Wave-current interactions representation by coupling spectral wave and coastal hydrodynamics models

A parallelized unstructured coupled model is developed to investigate wave-current interactions in coastal waters at regional scales. This model links the spectral wave model Simulating Waves Nearshore (SWAN; Booij et al., 1999) with the coastal hydrodynamics shallow-water equation model Thetis (Kärnä et al., 2018). SWAN is based on the action density equations encompassing the various source-terms accounting for deep- and shallow-water phenomena. Thetis solves the non-conservative form of the depth-averaged shallow water equations implemented within Firedrake, an abstract framework for the solution of Finite Element Method (FEM) problems. In resolving wave-current interactions in the proposed model, Thetis predicts water elevation and current velocities which are communicated in SWAN, while the latter provides radiation stresses information for the former. The numerical domain is prescribed by an unstructured mesh allowing higher resolution to areas of interest, while maintaining a reasonable computational cost. As the models share the same mesh, interpolation errors and certain computational overheads can be contained, whereas the choice to employ a sub-mesh for SWAN model is being considered to reduce the overall cost.

The model is initially validated and its performance assessed by a slowly varying-bathymetry. Predictions are compared against the analytical solutions for the wave setup and significant wave height (Longuet-Higgins and Stewart, 1964). Comparisons also extend to results from a coupled 3-D hydrodynamics model with a spectral wave model (Roland et al., 2012). The results of the proposed coupled model exhibit good correlations with the analytical solutions showcasing the same level of efficiency as the 3-D coupled model.

 

References

[1] Booij N, Ris RC, Holthuijsen LH. A third-generation wave model for coastal regions: 1. Model description and validation. Journal of geophysical research: Oceans 1999;104(C4):7649–7666.

[2] Kärnä T, Kramer SC, Mitchell L, Ham DA, Piggott MD, Baptista AM. Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations. Geoscientific Model Development 2018;11(11):4359–4382.

[3] Longuet-Higgins MS, Stewart R. Radiation stresses in water waves; a physical discussion, with applications. In: Deep sea research and oceanographic abstracts, vol. 11 Elsevier; 1964. p. 529–562.

[4] Roland A, Zhang YJ, Wang HV, Meng Y, Teng YC, Maderich V, et al. A fully coupled 3D wave-current interaction model on unstructured grids. Journal of Geophysical Research: Oceans 2012;117(C11).