Wave modulation: the geometry, kinematics, and dynamics of surface-wave packets

Abstract eng:
We derive a set of conserved quantities and moment evolution equations for the modified nonlinear Schrodinger equation (Dysthe 1979; MNLSE), with application to interpreting the geometry, kinematics, and dynamics of deep-water surface gravity wave packets. Our theory predicts modifications to the group velocity and explains the asymmetric leaning forward of the wave packet as focusing occurs. The theory is examined numerically for dispersive focusing wave packets, and these results are compared to numerical simulations of the fully-nonlinear potential flow equations. It is found that the MNLSE models the bulk scale features of the focusing event, and that the numerical results are consistent with the theoretical predictions.

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