Lagrangian kinematics of steep waves up to the inception of a spilling breaker

Abstract

Horizontal Lagrangian velocities and accelerations at the surface of steep water-waves are studied by Particle Tracking Velocimetry for gradually increasing crest heights up to the inception of a spilling breaker. Localized steep waves are excited using wavemaker-generated Peregrine breather-type wave trains. Actual crest and phase velocities are estimated from video recorded sequences of the instantaneous wave shape as well as from surface elevation measurements by wave gauges. Effects of nonlinearity and spectral width on phase velocity, as well as the relation between phase velocity and crest propagation speed are discussed. The inception of a spilling breaker is associated with the horizontal velocity of water particles at the crest attaining that of the crest, thus confirming the kinematic criterion for inception of breaking.