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Fig.23 shows the turbulent energy profiles in depthwise direction at points A and D. At point A, the turbulent energy is almost zero while, at point D, it is intensive on the free surface and it abruptly becomes weak at the depth of 0.02L from the free surface.

We can point out that the free surface turbulent flow referred to the sub-breaking wave generated without overturning waves. The numerical simulations neglecting the turbulence may lead a misunderstanding of the phenomena.

Fig. 23 Computed turbulent energy distributions at points A and D; NS12, Fn=0.30, Rn=1.0·105:

7
Concluding Remarks

Some characteristics of the turbulent and vortical flows around the free surface are numerically and experimentally investigated. Four different struts are used to investigate the curvature effect of the bow.

Findings through the present study are summarized as follow;

  1. The no-shearing stress condition on the free surface is important to generate the vorticity beneath the free surface. And the vorticity induces vortical motions beneath the free surface when the free surface curvature is large.

  2. The proposed LES method reveals the existence of the free surface turbulence called sub-breaking wave which is not followed by overturning waves.

  3. The bow with a larger curvature intensifies the concave curvature of the free surface and generates a stronger vorticity than the bows with smaller curvature.

  4. Grid density around the free surface is one of the important computational parameters; coarse grid can not detect the vortical flows beneath the free surface.

The authors express a lot of thanks to Dr. S.Ninomiya, research associate at Hiroshima University, for his kind support in experiments.

References

[1] Baba, E.: A New Component of Viscous Resistance of Ship, Journal of the Society of Naval Architects of Japan, Vol. 125, pp.23–34, 1969.

[2] Taneda, S. and Amamoto, H.: The Necklace Vortex of the Ship, Bulletin of Research Institute for Applied Mechanics, Kyushu Univ., No.31, pp.17–28, 1969 (in Japanese).

[3] Miyata, H., Kajitani, H., Shirai, M., Sato, T., Kuzumi, S. and Kanai, M.: Numerical and Experimental Analysis of Nonlinear Bow and Stern Waves of a Two-Dimensional Body (4th Report)-Simulation of Breaking Waves and Experimental Analysis , Journal of the Society of Naval Architects of Japan, Vol.157, pp.15–33, 1985.

[4] Grosenbaugh, M.A. and Yeung, R.W.: Nonlinear Bow Flows-An Experimental and Theoretical Investigation, Proceedings of 17th Symposium on Naval Hydrodynamics, Hague, Netherlands, pp.195–214, 1988.

[5] Honji, H.: The Necklace Vortex of the Ship, Bulletin of Research Institute for Applied Mechanics, Kyushu Univ., No.43, pp.11–17, 1975 (in Japanese).

[6] Kayo, Y. and Takekuma, K.: On the Free Surface Shear Flow related to Bow Wave-Breaking of Full Ship Models, Journal of the Society of Naval Architects of Japan, Vol. 149, pp.11–20, 1981.

[7] Patel, V.C., Landweber, L. and Tang, C.J.: Free-Surface Boundary Layer and the Origin of Bow Vortices, 2nd International Symposium on Ship Viscous Resistance, Gotenburg, Sweden, pp.23:1–23:13, 1985.



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