The role of wave kinematics in turbulent flow over waves

Espen Åkervik, Magnus Vartdal

Published 2019-01-31Version 1

The turbulent flow over monochromatic waves in the low to intermediate Reynolds number range is studied by means of wall resolved large eddy simulation, thus complementing existing direct numerical simulation Reynolds averaged Navier--Stokes simulation studies. Our results confirm the previously noted simple behaviour at high wave ages, and also the existence of a Reynolds number at which the form drag is maximised. At low wave ages, there is an increasing trend of transfer between different harmonics of the flow with increasing Reynolds number. This is caused both by the nonlinear advection terms and geometry terms stemming from the curved lower boundary. For higher wave ages the wave correlated velocities tend towards simple behaviour, and is accompanied by the loss of energy in higher harmonics of the turbulent stresses. The results are further analysed in a split system approach, where we first construct a laminar flow response to the wave kinematics. This in turn acts as a forcing to a turbulent shear flow subjected to homogeneous boundary conditions. By deconstructing the flow in this manner we are able to formulate an analytic functional dependence of the form drag associated with the laminar response, and show that this dominates for high wave ages. Also for the remaining turbulent part, approximate approximate functional dependencies are given. The reason for this simplicity, is that at high wave ages, the forcing from the laminar wave induced flow is so severe that the geometry induced interaction of the turbulent shear flow with itself is almost negligible. At low wave ages, the decomposition does not yield similar insight. This is because the nonlinearities stemming from geometry and turbulence are significant and the shear of the particular solution also varies with both wave age and Reynolds number.