Supplementary Files
How to Cite
Abstract
This study investigates surf zone wave heating due to the dissipation of breaking wave energy by using the Smoothed Particle Hydrodynamics method. We evaluate the surf zone wave heating by examining the increase of internal energy of the system, which is computed based on the conservation of energy. The equivalent temperature profile is calculated based on a simple conversion relationship between energy and temperature. We first examine the surf zone wave heating based on long-crested wave breaking over a planar beach, and we consider spilling breaker and weakly plunging breaker. Numerical results show that breaking of water waves in the surf zone increases the internal energy of water body. Furthermore, the dissipation of incident wave energy is fully converted into the internal energy in a thermally isolated system, confirming the energy conservation of the present numerical approach. It is further found that the long-crested wave breaking generates undertow, which transports the generated wave heating from the surf zone to deep waters. We further carry out numerical experiments to examine surf zone wave heating due to short-crested wave breaking over a beach. The internal energy generation mainly follows the isolated wave breakers, and there is a 3D pattern of wave heating due to the complicated wave breaking process and current system. In general, the magnitude of the generated internal energy or temperature by dissipation of breaking wave energy in the surf zone is relatively small. The present study shows that the generated water temperature is in the order of 10^-3 Kelvin for wave breaking over a typical coastal beach.References
T. Aagaard, K. P. Black, and B. Greenwood. Cross-shore suspended sediment transport in the surf zone: a field-based parameterization. Marine Geology, 185(3-4):283-302, 2002.
J. A. Battjes. Surf similarity. In Coastal Engineering 1974, pages 466-480. 1975.
D. B. Clark, S. Elgar, and B. Raubenheimer. Vorticity generation by short-crested wave breaking. Geophysical Research Letters, 39(24), 2012.
P.W. Cleary and J. Ha. Three-dimensional sph simulation of light metal components. J. Light Metals, 2(3): 169-183, 2003.
R. A. Dalrymple. A mechanism for rip current generation on an open coast. Journal of Geophysical Research, 80(24):3485-3487, 1975.
R. A. Dalrymple and B. D. Rogers. Numerical modeling of water waves with the SPH method. Coastal Engineering, 53(2):141-147, 2006.
R. G. Dean and R. A. Dalrymple. Water wave mechanics for scientists and engineers. World Scientific, Advanced Series on Ocean Engineering, 2, 1991.
D. A. Fulk. A numerical analysis of smoothed particle hydrodynamics. Technical report, Air Force Institute of Technology, Wright-Patterson AFB, OH, 1994.
R. A. Gingold and J. J. Monaghan. Smoothed particle hydrodynamics: theory and application to nonspherical stars. Monthly Notices of the Royal Astronomical Society, 181(3):375-389, 1977.
A. R. Harborne and P. J. Mumby. Novel ecosystems: altering fish assemblages in warming waters. Current Biology, 21(19):R822-R824, 2011.
A. Hérault, G. Bilotta, and R. A. Dalrymple. SPH on GPU with CUDA. Journal of Hydraulic Research, 48 (S1):74-79, 2010.
A. Hérault, G. Bilotta, A. Vicari, E. Rustico, and C. Del Negro. Numerical simulation of lava flow using a GPU SPH model. Annals of Geophysics, 54(5), 2011.
A. Iafrati. Energy dissipation mechanisms in wave breaking processes: Spilling and highly aerated plunging breaking events. Journal of Geophysical Research: Oceans, 116(C7), 2011.
N. Kumar, F. Feddersen, Y. Uchiyama, J. McWilliams, and W. OReilly. Midshelf to surfzone coupled ROMS-SWAN model data comparison of waves, currents, and temperature: Diagnosis of subtidal forcings and response. Journal of Physical Oceanography, 45(6):1464-1490, 2015.
D. Lakehal and P. Liovic. Turbulence structure and interaction with steep breaking waves. Journal of Fluid Mechanics, 674:522-577, 2011.
L. B. Lucy. A numerical approach to the testing of the fission hypothesis. The Astronomical Journal, 82: 1013-1024, 1977.
C. V. Makris, C. D. Memos, and Y. N. Krestenitis. Numerical modeling of surf zone dynamics under weakly plunging breakers with SPH method. Ocean Modelling, 98:12-35, 2016.
J. J. Monaghan. Smoothed particle hydrodynamics. Annual Review of Astronomy and Astrophysics, 30: 543-574, 1992.
J. J. Monaghan. Simulating free surface flows with SPH. Journal of Computational Physics, 110(2):399- 406, 1994.
J. J. Monaghan. Smoothed particle hydrodynamics. Reports on Progress in Physics, 68(8):1703, 2005.
K. Nadaoka, M. Hino, and Y. Koyano. Structure of the turbulent flow field under breaking waves in the surf zone. Journal of Fluid Mechanics, 204:359-387, 1989.
J. Pineda. Internal tidal bores in the nearshore: Warm-water fronts, seaward gravity currents and the onshore transport of neustonic larvae. Journal of Marine Research, 52(3):427-458, 1994.
R. J. Rapp and W. K. Melville. Laboratory measurements of deep-water breaking waves. Phil. Trans. R. Soc. Lond. A, 331(1622):735-800, 1990.
H. Shi, X. Yu, and R. A. Dalrymple. Development of a two-phase SPH model for sediment laden flows. Computer Physics Communications, 221(Supplement C):259 - 272, 2017.
G. Sinnett and F. Feddersen. The surf zone heat budget: The effect of wave heating. Geophysical Research Letters, 41(20):7217-7226, 2014.
E. B. Thornton. Distribution of sediment transport across the surf zone. In Coastal Engineering 1972, pages 1049-1068. 1973.
Z. Wei and R. A. Dalrymple. Numerical study on mitigating tsunami force on bridges by an SPH model. Journal of Ocean Engineering and Marine Energy, 2(3):365-380, 2016.
Z. Wei and R. A. Dalrymple. SPH modeling of vorticity generation by short-crested wave breaking. In Proceedings of 35th International Conference on Coastal Engineering, Antalya, Turkey, 2017a.
Z. Wei and R. A. Dalrymple. SPH modeling of short-crested waves. In Proceedings of 12th international SPHERIC workshop, Ourense, Spain, 2017b.
Z. Wei, R. A. Dalrymple, A. Hérault, G. Bilotta, E. Rustico, and H. Yeh. SPH modeling of dynamic impact of tsunami bore on bridge piers. Coastal Engineering, 104:26-42, 2015.
Z. Wei, R. A. Dalrymple, E. Rustico, A. Hérault, and G. Bilotta. Simulation of nearshore tsunami breaking by Smoothed Particle Hydrodynamics method. Journal of Waterway, Port, Coastal, and Ocean Engineering, 2016. doi: 10.1061/(ASCE)WW.1943-5460.0000334.
Z.Wei, R. A. Dalrymple, M. Xu, R. Garnier, and M. Derakhti. Short-crested waves in the surf zone. Journal of Geophysical Research: Oceans, 122, 2017. doi: 10.1002/2016JC012485.
Z. Wei, C. Li, R. A. Dalrymple, M. Derakhti, and J. Katz. Chaos in breaking waves. Coastal Engineering, 140:272 - 291, 2018.