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Accepted · first revision · record

Title: Effect of modulational instability on rogue wave statistics
Plain: Rogue waves are ocean or optical waves far taller than their neighbors. It is disputed whether they come mostly from random addition of ordinary waves or from a nonlinear focusing instability, and how much the instability raises their probability.
Precise: For directional random surface gravity waves in deep water described by the Zakharov equation or the 2D nonlinear Schrodinger equation, determine how the exceedance probability of crest-to-trough height $H > 2 H_s$ depends on the Benjamin-Feir index BFI (steepness divided by spectral bandwidth) and on directional spreading, and whether it exceeds second-order (bound-wave) statistics in realistic directional seas. An answer is a quantitative law tested against field and tank data.
Settled by: Large tank experiments and field records with measured spectra showing whether exceedance probabilities rise with BFI beyond second-order theory at realistic directional spreading.
Kind: phenomenon
Answer type: mechanism
References: (empty)
Literature status: contested
Status note: (empty)
Posed since: 2003