energy distribution in wavenumber space, in conjunction with 

 the constraints of momentum, energy and — in this case — 

 action conservation, explain the general +-+ distribution 

 of the nonlinear source function [20b], but not the posi- 

 tions of the individual lobes, which turn out to be essen- 

 tial for the stability of the spectral shape. 



5. THE OVERALL ENERGY BALANCE 



It follows from the computed nonlinear transfer rate 

 shown in Fig. 5 that for a spectrum of the general JONSWAP 

 form wave-wave interactions will produce a shift of the 

 peak towards lower frequencies at about the rate observed. 

 However, this says nothing about the origin of the peak, or 

 its persistence once it has been generated. To resolve 

 these questions, computations of the nonlinear energy 

 transfer were made for a series of spectral shapes which 

 were either broader or more sharply peaked than the mean 

 JONSWAP spectrum. It was found that the peak appears to be 

 a self-sustaining feature of the nonlinear energy transfer 

 which evolves from almost any initial spectral distribution, 

 independent of the details of the energy input. 



As an example, the left panel in Fig. 7 shows the 

 nonlinear transfer for a spectrum with a less pronounced 

 peak than the mean JONSWAP spectrum. Characteristic for 

 these broader distributions (in this case a Pierson- 

 Moskowltz spectrum) is the position of the positive lobe 



25-21 



