Interaction of Nonlinear Progressive Waves with Two Serially Arranged Submerged Obstacles
Publication: Journal of Engineering Mechanics
Volume 133, Issue 2
Abstract
The purpose of the present study is to develop a numerical model for the investigation of water waves propagating over a pair of impermeable submerged obstacles. The mathematic model is formulated by coupling solutions of the Navier–Stokes equations and transport equations for the surface elevation using the volume of fluid method. Based on a staggered computational mesh, an explicit numerical algorithm is employed with a predictor–corrector procedure of pressure and velocity field. The proposed model provides good agreement with other experimental results and validates its good performance. Regarding the spatial harmonic evolutions of various cases, it is noted that the present fluctuating mode of harmonic amplitudes exists upstream and at the gap between obstacles. The results show that the nonlinearity of propagating waves becomes stronger than the initial wave in such areas, and reveals much steeper wave profiles compared to the initial ones. The fluctuating harmonic amplitudes vary with the gap width and form two hydrodynamic cycles. The vortices play an important role in the wave reflection as they form a water column wall to reflect the incoming waves. The reflection ratio depends on the extent of vortex development near the upstream obstacle. The maximum wave reflection occurs in cases with dimensionless gap width equal to 3/8 and 7/8 in this study.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research was financially supported by the Institute of Physics, Academia Sinica, Taipei, Taiwan, and the National Science Council, R.O.C., Grant No. NSC 94-2611-E-001-001.
References
Grue, J. (1992). “Nonlinear water wave at a submerged obstacle.” J. Fluid Mech., 244, 455–476.
Harlow, F. H., and Welch, J. E. (1965). “Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface.” Phys. Fluids, 8, 2182–2189.
Hirt, C. W., and Nichols, B. D. (1981). “Volume of fluid method for the dynamics of free boundaries.” J. Comput. Phys., 39, 201–225.
Hirt, C. W., Nichols, B. D., and Romero, N. C. (1975). “SOLA—A numerical solution algorithm for transient fluid flows.” Rep. LA-5852, Los Alamos Scientific Laboratory, Los Alamos, N.M. 1–50.
Hsu, T. W., Liu, J. L., Liau, J. M., and Shin, C. Y. (2000). “Flow field around the submerged breakwater under wave action by FLDV measurements.” Proc., 22nd Ocean Engineering in Taiwan, Hsinchu, Taiwan, 119–126 (in Chinese).
Huang, C. J., and Dong, C. M. (1999). “Wave deformation and vortex generation in water waves propagating over a submerged dike.” Coastal Eng., 37, 123–1480.
Hwang, R. R., and Sue, Y. C. (1998). “Numerical simulation on nonlinear interaction of water waves with submerged obstacles.” Proc., 7th Flow Modeling and Turbulence Measurements, Tainan, Taiwan, 545–554.
Lamb, H. (1932). Hydrodynamics, 6th Ed., Cambridge University Press, Cambridge, U.K.
Lin, C. Y., and Huang, C. J. (2004). “Decomposition of incident and reflected higher harmonic waves using four wave gauges.” Coastal Eng., 51, 395–406.
Lowery, K., and Liapis, S. (1999). “Free-surface flow over a semicircular obstruction.” Int. J. Numer. Methods Fluids, 30, 43–63.
Massel, S. R. (1983). “Harmonic generation by waves propagating over a submerged step.” Coastal Eng., 7, 357–380.
Mei, C. C., and Black, J. L. (1969). “Scattering of surface waves by rectangular obstacles in waters of finite depth.” J. Fluid Mech., 38, 499–511.
Newman, J. N. (1965). “Reflection and transmission of water waves past long obstacles.” J. Fluid Mech., 23, 399–415.
Ohyama, T., and Nadaoka, K. (1992). “Modeling the transformation of nonlinear waves passing over a submerged dike.” Proc., 23rd Int. Coastal Engineering Conf., Venice, 526–539.
Orlanski, I. (1976). “A simple boundary condition for unbounded hyperbolic flows.” J. Comput. Phys., 21, 251–269.
Petti, M., Quinn, P. A., Liberatore, G., and Easson, W. J. (1994). “Wave velocity field measurement over a submerged breakwater.” Proc., 24th Int. Coastal Eng. Conf., Japan, 525–539.
Rey, V., Belzons, M., and Guazzelli, E. (1992). “Propagation of surface gravity waves over a rectangular submerged bar.” J. Fluid Mech., 235, 453–479.
Seabra-Santos, F. J., Renouard, D. P., and Temperville, A. M. (1987). “Numerical and experimental study of transformation of a solitary wave over a shelf or isolated obstacle.” J. Fluid Mech., 176, 117–134.
Ting, F. C. K., and Kim, Y. K. (1994). “Vortex generation in water waves propagation over a submerged obstacle.” Coastal Eng., 24, 23–49.
Information & Authors
Information
Published In
Copyright
© 2007 ASCE.
History
Received: May 3, 2005
Accepted: Jul 7, 2006
Published online: Feb 1, 2007
Published in print: Feb 2007
Notes
Note. Associate Editor: Robert J. Martinuzzi
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.