A new solution for oscillatory flows over permeable beds

Water waves propagating though the ocean induce boundary layers flows near the seabed due to viscous effects. These boundary layer flows are important because they can drive different physical processes, such as sediment transport, wave damping, and mass transport. In this work, we considered the propagation of oscillatory waves over permeable beds. Using perturbation theory, the fluid velocity in the boundary layer was decomposed into an irrotational and rotational component, while the velocity inside the permeable bed followed Darcy's law. To treat the influence of the permeable bed on the boundary layer flows, three different boundary conditions were considered at the upper edge of the permeable bed: Darcy's law, Beavers and Joseph (1967), and Le Bars & Worster (2006). We also developed a set of analytical solutions that exhibit this behavior and show an agreement with the numerical solutions for different boundary conditions. Our results show that velocities and mass transport velocity modify their structure close to the boundary by increasing their magnitudes as the dimensionless hydraulic conductivity increases, while bed shear stresses behave in an opposite manner decreasing their magnitudes.