Circulations caused by interaction of underwater currents and surface waves

The interaction between non-uniform near-surface currents and long surface waves is shown to produce large-scale secondary circulations. The circulations are caused by the Craik–Leibovich vortex force imposed on the existing non-uniform current by the surface waves. The current could be produced by different types of sources, such as by ship wakes or by river and sewer outflows. In this paper the circulations are considered for three representative types of currents: a near-surface jet, a shear current, and an underwater jet. A model similar to the model of Langmuir circulations is formulated and studied numerically. The general model takes into account the effect of viscosity on the main current as well as the effect of the circulation-related advection on the main current and secondary flow itself. A simplified model that describes the initial stage of the development of circulations was used in order to demonstrate the strength of the phenomenon and its dependence on some parameters of the problem. At this initial stage, the effect of viscosity on the main current as well as the effect of advection caused by the circulations was neglected (under assumption that the perturbation velocity is small). The effect of the viscosity on the circulations was included in the solution, and it was shown that initial development of the circulations is practically independent of the viscosity. This fact simplifies the solution of the problem and removes the uncertainty related to the value of the turbulent viscosity at the initial stage of the circulations. The results obtained demonstrate that strong circulations are generated under very realistic assumptions regarding the parameters of the current and the surface waves. The maximum velocity at the surface produced by such circulations can easily reach several centimeters per second. A circulatory flow with this magnitude of velocity at the surface can significantly affect short surface waves and, correspondingly, radar and optical signatures produced by the initial currents on the sea surface. Some important conclusions about the nature of these signatures are made based on numerical results and simple qualitative arguments. Theoretical predictions include, for example, the asymmetry of centerline ship wakes and the difference in the width and length between images of two wakes of similar ships moving in opposite directions when ambient surface waves are present.

► Non-uniform currents and long surface waves interact to produce paired circulations.
► The resulting circulations are similar in nature to Langmuir circulations.
► The circulation signs are dependent on the relative directions of current and waves.
► Strong circulations are generated for real values of ship currents and ocean waves.
► Circulations can increase persistence of ship wakes.