Large waves on the deep ocean propagate at the speed v =√g/k, where g is the magnitude of the acceleration due to gravity and k is the wavenumber Seafaring mariners report that in great storms when the average peak-to-peak wave height becomes about 1/7 of the wavelength, the tops of the largest ocean waves can become separated from the rest of the wave. They claim that the wind and the wave's forward velocity cause huge hunks of water to tumble down the face of the wave. Some are reportedly large enough to damage or capsize small vessels. The reason these rogue waves appear is that the amplitude of the water waves becomes so large that the acceleration of the water in the top of the wave would have to be greater than g for the wave to stay in one piece. Because gravity is the only significant vertical force on the water, the acceleration cannot exceed g, so instead the water at the top of the wave breaks off and is blown down the side of the wave. Find the angular frequency w of water waves as a function of the wave number k
Find the maximum acceleration of the water in the downward direction, as a function of wave amplitude A and angular frequency w
Assume the maximum acceleration of the water in the downward direction is equal to g, and find the peak-to-peak amplitude in terms of the wavelength. Does this confirm the reports of seafaring mariners?