Tidlegare gjesteforelesninger og seminarer - Side 95

Fredagskollokvium

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.

Fredagskollokvium

Fredagskollokvium

The problem of the long wave runup on a beach is discussed in the framework of the rigorous solutions of the nonlinear shallow-water theory. The key and novel moment here is the analysis of the runup of a certain class of asymmetric waves, the face slope steepness of which exceeds the back slope steepness. Shown is that the runup height increases when the relative face slope steepness increases whereas the rundown weakly depends on the steepness. The results partially explain why the tsunami waves with the steep front (as it was for the 2004 tsunami in the Indian Ocean) penetrate deeper into inland compared with symmetric waves of the same height and length.

Fredagskollokvium

Felleskollokvium

Fredagskollokvium

Fredagskollokvium

Fredagskollokvium

Fredagskollokvium

Fredagskollokvium

Fredagskollokvium

Fredagskollokvium

Fredagskollokvium

Fredagskollokvium

Fredagskollokvium

Fredagskollokvium

Fredagskollokvium

Fredagskollokvium

Fredagskollokvium

Fredagskollokvium

Fredagskollokvium

Fredagskollokvium