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The kinematic properties of unsteady highly non-linear 3D wave groups havebeen investigated using a numerical wave tank. Although carrier wave speedsbased on zero-crossing analysis remain within +-7% of linear theorypredictions, crests and troughs locally undertake a systematic cyclical leaningfrom forward to backward as the crests/troughs transition through their maximumamplitude. Consequently, both crests and troughs slow down by approximately 15%of the linear velocity, in sharp contrast to the predictions of finiteamplitude Stokes steady wavetrain theory. Velocity profiles under the crestmaximum have been investigated and surface values in excess of 1.8 times theequivalent Stokes velocity can be observed. Equipartitioning betweendepth-integrated kinetic and potential energy holds globally on the scale ofthe wave group. However, equipartitioning does not occur at crests and troughs(even for low amplitude Stokes waves), where the local ratio of potential tototal energy varies systemically as a function of wave steepness about a meanvalue of 0.67.

On the local properties of highly nonlinear unsteady gravity water waves. Part 1. Slowdown, kinematics and energetics