Effects of waves on the boundary layer of a surface-piercing body

The boundary-value problem associated with the boundary-layer development on a surface-piercing body is formulated in a rigorous manner in which proper consideration is given both to the kinematic and dynamic boundary conditions and to the deformation of the potential-flow free surface within the boundary layer. Simplifications that are appropriate for small amplitude waves are then investigated. The flow field in the neighborhood of the body-boundary-layer/free-surface juncture is divided into five regions and order-of-magnitude estimated for each region are provided. Of particular interest is the body free-surface boundary layer in the region very close to the free surface in which the free-surface boundary conditions have a significant influence. In this region, it is shown that, for laminar flow, the parameter Ak/e (where Ak is the wave-steepness parameter and e = delta/L is the nondimensional boundary-layer thickness) is an important parameter for characterizing the flow. Different solution regimes are identified depending on the magnitude of Ak/e. In particular, for Ak/e the magnitude is sufficiently large such that the free-surface boundary conditions have a significant influence. A consistent formulation requires the solution of the partially-parabolic Navier-Stokes equations. For turbulent flow, these conclusions cannot be reached with the same degree of certainty due to the present uncertainties in turbulence modelling, especially when a free surface is present. Numerical results are provided for the idealized geometry of a combination Stokes-wave/flat-plate.