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本文检验了水波对依深变化水流的近似弥散关系。对于无限深水,近似弥散关系给出的渐近结果等同于在高波数和低波数下建立的渐近公式结果。此外,近似弥散关系对已知的整个波数范围的真实弥散关系给出了十分满意的描述。对于有限深水,近似弥散关系的渐近结果等同于在高波数下的渐近结果。对于低波数(长波),近似弥散关系的渐近结果与已建立的渐近公式有出入,其差值与水流对其均值的标准差成正比,对于那些获得近似弥散的条件来说,这个误差並不大。近似弥散关系的好处在于,它可以将波浪运动学/波浪作用表达式延伸,以供在依深变化的流场中,分析波—流的相互作用。
This paper examines the approximate dispersion of water waves over deeply varying water currents. For infinitely deep water, the asymptotic result given by the approximate dispersion relation is equivalent to the asymptotic formula established at high wave numbers and low wave numbers. In addition, the approximate dispersion relation gives a very satisfactory description of the true dispersion relation of the known wave number range. For finite deepwater, the asymptotic result of the approximate dispersion relationship is equivalent to the asymptotic result at high wave numbers. For low wave numbers (long wave), the asymptotic result of the approximate dispersion relationship is different from the established asymptotic formula, and the difference is proportional to the standard deviation of the mean value of the water flow. For those conditions that obtain approximate dispersion, Not big. The advantage of an approximate dispersion relationship is that it extends the wave kinematics / wave action expression to analyze wave-flow interactions in a deeply-varying flow field.