The role of wave kinematics in turbulent flow over waves

The turbulent flow over monochromatic waves of moderate steepness is studied by means of wall resolved large eddy simulations. The simulations cover a range of wave ages and Reynolds numbers. At low wave ages the form drag is highly sensitive to Reynolds number changes, and the interaction between turbulent and wave-induced stresses increases with Reynolds number. At higher wave ages, the flow enters a quasi-laminar regime where wave-induced stresses are primarily balanced by viscous stresses, and the form drag displays a simple Reynolds number dependence. To exploit the quasi-laminar response to the wave kinematics, we split the flow field into a laminar wave-generated response and a turbulent shear flow. The former is driven by the non-homogeneous boundary conditions, whereas the latter is driven by the laminar solution as well as turbulent stresses. For high wave ages, the splitting enables approximate functional dependencies for the form drag to be formulated. In the low wave age regime, where the wave-induced stresses are tightly connected with higher harmonics in the turbulent stresses, the flow is more challenging to analyse. Nevertheless, the importance of higher harmonics in the turbulent stresses can be quantified by explicitly choosing which modes to include in the split-system forcing.