UiO Mechanics Seminar Series - Page 8

In order to secure the safety of ships travelling along the Norwegian coast, several fine-scale wave models have been applied for the most dangerous wave areas, such as the Steady State Irregular Wave Model (STwave) and a refraction model (www.met.no: kyst_og_hav). Lately, the model Simulating Waves Nearshore (SWAN) from TUDelft, The Netherlands, was employed to forecast waves in Trondheim ship lane. SWAN is a spectral wave model, similar to WAM, developed for shallow water or coastal areas by including depth-induced wave breaking, triad wave-wave interaction and an implicit numerical scheme that allows SWAN to run efficiently on high horizontal resolution. At met.no, SWAN was set up with 418x150 grid points and a 500mx500m grid cell size. It receives spectra on the outer boundaries from met.no's operational version of WAM and is driven by winds from a 4 km x 4 km atmospheric model. The model has furthermore the option to include varying current fields (refraction, blocking, and frequency shift) which we would like to test. Current fields can be obtained from an ocean or tidal model. We will present our experience with SWAN and results so far of comparing the forecasted wave parameters with those from a buoy located at Stor-Fosna in the ship lane. Acknowledgements: The work is performed in collaboration with the Norwegian Coastal Authorities (Kystverket).

The temporal evolution of the energy spectrum of a field of random surface gravity waves in deep water is investigated by means of direct numerical simulations of the deterministic primitive equations. The detected rate of change of the spectrum is shown to be proportional to the cubic power of the energy density and agree quite well with the nonlinear energy transfer $S_{nl}$ as predicted by Hasselmann. In spite of the fact that use of various asymptotic relations which are valid only for $t\to\infty$ or integration with respect to time over a time scale much longer than $O({\rm period}\times (ak)^{-2})$ are necessary in the derivation of Hasselmann's $S_{nl}$, it is clearly demonstrated that the rate of change of the spectrum given by the numerical simulation agrees quite well with Hasselmann's $S_{nl}$ at every instant of ordinary time scale comparable to the period. The result implies that the four-wave resonant interactions control the evolution of the spectrum at every instant of time, while non-resonant interactions do not make any significant contribution even in a short-term evolution. It is also pointed out that the result may call for a reexamination of the process of derivation of the kinetic equation for the spectrum.