and c, respectively; however, its negative partner appears only at x/L=0.91 (Figure 9e). Figure 10 shows the second pair (but in a different run) moving away from the surface, shortly after the negative vortex is generated. These images are recorded with a video camera using the setup of Figure 1c. As noted before, one of the vortices in Figure 9e traps a bubble. Figure 11c attempts to illustrate the sequence of vortex generation on the model. The entire process has some resemblance to three dimensional, open separation in the lee side of inclined bodies of revolution. However, considerably more data analysis, which is still in progress, is required before we are able to construct the complete flow topology. In addition to the repeatable vortices that develop near on the model, the flow near the free surface contains numerous vortices with alternating signs. Their locations and spatial distributions are unsteady and they regularly entrap bubbles.
For the present surface piercing model with a long draft a bubbly wake is generated at the trough between the bow and the shoulder wave. This phenomenon occurs at x/L=0.41 and FrL≥0.153 due to impingement of the flow on the model, a process associated with energy dissipation in the bow wave. Consequently, the origin of the shoulder wave consists of several powerful counter-rotating vortices which entrain bubbles from the free surface. The wave crest becomes milder and eventually irrotational with increasing distance from the model. Behind the shoulder wave, at x/L=0.7, boundary layer separation begins, but only near the free surface. The flow within the separated region consists of two pairs of counter rotating vortices that detach from the boundary layer on the model. The first vortex is generated at the intersection of the body with the free surface, but the following ones are originated below the free surface. At FrL=0.255 there is no reverse flow within the separated region, but flow reversal seems to occur at FrL≥0.307. The flow structure is turbulent and involves considerable dissipation.
This project is sponsored by the Office of Naval Research under grant number N00014–93–10–204, under the management of Dr, Edwin Rood. Thanks are also due to R.Dong for his assistance.
1. Miata, H., Inui, T., “Nonlinear Ship Waves,” Advances in Applied Mechanics, Vol. 24, 1984, pp. 215–288.
2. Fry, D.J., and Kim, Y.H., “Bow Flow of Surface Ships,” Proc. of the 15th Symp. on Naval Hydrodynamics, Hamburg, Germany, pp. 319–346.
3. Toda, Y., Stern, F., and Longo, J., “Mean-Flow Measurements in the Boundary Layer and Wake and Wave Field of a series 60 CB=0.6 Ship Model—Part 1: Froude Numbers 0.16 and 0.316,” J. of Ship Res., Vol. 36, No. 4, 1992, pp. 360–377.
4. Longo, J., Stern, F., and Toda, Y., “Mean-Flow Measurements in the Boundary Layer and Wake and Wave Field of a series 60 CB=0.6 Ship Model—Part 2: Scale Effects on Near-Field Wave Patterns and Comparisons with Inviscid Theory,” J. of Ship Res., Vol. 37, No. 1, 1993, pp. 16–24.
5. Dong, R.R., Katz, J., and Huang, T.T., “PIV Measurements of the Flow Structure Around a Ship Model,” ASME/EALA Sixth International Symp. on Laser Anemometry, 1995, pp. 425–434.
6. Stern, F., Hwang, W.S., Jaw, S.Y., “Effects of Waves on the Boundary Layer of a Surface-Piercing Flat Plate: Experiments and Theory,” J. Ship Res., Vol. 33, No. 1, 1989, pp. 63–80.
7. Zhang, Z.J., and Stern, F., “Wave-Induced Separation,” Forum on Advances in Numerical Modeling of Free Surface and Interface Fluid Dynamics, 1995, ASME IMECE, San Francisco, CA.
8. Dong, R., Chu, S., and Katz, J., ( 1992), “Quantitative Visualization of The Flow Structure Within The Volute of a Centrifugal Pump, Part A: Technique,” J. Fluids Eng., Vol. 114, No. 3, 1992, pp. 390–395.
9. Roth, G., Hart, D., and Katz, J., “Feasibility of Using the L64720 Video Motion Estimation Processor (MEP) to Increase Efficiency of Velocity Map Generation for PIV, ” ASME/EALA 6th International Symp. on Laser Anemometry, August 1995, pp. 387–394.
10. Lin, J.C., and Rockwell, D., “Instantaneous Structure of a Breaking Wave,” Physics of Fluids, Vol. 6, No. 9, 1994, pp. 2877–2879.
11. Lin, J.C, and Rockwell, D., “Evolution of a Quasi-Steady Breaking Wave,” Journal of Fluid Mech., vol. 302, 1995, pp. 29–44.
12. Sarpkaya, T., “Vorticity, Free Surface, and Surfactants,” Ann. Rev. Fluid. Mech., Vol. 28, 1996, pp. 83–128.
13. Pogozelski, E., Katz, J., and Huang, T., “How Structure Around a Surface-Piercing Blunt Body,” Proc. 20th ONR Symposium on Naval Hydrodynamics, August 1994.
14. Hendrix, D., and Noblesse, F., “Recipes for Computing the Free-Surface How Due to a Source Distribution, ” Journal of Ship Research, vol. 36, No. 4, Dec. 1992, pp. 346–359.