Trochoidal wave theory

Trochoidal (Gerstner) wave theory models a finite-amplitude deep-water gravity wave whose surface profile is traced by a point on a rolling circle, a trochoid, with crests sharper and troughs flatter than a sine. Water particles move in closed circles whose radius decays with depth as exp of k z, and the celerity is c = square root of g over k = square root of g L over 2 pi. It was the standard naval-architecture wave for statically balancing a ship on a wave (length equal to ship length, height L over 20) in hogging and sagging analysis before linear (Airy) theory took over. Its drawback is rotational particle motion, which an ideal fluid does not support.