1 NUMERICAL MODELLING OF WIND WAVES. PROBLEMS, SOLUTIONS, VERIFICATIONS, AND APPLICATIONS V. G. Polnikov1 CONTENTS Abstract 1. Introduction 2. Fundamental equations and conceptions 3. Wave evolution mechanism due to nonlinearity 4. Wind wave energy pumping mechanism 5. Wind wave dissipation mechanism 6. Verification of new source function 7. Future applications 8. References 1 Research professor, A.M. Obukhov Institute for Physics of Atmosphere of Russian Academy of Sciences, Moscow, Russia 119017, e-mail:
[email protected] 2 ABSTRACT Due to stochastic feature of a wind-wave field, the time-space evolution of the field is described by the transport equation for the 2-dimensional wave energy spectrum density, σ θ x, tS ),;( , spread in the space, x, and time, t. This equation has the forcing named the source function, F, depending on both the wave spectrum, S , and the external wave-making factors: local wind, W(x, t), and local current, U(x, t). The source function, F, is the “heart” of any numerical wind wave model, as far as it contains certain physical mechanisms responsible for a wave spectrum evolution. It is used to distinguish three terms in function F: the wind-wave energy exchange mechanism, In; the energy conservative mechanism of nonlinear wave-wave interactions, Nl; and the wave energy loss mechanism, Dis, related, mainly, to the wave breaking and interaction of waves with the turbulence of water upper layer and with the bottom. Differences in mathematical representation of the source function terms determine general differences between wave models. The problem is to derive analytical representations for the source function terms said above from the fundamental wave equations.