Generation of Stable Linear Waves in Shallow Water in a ‎Numerical Wave Tank

Document Type : Regular Article


Department of Mechanical Engineering, National Institute of Technology, Silchar, Assam -788010, India‎



This paper aims to investigate numerically linear stable waves at low wave steepness in shallow water using ANSYS Fluent software. The authors mainly determined how, when, and where a linear wave will reach its stable state in shallow water. The finite volume method is used to solve the Navier-Stokes equations. The inflow velocity method and the Dirichlet boundary condition are used to generate a suitable linear wave. Numerical damping is used at the end of the tank to reduce the reflection of the wave. The accuracy and stability of the waves are judged under wave height variation between the CFD results and the analytical results. The test has been conducted in four different cases (Case 1, Case 2, Case 3, and Case 4). Wave evolution and particle velocity are obtained in the velocity field to understand the wave stability in the numerical wave tank. Numerical data are captured from the free surface to compare the surface profile and wave velocity. The results have revealed that the accuracy, stability, and consistency of the linear waves are in good agreement with the analytical solution.  The relative error between the two results is 1.43% for Case 3. This research is a highly relevant source of information in realistic wave generation to design various practical systems such as wave energy converters, offshore marine structures, and many ocean engineering problems‎.


Benjamin, T. B. and M. J. Lighthill (1954). On cnoidal waves and bores. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 224 (1159), 448-460.##
Boussinesq, M. J. (1871). Théorie de l’intumescence liquide, appelée onde solitaire ou de translation, se propageant dans un canal rectangulaire. Comptes rendus de l'Académie des Sciences 72, 755-759.##
Cornejo, P. and H. H. Sepulveda (2016). Computational fluid dynamics modelling of a midlatitude small scale upper ocean front. Journal of Applied Fluid Mechanics 9 (4), 1851-1863.##
Dean, R. G. and R. A. Dalrymple (1984). Water wave mechanics for engineers and scientists. Prentice Hall, N.J.##
Farhadi, A., H. Ershadi, H. Emdad and G. RadE (2016). Comparative study on the accuracy of solitary wave generations in an ISPH- based numerical wave flume. Applied Ocean Research 54, 115-136.##
Goring, D. G. (1978). Tsunamis the Propagation of Long Waves onto a Shelf. Ph.D. Thesis, California Institute of Technology, Pasadena, California.##
Grilli, S. T., I. A. Svendsen and R. Subramanya (1997). Breaking criterion and characteristics for solitary waves on slopes. Journal Waterway Port Coastal Ocean Engineering 123, 102-112.##
Gualtieri, C. and H. Chanson (2011). Experimental study of a positive surge. Part 2: Comparison with literature theories and unsteady flow field analysis. Environmental Fluid Mechanics 11, 641–651.##
Gualtieri, C. and H. Chanson (2012). Experimental study of a positive surge. Part 1: Basic flow patterns and wave attenuation. Environmental Fluid Mechanics 12, 145-159.##
Guyenne, P. and S. T. Grilli (2006). Numerical study of three dimensional overturning waves in shallow. Journal of Fluid Mechanics 547, 361-388.##
Hirt, C. W. and B. D. Nichols (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics 39, 210-225.##
Huang, C. J. and C. M. Dong (2001). On the interaction of a solitary wave and a submerged dike. Coastal Engineering 43 (3/4), 256-286.##
Jensen, A., G. K. Pedersen and D. J. Wood (2003). An experimental study of wave run up at a steep beach. Journal of Fluid Mechanics 486, 161-188.##
Keulegan, G. H. (1948). Gradual damping of solitary waves. Journal Research of the National Bureau of Standards 40, 487-498.##
Lal, A. and M. Elangovan (2008). CFD simulation and validation of flap type wave maker. World Academy of Science Engineering and Technology 46, 7.##
Le Mehaute, B. (1976). An introduction to hydrodynamics and water waves. Limnology and Oceanography (New York: Springer-Verlag).##
Leng, X. and H. Chanson (2017). Unsteady velocity profiling in bores and positive surges. Flow Measurement and Instrumentation 54, 136-145.##
Leng, X., B. Simon, N. Khezri, P. Lubin and H. Chanson (2018a). CFD modeling of tidal bores: development and validation challenges. Coastal Engineering Journal 60(4), 423-436.##
Leng, X., H. Chanson and D. Reungoat (2018b). Turbulence and turbulent flux events in tidal bores: case study of the undular tidal bore of the Garonne River. Environmental Fluid Mechanics 18(4), 807-828.##
Li, Y. and F. Raichlen (2001). Solitary wave runup on plane slopes. Journal Waterway Port Coastal Ocean Engineering 127(1), 33-44.##
Liang, X. F., J. M. Yang, J. Li, L. F. Xiao and X. Li (2010). Numerical simulation of irregular wave simulation irregular wave train. Journal of Hydrodynamics, Ser. B 22(4), 537-545.##
Lin, P. and P. L. F. Liu (1998). A numerical study of breaking waves in the surf zone. Journal of Fluid Mechanics 359, 239-264.##
Liu, H., W. Wu and B. L. Wang (2000). Vertical wall reflection of a fully nonlinear solitary wave. Ocean Engineering 18 (1), 1-6.##
Lu, J. and X. Yu (2008). Numerical study of solitary wave fission over an underwater step. Journal of Hydrodynamics, Ser. B 20(3), 398-402.##
Lynett, P. J., T. R. Wu and P. L. F. Liu (2002). Modeling wave runup with depth integrated equations. Coastal Engineering 46(2), 89-107.##
Mei, C. C. (1983). The applied dynamics of ocean surface wave (World Scientfic)##
Peng, QI. and H. Yijun (2006). A VOF-based numerical model for breaking waves in surf zone. Chinese Journal of Oceanology and Limnology 24(1), 57-64.##
Saincher, S. and J. Banerjee (2015). Design of a numerical wave tank and wave flume for low steepness waves in deep and intermediate water. Procedia Engineering 116, 221-22.##
Seiffert, B., M. Hayatdavoodi and R. C. Ertekin (2014). Experiments and computations of solitary wave forces on a coastal bridge deck Part I: flat plate. Coastal Engineering 88, 194-209.##
Wijetunge, J. J. (2010). Numerical simulation of the 2004 Indian ocean tsunami: case study of effect of sand dunes on the spatial distribution of inundation in hambantota, Sri Lanka. Journal of Applied Fluid Mechanics 3 (2), 125-135. ##  
Wu, N. J., S. C.  Hsiao, H. H. Chen and R. Y. Yang (2016). The study on solitary waves generated by a piston type wave maker. Ocean Engineering 117, 114-129.##
Wu, N. J., T. K. Tsay and Y. Y. Chen (2014a). Generation of stable solitary waves by a piston type wave maker. Wave Motion 54(2), 240-255.##
Wu, Y. T. and S. C. Hsiao (2013). Propagation of solitary waves over a submerged permeable breakwater. Coastal Engineering 81, 1-18.##
Wu, Y. T. and S. C. Hsiao (2017). Propagation of solitary waves over double submerged barriers. Water 9(12), 917.##
Wu, Y. T., C. L. Yeh and S. C. Hsiao (2014b). Three dimensional numerical simulation on the interaction of solitary waves and porous breakwaters. Coastal Engineering 85, 12-29.##
Wu, Y. T., S. C. Hsiao, Z. C. Huang and K. S. Hwang (2012). Propagation of solitary waves over a bottom mounted barrier. Coastal Engineering 62, 31-47.##
Yang, W. J., T.T Zhang, C. Li, S. M. Li and X. H. Xu (2019). Numerical simulation of pitching sloshing under microgravity. Journal of Applied Fluid Mechanics 12 (5), 1527-1537.##