Abstract
Interactions between waves and high-relief bottom roughness were investigated using Large Eddy Simulations of oscillatory flow over an infinite array of regularly spaced hemispheres. Simulation results were analyzed using a spatially- and phase-averaged momentum balance to provide insight into how flow-topography interactions affect wave-driven oscillating flows. Phase-averaging was applied first, and then spatial averaging was applied over volumes with horizontal length scales greater than the size of a single solid obstacle but fine enough in the vertical direction that the vertical structure of the dynamics was resolved. Spatial averaging of the momentum equation results in terms that represent drag and inertial forces, and a dispersive stress term that represents a vertical momentum flux induced by the spatial heterogeneity of the phase-averaged flow. These new terms require parameterization in coastal ocean wave and circulation models.
Highlights
Most models that are commonly used to estimate the friction factor fw were developed for z/ks >> 1, when the wave boundary layer thickness (z) is large compared with roughness element height (ks), shear stress at the top of the roughness layer is similar to form drag per unit area exerted by the bed, and the inertial force is small compared with form drag
Flow dynamics strongly depends on KeuleganCarpenter number KC=U0T/D, where U0 is the amplitude of the wave velocity, T is the wave period and D is the diameter of a single hemisphere
The dispersive stress was the main mechanism for vertical momentum transfer, the stress gradient term was small compared with drag and inertial force terms
Summary
Most models that are commonly used to estimate the friction factor fw were developed for z/ks >> 1, when the wave boundary layer thickness (z) is large compared with roughness element height (ks), shear stress at the top of the roughness layer is similar to form drag per unit area exerted by the bed, and the inertial force is small compared with form drag. Flow dynamics strongly depends on KeuleganCarpenter number KC=U0T/D, where U0 is the amplitude of the wave velocity, T is the wave period and D is the diameter of a single hemisphere. The inertial force dominated flow dynamics, form drag was small, and both Reynolds and dispersive stresses were negligible.
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