| Numerical simulations of laminar and turbulent open channel flows under a moving wavy surface that has the form of a second order Stokes wave are performed. A constant tangential stress imposed at the top drives a mean current that interacts with the surface wave and generates Langmuir circulations. The Navier-Stokes equations are solved in a curvilinear coordinate system with a modified version of the fractional step method of Zang et al. (1994). Large eddy simulation is used for turbulent flows with the sub-grid stresses modeled with a dynamically determined Smagorinsky constant.; First, two components of the velocity field important to Langmuir circulations are identified in two dimensional free wavy surface flows: the Stokes drift caused by the irrotational wave motion, and the Eulerian mean flow induced by the top wavy boundary layer.; Numerical simulations based the Craik-Leibovich (CL) theory show that the second order Eulerian mean flow induced by the surface is essential in predicting the correct quantitative properties of Langmuir circulations, especially the pitch, defined as the ratio of the maximum downwind jet velocity to the maximum downwelling velocity. In laminar flows, with the Eulerian mean flow effect included, excellent agreement is achieved between the computed streamwise-averaged wavy flow and that predicted by the CL theory. The averaging in the CL theory is thus justified.; For the turbulent case, the Langmuir circulations are embedded in a much stronger, chaotic instantaneous field; nonetheless, they can be identified by time averaging. In Langmuir turbulence, the mixing due to the turbulence and the mean Langmuir circulations are approximately of equal importance. Relative to turbulent Couette flows, the logarithmic region near the bottom wall is modified and most of the logarithmic profile near the surface is destroyed by the Langmuir circulation, leading to a more uniform mean current. Furthermore, the production of turbulence is enhanced in the top surface layer and the pressure transport term is significant. Although the Langmuir circulation structure is similar in turbulent wavy flow and the flow from the CL theory, the CL theory produces stronger Langmuir cells but weaker turbulence. |
