Third-order theory for bichromatic bidirectional water waves partially reflected from vertical breakwaters

To overcome the internal limitation of standing wave forces on vertical breakwaters and describe multichromatic multidirectional water waves in front of the breakwaters, a third-order theory, including the classical solutions of two-dimensional long-crested waves and monochromatic unidirectional short-crested waves, for bichromatic bidirectional water waves partially reflected from the breakwaters is developed. A universal law applicable to a higher-order multichromatic multidirectional wave system is proposed, that is, the even-order frequencies are zero, the numbers of the odd-order frequencies constitute a geometric progression.