Effect of Ship-Induced Langmuir-Type Circulations on Distribution of Surface-Active Substances and Damping of Short Wind Waves

It has recently been shown that the interaction of ship-generated nonuniform currents with ambient surface waves can lead to the generation of Langmuir-type circulations (LTCs) (Basovich 2011) and a persistent wake (Somero et al. 2018). Based on this work, it is shown here that the LTC and surface currents of the persistent wake are responsible for the redistribution of surface-active substances (SAS) and a corresponding change in the damping of short surface waves. The persistent wake is a region of the ship wake, where initial ship-generated perturbations have mostly decayed. The LTCs are similar in nature to Langmuir circulations which arise as a result of instability of wind-driven current. LTCs produce a secondary flow with velocity transverse to the direction of the ship, and width significantly larger than the ship beam. Because LTCs are generated in large scale, they persist for a long time after the passage of the ship. Transverse surface currents produced by LTCs in the ship wake redistribute the SAS films at the sea surface. These currents create strong convergence and divergence zones which in turn produce streaks with different concentrations of SAS. The change in concentration of SAS affects the film pressure and the damping effect of SAS on the short surface waves. This effect is represented by a damping factor and is a crucial parameter in determination of the spectral density of short wind waves. Therefore, the damping effect of the film, as represented by the damping factor, is responsible for sea surface roughness modification and is important for prediction of synthetic-aperture RADAR (SAR) imagery of ship wakes on the ocean surface. In this article, we present the mathematical and computational methods, along with simulation results for a naval surface combatant operating in calm, head, and following seas. The simulation results clearly show that the convergence and divergence zones strongly influence the relative SAS concentration and the spatial distribution of the damping factor, the latter of which defines the structure of SAR images of the persistent wake. Comparisons of the magnitude of the damping factor with available SAR data are shown to be in good agreement.