A theory of steady breakers

Abstract

The mechanics of the quasi-steady breaking wave created above a submerged hydrofoil, first studied experimentally by Duncan (1981), is elucidated here. It is an example of a flow wherein the resistance of the body manifests itself in a detached separation eddy located away from the body (i.e. on the free surface). As we show, the conditions for inception of separation and the prediction of the breaking configuration follow from simple considerations, without extensive calculation.The physical model of the breaker, based on observations, consists of an essentially stagnant eddy riding on the forward face of the leading wave in the wave train behind the hydrofoil. This eddy is sustained by turbulent stresses acting in the shear zone separating the eddy and the underlying flow. These stresses result in a trailing turbulent wake just beneath the water surface. The breaker eddy contains air entrained at breaking, and the degree of aeration is a parameter of the problem.The eddy—breaker model is quantified utilizing independent measurements of turbulent shear stress in shear zones. It is then shown that the hydrostatic pressure acting on the dividing streamline underneath the eddy creates a trailing wave which largely cancels the trailing wave that would exist in the absence of breaking. The ‘wave’ resistance of the hydrofoil then manifests itself in the momentum flux of the residual trailing wave, plus the momentum flux in the breaker wake, i.e. the breaker resistance.For a fixed hydrofoil speed the total momentum flux, or resistance, in the presence of breaking is shown to have a minimum corresponding to a particular value of the trailing-wave steepness. It is thus concluded that the wave resistance must exceed this value for breaking to ensue. For hydrofoil resistance in excess of this minimum, both a weak and strong breaker would seem to exist. It is shown, however, that the weak breaker is unstable. It is also shown that a maximum steady breaking resistance exists, limited by the size of the breaker and dependent on the extent of its aeration.Good quantitative comparisons between theory and experiments are shown.