of the influence away from the lateral boundary. The numbers in the figure give the relative importance of the seaward boundary in terms of Hs; so 0.95 means that Hs has an error of 5% there.
Fortunately in practice the situation is not as dramatic as the figure suggests. This figure is based on an academic computation without refraction, shoaling or source terms. In practice the other effects often make the region of influence of the lateral boundary smaller, as is illustrated by the example below.

The area considered in this example is the Friese Zeegat, a tidal entrance between two islands in the North of the Netherlands. The bathymetry is shown below:

Two computations are performed; the colors in both pictures represent Hs; the arrows represent the average propagation direction. In the first computation the incoming wave field (as measured at the SON location on the Northern boundary) is applied on the seaward boundary, in this case the Northern boundary.
On the Western boundary no incoming waves are assumed.

In the second computation the incoming wave field that is assumed on the Northern boundary is also applied on the Northern half of the Western boundary.
It is seen that there is a significant difference between the two results in the upper left corner. In the area of interest which is the tidal entry between the two islands the difference is very small. Therefore it is concluded that the Western lateral boundary is sufficiently far away from the area of interest.

Exercise: make a set of computation using the GUI in which you determine the correct lateral boundaries using the bathymetry of the Haringvliet area (bottom file: HARINGV2.BOT).

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