L12. Diffraction around a shoal

The purpose of this test is to validate the diffraction approximation in Swan. The approximation is described by Holthuijsen, Herman and Booij (2003).
The results are compared with observations reported by Vincent and Briggs (1989) and with computational results obtained by Ozkan and Kirby (1993) using their parabolic refraction-diffraction model.
Results of computations by Panchang et al (1990) are also shown in the graphs. These results and the observation by Vincent and Briggs (1989) are for regular waves whereas the Swan results and the computations by Ozkan and Kirby (1993) are for irregular waves. As expected the deviation between the latter two is smaller than the deviation between Swan and the first two.
The upper panel of plot L12.plt shows the values of Hs/Hs,inc along the line normal to the main wave direction, tangent to the shoal (line A-A), and the lower panel show the same quantity along the centre line over the top of the shoal.

Boundary conditions are applied at 3 sides of the computational grid.

2 cases are considered:

Swan without diffraction
Swan with standard diffraction

Graphs are shown for cases a, b and c, along the centre line across the shoal and along the line tangent to the circumference of the shoal at its most downwave point.

L.H. Holthuijsen, A. Herman, N. Booij (2003)
Phase-decoupled refraction-diffraction in a spectral wave model, Coastal Engineering, vol.49, PP.291-305
H.T. Ozkan and J.T. Kirby (1993)
Evolution of breaking directional spectral waves in the nearshore zone, Proc. 2nd Int. Conf. Ocean Wave Measurement and Analysis, WAVES '93, ASCE, New York, pp. 849-863
V.G. Panchang, B.R. Pearce and M.J. Briggs (1990)
Numerical simulation of irregular waves propagating over shoal, J. Waterw., Port, Coastal and Ocean Engng., vol. 116, nr. 3, pp. 324-340
C.L. Vincent and M.J. Briggs (1989)
, J. Waterway, Port, Coastal and Ocean Engng, vol. 115, no. 2, pp. 269-284

© 2012: Nico Booij