Abstract
Finding a parameter whose threshold controls the onset of breaking in nonlinear modulating surface gravity wave trains has been an elusive problem. Our numerical study of the fully nonlinear two-dimensional inviscid problem on a periodic spatial domain for a range of wave group structures examined the behavior of dimensionless relative growth rates of the local mean wave energy and momentum densities. We found that these growth rates at the envelope maxima of the wave group oscillate on a fast time scale with a significant dynamic range and that a universal threshold exists for the maximum of either of these growth rates that determines whether breaking will occur.
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