1962/03/01 by M. S. Longuet‐Higgins · 1 citation
Earth and Planetary Sciences · #Ocean Waves and Remote Sensing #Oceanographic and Atmospheric Processes #Coastal and Marine Dynamics #Physics #Amplitude #Wavenumber #Gravitational wave #Wavelength #Gravity wave #Antiparallel (mathematics) #Optics #Wave propagation #Quantum mechanics
paper · doi:10.1017/s0022112062000233
openalex publication_date 1962/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a previous paper, Phillips (1960) showed that two or three trains of gravity waves may interact so as to produce a fourth (tertiary) wave whose wave-number is different from any of three primary wave-numbers k 1 , k 2 , k 3 , and whose amplitude grows in time. Such resonant interactions may produce an appreciable modification of the spectrum of ocean waves within a few hours. In this paper, by a slightly different method, the interaction is calculated in detail for the simplest possible case: when two of the three primary wave-numbers are equal ( k 3 = k 1 ). It is found that, when k 1 and k 2 are parallel or antiparallel, the interaction vanishes unless k 1 = k 2 . Generally, if θ denotes the angle between k 1 and k 2 , the rate of growth of the tertiary wave with time is a maximum when θ [eDot ] 17°; the rate of growth with horizontal distance is a maximum when θ [eDot ] 24°. The calculations show that it should be possible to detect the tertiary wave in the laboratory.