6.7: Limits of the Linear Theory

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Page ID: 49045

Franz S. Hover & Michael S. Triantafyllou
Massachusetts Institute of Technology via MIT OpenCourseWare

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The approximations that are inevitably made will affect the accuracy of the linear wave model. Here are some considerations. The ratio of wave height to wavelength is typically in the range of 0.02-0.05; a one-meter wave in sea state 3 has wavelength on the order of fifty meters. When this ratio approaches 1/7, the wave is likely to break. Needless to say, at this point the wave is becoming nonlinear! Ultimately, however, even smaller ocean waves interact with each other in a nonlinear way. There are effects of bottom topography, wind, and currents. Nonlinear interaction causes grouping (e.g., rogue waves), and affects the propagation and directionality of waves. It is impossible to make a forward prediction in time - even with dense and perfect measurements - of a wave field, unless these effects are included. In fact, there is some recent work by Yue’s group at MIT on the large-scale prediction problem.