Abstract
In this research, interactions between a solitary wave and two submerged rectangular obstacles with different distances were studied experimentally. The particle image velocimetry (PIV) technique was used to measure the velocity field on the weather and lee sides of the two obstacles. Two submerged rectangular obstacles with 12-cm height and 8-cm length were installed in an open water channel with 7-m length. The velocity fields were obtained with 5 fields of view (FOVs) and then synchronized together. The vortices that formed on the weather and lee sides of the rear and front obstacles were compared to each other. It was found that the vortex on the weather side of the rear obstacle was flatter and smaller than that on the weather side of the front obstacle. Moreover, the weather-side vortex of the front obstacle grew more. After the wave passes over the two obstacles, the vortices on the weather and lee sides of the front obstacle are merged together and form a larger vortex. A higher vorticity at the center of the weather side vortex of the front obstacle was observed. By increasing the distance between the obstacles, the vortex between the obstacles expands more, and the interaction of the flow with the obstacles is more intensive so that more and larger vortices are formed. These vortices depreciate the wave energy. The measurement of the wave height before and after the obstacles showed that the larger the distance between the obstacles, the higher wave energy loss will be.
Similar content being viewed by others
Abbreviations
- h :
-
Water depth
- H :
-
Wave amplitude
- b :
-
Width of channels
- ρ :
-
Water density
- g :
-
Gravity
- η :
-
Free surface elevation
- t :
-
Time
- t * :
-
Dimensionless time
- c :
-
Wave speed
- E :
-
Total energy of the wave
- A :
-
Vortex area
- ω :
-
Vorticity
- Г :
-
Circulation
References
Mei CC, Black JL (1969) Scattering of surface waves by rectangular obstacles in waters of finite depth. J Fluid Mech 38(3):499–511
Seabra-Santos FJ, Renouard D, Temperville A (1987) Numerical and experimental study of the transformation of a solitary wave over a shelf or isolated obstacle. J Fluid Mech 176:117–134
Silva R, Losada IJ, Losada MA (2000) Reflection and transmission of tsunami waves by coastal structures. Appl Ocean Res 22(4):215–223
Chang KA, Hsu TJ, Liu PLF (2001) Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle: Part 1 Solitary waves. Coast Eng 44(1):13–36
Lin P (2004) A numerical study of solitary wave interaction with rectangular obstacles. Coast Eng 51(1):35–51
Zarruk GA, Cowen EA, Wu TR, Lin PL (2015) Vortex shedding and evolution induced by a solitary wave propagating over a submerged cylindrical structure. J Fluids Struct 52:181–198
Hsieh CM, Hwang RR, Hsu JR, Cheng MH (2015) Numerical modeling of flow evolution for an internal solitary wave propagating over a submerged ridge. Wave Motion 55:48–72
Madsen OS, Mei CC (1969) The transformation of a solitary wave over an uneven bottom. J Fluid Mech 39:781–791
Goring DG, Raichlen F (1992) Propagation of long waves onto shelf. J Waterw Port Coast Ocean Eng 118(1):43–61
Otta A, Svendsen IA, Grilli ST (1992) The breaking and run-up of solitary wave on beaches. Proceeding of 23rd International Conference on Coastal Engineering, ASCE. Venice, Italy 1461–1474.
Grilli ST, Losada MA, Martin F (1994) Characteristics of solitary wave breaking induced by breakwaters. J Waterw Port Coast Ocean Eng 120(1):74–92
Ting FCK, Kim YK (1994) Vortex generation in water waves propagating over a submerged obstacle. Coast Eng 24(1):23–49
Decheng W, Guoxiong W (1998) Numerical simulation of a solitary wave interaction with submerged multi-bodies. Chines J Mech Press 14:297–305
Zhang DH, Chwang AT (1999) On solitary waves forced by underwater moving objects. J Fluid Mech 389:119–135
Huang CJ, Dong CM (1999) Wave deformation and vortex generation in water waves propagating over a submerged dike. Coast Eng 37:123–148
Huang CJ, Dong CM (2001) On the interaction of a solitary wave and a submerged dike. Coast Eng 43:265–286
Hsu TW, Hsieh CM, Hwang RR (2004) Using RANS to simulate vortex generation and dissipation around impermeable submerged double breakwaters. Coast Eng 51:557–579
Wu YT, Hsiao SC, Huang ZC, Hwang KS (2012) Propagation of solitary waves over a bottom-mounted barrier. Coast Eng 62:31–47
Zhou Q, Zhan JM, Li YS (2014) Numerical study of interaction between solitary wave and two submerged obstacles in tandem. J Coastal Res 30:975–992
Lin MY, Huang LH (2009) Study of water waves with submerged obstacles using a vortex method with Helmholtz decomposition. Int J Numer Methods Fluids 60:119–148
Lin MY, Huang LH (2010) Vortex shedding from a submerged rectangular obstacle attacked by a solitary wave. J Fluid Mech 651:503–518
Goring DG (1978) Tsunamis—the propagation of long waves onto a shelf. Rep. KH-R-38, California Institute of Technology, USA.
Grue J (1992) Nonlinear water waves at a submerged obstacle or bottom topography. J Fluid Mech 244:455–476
Rey V, Belzons M, Guazzelli E (1992) Propagation of surface gravity waves over a rectangular submerged bar. J Fluid Mech 235:453–479
Beji S, Battjes JA (1993) Experimental investigation of wave propagation over a bar. Coast Eng 19:151–162
Zhuang F, Lee JJ (1996) A viscous rotational model for wave overtopping over marine structure. Proceeding of 25th International Conference on Coastal Engineering, ASCE, Orlando, Florida, USA 2178–2191.
Tang CJ, Chang JH (1998) Flow separation during solitary wave passing over submerged obstacle. J Hydraul Eng 124:742–749
Chang KA, Hsu TJ, Liu PLF (2005) Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle: Part II Cnoidal waves. Coast Eng 52:257–283
Lin C, Ho TC, Chang SC, Hsieh SC, Chang KA (2005) Vortex shedding induced by a solitary wave propagating over a submerged vertical plate. Int J Heat Fluid Flow 26:894–904
Lin C, Chang SC, Ho TC, Chang KA (2006) Laboratory observation of solitary wave propagating over a submerged rectangular dike. J Eng Mech 132:545–554
Shih RS, Weng WK, Chou CR (2013) Numerical modeling of wave field around multiple submerged breakwaters. Marine Sci 3(3):65–78
Gilbert R, Johnson DA (2003) Evaluation of FFT-based cross-correlation algorithms for PIV in a periodic grooved channel. Exp Fluids 34(4):473–483
Thielicke W, Stamhuis EJ (2014) Affordable and accurate digital particle image velocimetry in MATLAB. J Open Res Softw 2:30–31
Dean RG, Dalrymple RA (1991) Water wave mechanics for engineers and scientists. Singapore, Word Scientific
McKenna SP, McGillis WR (2002) Performance of digital image velocimetry processing techniques. Exp Fluids 32(1):106–115
Acknowledgments
This study was supported by the Brain Pool Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF-2019H1D3A2A01061428). This work was also supported by the National Research Foundation of Korea (NRF) grant, which is funded by the Korean government (MSIT) (No. 2020R1A5A8018822).
Author information
Authors and Affiliations
Corresponding author
Additional information
Technical Editor: Erick Franklin.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Karbasi pour, M., Nili-Ahmadabadi, M., Zaghian, R. et al. Experimental study of flow structures of a solitary wave over two rectangular tandem obstacles. J Braz. Soc. Mech. Sci. Eng. 43, 252 (2021). https://doi.org/10.1007/s40430-021-02944-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40430-021-02944-3