Focusing of the wave packets on currents
Résumé
The focusing of the transient wave groups on currents is studied analytically and numerically.Two linear models are analyzed. The first model is based on the kinematicequations of hyperbolic type for the wave amplitude and frequency. The second one isbased on linear parabolic equation for the complex amplitude, which is parabolic. Thewave current modifies the dispersion relation for water waves (Doppler effect), andhas an influence on the wave speed and wave dispersion. Detailed calculations havebeen done for both directions of the current-wave propagation.