Extreme waves induced by strong depth transitions: Fully nonlinear results

focus on the case of a random, one-directional wave field with prescribed statistics
propagating over a submerged step, and consider different depth variations, up to an
almost deep-to-shallow transition (kp H ≈ 1.8 − 0.78, where kp is the characteristic
wavenumber and H the water depth). Strongly non-Gaussian statistics are observed
in a region localized around the depth transition, beyond which they settle rapidly on
the steady statistical state of finite-depth random wave fields. Extreme fluctuations
are enhanced by stronger depth variations. Freak-wave formation is interpreted as
a general signature of out-of-equilibrium dynamics, associated with the spectral
settling from the deep-water to the finite-depth equilibrium. We also document that
during such a transition the wave spectrum shows remarkable similarity with Phillips
ω−5 -law for the strongest depth variations considered.

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