Bow flows with surface tension

Abstract

Two-dimensional free surface flow past a semi-infinite plate is considered. Surface tension is included in the free surface condition, and the effect of gravity is neglected. The configuration models a bow flow, i.e. the flow occurring at the front of an object moving at a constant velocity at the surface of a fluid. It is shown analytically and numerically that flows with waves do not meet the plate tangentially: there is an angle $\delta \neq $ 0 between the plane of the plate and the free surface at the separation point. The shape of the free surface is computed by a boundary integral equation method as a function of $\delta $. The exact form of the wave in the far field is derived as a function of $\delta $ from the principle of conservation of momentum. In particular it is found that the dimensionless wavelength $\lambda $ = $\pi $(1 + cos $\delta $). The numerical results are shown to be consistent with the exact results.