The JONSWAP experiment provided the wave modelling community with much needed wave data and led to the determination of growth curves for parameters describing the evolution of the wave energy spectrum with fetch such as the total energy and the peak frequency. On the other hand mathematical models have been developed to solve the wave energy transport equation. The interest here is to find out if it is possible to “tune” certain parameters in the wind input and in the dissipation term automatically so that the solution of the energy transport equation for fetch limited conditions fits the measurements as closely as possible. Use is made of standard mathematical optimization routines to minimize a sum of squares cost function. Numerical experiments were done with the energy transport equation in deep water . The Snyder-type wind input term with a linear dependency on the friction velocity gives for the proposed growth curve and the current numerical scheme slightly better results compared to the Stewart-type wind input term with a quadratic dependency on the friction velocity. However, the optimization routine proposes for both expressions physically unrealistic negative damping values. It is felt that the wave steepness could influence the wind input. Although over steeper waves the drag coefficient is larger than over waves near full development, this should not necessarily translate into a greater wind input. The Miles' mechanism (or wave generation) is probably more effective and better coordinated near full development than when the waves are rough and generate larger turbulence levels in the air. Therefore the wind input was made dependent on the wave steepness. A substantial improvement in the fits 10 the JONSW AP growth curves is noticed.
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