Direct numerical simulations of wave-current boundary layer over rough walls

Turbulence in estuarine bottom boundary layers influence a large variety of biological and anthropogenic activities by driving the hydrodynamics and morphodynamic response of such large-scale coastal ocean systems. Thus, a detailed understanding of these boundary layers enables accurate, long-term prediction of the fate of nutrients, pollutants, sediments, and other relevant quantities within estuarine environments. Typically, estuaries are driven by the mean turbulent currents and oscillatory wave motion that interact over naturally rough bottom boundaries. These wave-current interactions often occur non-linearly resulting in complex mean flow responses across the water column.

A direct forcing immersed boundary method (IBM) was implemented in a second-order accurate, staggered finite-difference code enabling the modeling of rough-wall channel flows. Through the definition of the Corey shape factor (Co), the effect of roughness shape characterisation on the mean flow drag was validated to show that the mean flow drag increases with decreasing Co. Using a wide range of full- and minimal-span channel flow simulations with varying Co and friction Reynolds number (Re*), direct solutions of the governing equations were used to provide insights into this mean flow drag increase.

Having established a consistent way to estimate the mean flow drag as a function of the Corey shape factor, the dynamics of current-dominated, wave-current boundary layers over hydraulically smooth walls were studied using direct numerical simulations. For the flat wall wave-current boundary layer, the mean flow drag did not exhibit any substantial change when compared to the canonical flat wall channel flow. However, the bumpy wall wave-current boundary layer showed elevated mean flow drag when compared to the canonical flat and bumpy wall channels. Using a turbulent kinetic energy (TKE) and Reynolds stress budget analysis, it was found that there was a decrease in the net TKE production to dissipation rate ratio as a result of the increased TKE dissipation rate. It was also observed that the pressure-strain rate correlations that scramble the TKE across the three diagonal components were comparatively enhanced for the bumpy wall, wave-current case. Consequently, unlike the flat wall wave-current case, the bumpy wall, wave-current boundary layer exhibits increased mean flow drag.

Finally, using direct numerical simulations of the wave-dominated, wave-current boundary layer over rough walls, it was shown that the simple eddy-viscosity-based drag model proposed by Grant & Madsen (1979), which is meant for the wave-dominated regime, applies because the near-wall flow is three-component-like and isotropic. Additionally, it was observed that the turbulence in the boundary layer responds quickly to the imposed wave-driven mean shear, thus validating the assumption in the eddy-viscosity type models that the turbulence and mean wave-driven shear are in phase. Collectively, these observations validate the use of simple drag models of wave-current boundary layers in large-scale coastal ocean models in the wave-dominated regime. Further work is needed to develop parameterisations for the bottom drag in current-dominated boundary layers.