A THEORY OF STEADY BREAKERS

The mechanics of the quasi-steady breaking wave created above a submer ged hydrofoil, first studied experimentally by Duncan (1981), is eluci dated here. It is an example of a flow wherein the resistance of the b ody manifests itself in a detached separation eddy located away from t he body (i.e. on the free surface). As we show, the conditions for inc eption 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 e ssentially stagnant eddy riding on the forward face of the leading wav e in the wave train behind the hydrofoil. This eddy is sustained by tu rbulent stresses acting in the shear zone separating the eddy and the underlying flow. These stresses result in a trailing turbulent wake ju st 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 measuremen ts 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 residu al trailing wave, plus the momentum flux in the breaker wake, i.e. the breaker resistance. For a fixed hydrofoil speed the total momentum fl ux, or resistance, in the presence of breaking is shown to have a mini mum 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 min imum, 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 m aximum steady breaking resistance exists, limited by the size of the b reaker and dependent on the extent of its aeration. Good quantitative comparisons between theory and experiments are shown.