A13. Waves in a slanting current field

A stationary, 1-d, deep water case is considered, where the current velocity in y-direction varies with x. At the W boundary the current velocity is 0, the regular incoming waves have a period of 6.35 s and an angle of 60°. In the domain the Uy varies linearly with x; the coefficient of proportionality is 0.01 (m/s/m).
In order to be able to compare directions a fInite sector of spectral directions is considered: from 0° to 100° (Cartesian convention).

The theory shows that a caustic will develop on a line x=79.3 m.

4 cases are considered:

A13a
1d computation
A13b
regular 2d grid in standard orientation
A13c
1d computation where the number of iterations is forced to be larger, in order to test whether run A13a has converged
A13d
repeated 2d grid in order to test whether the grid of run A13b was long enough in y-direction
The solutions of A13a, A13b and A13d are Compared with the analytical solution for Hs (see plot A13.ps). The analytic solutions have been computed by the program 'slanting.for' which is found in the subdirectory 'Verif.dat'.
The graph also indicates the line along which the caustic is expected to be present. The theory supposes a regular wave field, so a very narrow spectrum is used.
Due to the fInite width of this spectrum the behaviour near the caustic is smooth where the theory forecasts a discontinuous behaviour. The three graphs of analytic solutions (incident directions 55, 60 and 65 degrees) show that the position of the caustic is very sensitive to the incident wave direction.
No explanation has been found for the fact that the computed wave heights for low values of x are above 1.

The second and third panel show the computed and analytic wave directions: panel 2: average wave directions (crest normal directions), panel 3: energy transport directions (i.e. directions of the energy transport vector).
It seems that SWAN overestimates the transport of energy over directions. This effect is probably due to the presence of reflected components (reflected on the caustic); this is illustrated by the star-plot in file 'A13/A13dstar.plt' and in the spectral plot 'A13/A13a.spl'.

© 2012: Nico Booij