Large scale modelling of oscillatory flows over a rippled bottom

Abstract

Large scale models for oscillatory flows over rippled sandy bottoms require new “turbulence” closures and boundary conditions to account for the ripple scale flow. In the present study the large scale flow with the unknown flux terms is estimated by means of a standard RANS model. The simulations do not support the application of the Boussinesq viscosity approximation in wave dominated flows, but other tentative ideas on such type of modelling are confirmed. The characteristic wave wavelength average thickness of the oscillatory boundary layer is estimated as comparable to four times the ripple height. The characteristic wave wavelength average near bottom sediment concentration is estimated to be proportional to the maximum Shields number to the third power. The characteristic wave wavelength near bottom friction is suggested to be proportional to the near bottom current and wave velocity amplitude. The characteristic ripple wavelength average thickness of the oscillatory boundary layer is estimated to be comparable to the characteristic wave wavelength averaged thickness. The characteristic ripple wavelength averaged oscillatory flux terms are estimated to be much larger than the corresponding average turbulent flux terms. The ripple wavelength averaged total flux terms appear to have extrema that are associated both with the flow- and acceleration maxima.