On the Formation of Coherent Vortices beneath Nonbreaking Free-Propagating Surface Waves

Abstract

umerical simulations of monochromatic surface waves freely propagating over an initially quiescent flow field are conducted and found to reveal an array of quasi-streamwise vortices of alternating orientation in a manner akin to that of Langmuir circulation beneath wind-driven surface waves. A linear instability analysis of the wave-averaged Craik?Leibovich (CL) equation is then conducted to determine whether the structures in the simulations can be explained by the Craik?Leibovich type 2 (CL2) instability, which requires the presence of spanwise-independent drift and mean shear of the same sign. There is no imposed shear in the simulations, but they confirm the theoretical analysis of Longuet-Higgins that an Eulerian-mean shear with a magnitude comparable to that of Lagrangian Stokes drift occurs at the edge of the surface boundary layer in the otherwise irrotational oscillatory flow. The spanwise wavelength of the least stable disturbance is found to be close to the spacing between predominant vortex pairs, which likely are excited by the CL2 instability.