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assuming the balance of a surface tension and a normal component of a viscous stress.

Mori[8] discussed the free surface flows before the wave breaking took place. He divided the flow into three stages; the development of the free surface shear layer, the formation of the necklace vortex and the production of unsteady turbulent free surface flow. It was called ”sub-breaking waves” as a free surface turbulent flow in distinction from spilling or plunging breakers. He also deduced that the free surface curvature played a role to generate a vorticity on the curved free surface and the vorticity could be one of the sources of the necklace vortex. The theoretical background of the free surface shear layer was also given by Batchelor[9].

Mori and Shin[10] simulated the sub-breaking wave generated by two-dimensional submerged hydrofoil. They used experimental results to set the free surface boundary condition strictly. Mori and Lungu[11] simulated two-dimensional sub-breaking waves directly by imposing a disturbance for vertical velocity component while Coleman[12] used a disturbance of pressure on the free surface. The role of these disturbances might be a kind of a trigger for the transition to the turbulent flow and it might be assumed as a source that maintains the turbulence on the free surface.

Main objective of the present study is to make clear the characteristics of the flow at the early stage of bow wave breaking around surface piercing struts, especially the effect of the vorticity generated on the free surface on the vortical and turbulent flows beneath the free surface. To simplify the problem, the surface tension is excluded in the present investigations. Numerical investigations are made by solving the Reynolds averaged Navier-Stokes(NS) and continuity equations by finite difference method(FDM). Several computations are performed to investigate the effects of computational and physical parameters, for examples, grid dependency, the effects of the Reynolds and Froude numbers, free surface treatment and so on. To investigate the curvature effect of the bow, four different struts having NACA0005, NACA0008, NACA0012, and NACA0024 sections are used(called NS05, NS08, NS12 and NS24 respectively hereafter). The fluctuated free surface flows called sub-breaking waves are also studied by Large Eddy Simulation(LES). Some computed results are compared with the experimental results.

Observation of Bow Wave Patterns

An observation of bow wave patterns was performed for NS08, NS12 and NS24 models at the circulating water channel(CWC) of Hiroshima University. The length and draft of the models were 0.8m and 0.4m respectively. Experimental arrangement is shown in Fig.1. The wave patterns were photographed under the CWC. The striped-screen was fixed above the free surface to make the pictures clear. To remove a surface tension, a surfactant was used[13].

Fig. 1 Experimental set-up.

Fig.2 shows a schematic view of the bow wave on the center plane. The ”Zone-I” where the free surface has smooth concave curvature is the part ahead of the bow wave. Through a sharp change of the curvature, the flow enters ”Zone-II” where the flow can not be stable any more. A border of these two zones is ”wave front” where the curvature has a maximum[8].

Fig. 2 Schematic view of bow wave.

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