A22. 2d propagation, stationary, spherical coordinates

The purpose of this test is to verify the correct implementation of spherical coordinates, both for the first and the second order scheme. The waves propagate over a very long dsitance, half the globe. Also the transition from 360° to 0° is in the computational domain, so that periodicity of the spatial coordinates is tested as well.

A domain with deep water is considered (i.e. it is assumed that the globe is entirely covered with water). The computational domain extends from longitude -40° to 140°, and from latitude -60° to +60°.

At the Western boundary an incident wave field is assumed which propagates in E direction. This incident wave field has a Jonswap spectrum with a narrow directional distribution. The peak period is 10 s.

According to theory the waves should concentrate on the location 90° East of the incident wave boundary, at the equator; the wave height should be constant again over the meridian 180° east of the incident wave boundary.

The distribution of Hs over space (in the form of isolines) together with the distribution over directions (so-called STAR plot) is shown for 2 cases:

the BSBT scheme,
the SORDUP scheme.

Furthermore the 2d spectrum is shown for the location (x,y)=(50,0) where the waves should concentrate.

3 cases are considered:

1st order BSBT computation
2nd order upwind computation (SORDUP)
nonstationary computation with S&L scheme

© 2012: Nico Booij