深水风浪的风区指数律

On the Fetch Law for Wind Waves in Deep Water

对已有根据观测提出的幂函数形式风浪成长关系进行了分析。发现这些风浪成长关系在消去无因次风区后一致地与 3 /2指数律相协调 ,尽管它们原来存在较大的不协调性。发现Jeffreys ,Sverdrup和Munk以及Plant的风能输入源函数在谱积分意义下具有相似性 ,而Tsikunov ,Hasselmann和Phillips的破波耗散源函数在谱积分意义下也具有相似性 ,尽管这些源函数的原始形式和物理背景显著地不同。利用有效波能量平衡方程 ,将 3 /2指数律和发现的风能输入及破波耗散源函数相似性相结合 ,提出了深水风浪随风区成长的分式指数律 ,以得到的分式指数律拟合已有基于观测提出的风浪成长关系提出了半经验的风浪成长关系 ,与已有观测数据符合。

The existing wind wave growth formulas (WWGFs) in the form of power function, which were presented on the basis of measurements, are analyzed. It is shown that these WWGFs after eliminating the fetch are uniformly consistent with the 3/2 power law, though there are considerable discrepancy among them.It is found that there are similarities in terms of spectral integral among the wind input source terms given by Jeffreys, Sverdrup and Munk, and Plant and among the wave breaking dissipation source terms given by Tsikunov,Hasselmann and Philips,although the original forms and the physical considerations of these source terms are significantly different. A fractional fetch power law for wind wave growth in deep water is presented by combining the energy balance equation for significant waves with the observed similarities and the 3/2 power law. Semi-empirical WWGFs have been proposed by fitting the existing WWGFs with the derived fetch law. The proposed formulas are agreeably consistent with the available observational data.