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本文讨论了成长过程中非线性水波的色散关系。得到了精确到波陡二次方的非线性色散关系,证明了在偶合机制控制下的非线性成长过程具有多重时间尺度(即振荡、演化和成长的时间尺度)。还证明了即使在成长过程中的水波色散关系中也不含有与波陡一次方成正比的非线性修正项。在极限情况下,我们又得到了非成长水波色散关系的一般表达式。用Wallops谱进行数值计算的结果表明,我们的理论适用于低频波和含能波段;与实验数据的比较表明,在含能波段的理论值和实测值很接近。
This paper discusses the dispersion of nonlinear water waves in the growth process. The nonlinear dispersion relationship to the square of wave steepness is obtained. It is proved that the nonlinear growth process under the control of coupling mechanism has multiple time scales (ie, time scales of oscillation, evolution and growth). It is also demonstrated that there is no non-linear correction term proportional to the first-order wave steepness, even in the wave dispersion relation during the growth. In the limit case, we get the general expression of non-growing wave dispersion relation. The results of Wallops spectral calculations show that our theory is applicable to low-frequency and energy-wavebands. Comparing with the experimental data, the theoretical and measured values in the energy band are close to each other.