Nonhydrostatic Model for Surf Zone Simulation
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 137, Issue 4
Abstract
A previously developed model for nonhydrostatic free surface flow is adapted to simulate breaking waves in the surf zone. The model solves the Reynolds-averaged Navier-Stokes equations in a fraction step manner with the pressure split into hydrostatic and nonhydrostatic components. The hydrostatic equations are first solved with an approximate Riemann solver. This approach is particularly well suited for simulating discontinuous flow associated with breaking waves because the model prediction converges to the classical solution for a turbulent bore, which closely resembles breaking waves in the surf zone. The hydrostatic solution is then corrected by including the nonhydrostatic pressure. The model uses a sigma coordinate discretization in the vertical direction, which has been previously demonstrated to yield significant truncation errors with highly skewed grids over large bottom slopes. This potential problem is investigated in the context of highly skewed (but transient) grids that occur with steep breaking waves.
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References
Bradford, S. F. (2000). “Numerical simulation of surf zone dynamics.” J. Waterway, Port, Coastal, Ocean Eng., 126(1), 1–13.
Bradford, S. F. (2004). “Stability and accuracy of a semi-implicit Godunov scheme for mass transport.” Int. J. Numer. Methods Fluids, 45(4), 365–389.
Bradford, S. F. (2005). “Godunov-based model for nonhydrostatic wave dynamics.” J. Waterway, Port, Coastal, Ocean Eng., 131(5), 226–238.
Bradford, S. F., and Sanders, B. F. (2002a). “Finite volume model for shallow water flooding of arbitrary topography.” J. Hydrol. Eng., 128(3), 289–298.
Bradford, S. F., and Sanders, B. F. (2002b). “Finite volume models for uni-directional, nonlinear, dispersive waves.” J. Waterway, Port, Coastal, Ocean Eng., 128(4), 173–182.
Chen, G., Kharif, C., Zaleski, S., and Li, J. (1999). “Two-dimensional Navier-Stokes simulation of breaking waves.” Phys. Fluids, 11(1), 121–133.
Christensen, E. D. (2006). “Large eddy simulation of spilling and plunging breakers.” Coastal Eng., 53(5-6), 463–485.
Dalrymple, R. A. (1974). “A finite amplitude wave on a linear shear current.” J. Geophys. Res., 79(30), 4498–4504.
Dommermuth, D. G., Yue, D. K. P., Rapp, R. J., Chan, E. S., and Melville, W. K. (1988). “Deep-water plunging breakers: A comparison between potential theory and experiments.” J. Fluid Mech., 189(1), 423–442.
Galperin, B., Kantha, L. H., Hassid, S., and Rosati, A. (1988). “A quasi-equilibrium turbulent energy model for geophysical flows.” J. Atmos. Sci., 45(1), 55–62.
Grilli, S. T., Guyenne, P., and Dias, F. (2001). “A fully non-linear model for three-dimensional overturning waves over an arbitrary bottom.” Int. J. Numer. Methods Fluids, 35(7), 829–867.
Haney, R. L. (1991). “On the pressure gradient force over steep topography in sigma coordinate ocean models.” J. Phys. Oceanogr., 21(4), 610–619.
Hansen, J. B., and Svendsen, I. A. (1979). “Regular waves in shoaling water: Experimental data.” Technical Rep.: ISVA Paper 21, Technical Univ. of Denmark, Lyngby, Copenhagen, Denmark.
Harlow, F. H., and Welch, J. E. (1965). “Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface.” Phys. Fluids, 8(12), 2182–2189.
Hirt, C. W., and Nichols, B. D. (1981). “Volume of fluid (VOF) method for the dynamics of free boundaries.” J. Comput. Phys., 39(1), 201–225.
Iafrati, A., and Campana, E. F. (2003). “A domain decomposition approach to compute wave breaking (wave breaking flows).” Int. J. Numer. Methods Fluids, 41(4), 419–445.
Karambas, T. V., and Koutitas, C. (1992). “A breaking wave propagation model based on the Boussinesq equations.” Coastal Eng., 18(1-2), 1–19.
Kennedy, A. B., Chen, Q., Kirby, J. T., and Dalrymple, R. A. (2000). “Boussinesq modeling of wave transformation, breaking, and runup. I:1D.” J. Waterway, Port, Coastal, Ocean Eng., 126(1)39–47.
Khayyer, A., Gotoh, H., and Shao, S. D. (2008). “Corrected incompressible SPH method for accurate water-surface tracking in breaking waves.” Coastal Eng., 55(3), 236–250.
Lemos, C. M. (1992). “Wave breaking: A numerical study.” Lecture notes in engineering, Vol. 71, Springer-Verlag, New York.
Li, B., and Fleming, C. A. (2001). “Three-dimensional model of Navier-Stokes equations for water waves.” J. Waterway, Port, Coastal, Ocean Eng., 127(1), 16–25.
Lin, P., and Li, C. W. (2002). “A -coordinate three-dimensional numerical model for surface wave propagation.” Int. J. Numer. Methods Fluids, 38(11), 1045–1068.
Lin, P., and Liu, P. L. F. (1998). “A numerical study of breaking waves in the surf zone.” J. Fluid Mech., 359, 239–264.
Longuet-Higgins, M. S., and Cokelet, E. D. (1976). “The deformation of steep waves on water. I: A numerical method of computation.” Proc. R. Soc. London, Ser. A, 350(1660), 1–26.
Lynett, P. J. (2006). “Wave breaking velocity effects in depth-integrated models.” Coastal Eng., 53(4), 325–333.
Madsen, P. A., and Sorensen, O. R. (1992). “A new form of the Boussinesq equations with improved linear dispersion characteristics, Part 2: A slowly varying bathymetry.” Coastal Eng., 18(3-4), 183–204.
Mahadevan, A., Oliger, J., and Street, R. (1996). “A nonhydrostatic mesoscale ocean model. Part II: Numerical implementation.” J. Phys. Oceanogr., 26(9), 1881–1900.
Mellor, G. L., and Yamada, T. (1982). “Development of a turbulence closure model for geophyscial fluid problems.” Rev. Geophys. Space Phys., 20(4), 851–875.
New, A. L., McIver, P., and Peregrine, D. H. (1985). “Computations of overturning waves.” J. Fluid Mech., 150(1), 233–251.
Nwogu, O. (1993). “An alternate form of the Boussinesq equations for modeling the propagation of waves from deep to shallow water.” J. Waterway, Port, Coastal, Ocean Eng., 119(6), 618–638.
Peregrine, D. H. (1996). “Calculations of the development of an undular bore.” J. Fluid Mech., 25(2), 321–330.
Phillips, N. A. (1957). “A coordinate system having some special advantages for numerical forecasting.” J. Meteorol., 14(2), 184–185.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992). Numerical recipes in FORTRAN, Cambridge University Press, New York.
Roe, P. L. (1981). “Approximate Riemann solvers, parameter vectors, and difference schemes.” J. Comput. Phys., 43(2), 357–372.
Schaffer, H. A., Madsen, P. A., and Deigaard, R. (1993). “A Boussinesq model for waves breaking in shallow water.” Coastal Eng., 20(3-4), 185–202.
Stive, M. J. V. (1984). “Energy dissipation in waves breaking on gentle slopes.” Coastal Eng., 8(2), 99–127.
Svendsen, I. A. (1984a). “Mass flux and undertow in a surf zone.” Coastal Eng., 8(4), 347–365.
Svendsen, I. A. (1984b). “Wave heights and set-up in a surf zone.” Coastal Eng., 8(4), 303–329.
Ting, F. C. K., and Kirby, J. T. (1994). “Observation of undertow and turbulence in a laboratory surf zone.” Coastal Eng., 24(1-2), 51–80.
Ting, F. C. K., and Kirby, J. T. (1995). “Dynamics of surf-zone turbulence in a strong plunging breaker.” Coastal Eng., 24(3-4), 177–204.
Ting, F. C. K., and Kirby, J. T. (1996). “Dynamics of surf-zone turbulence in a spilling breaker.” Coastal Eng., 27(3-4), 131–160.
Van Leer, B. (1979). “Towards the ultimate conservative difference scheme. V: A second order sequel to Godunov’s method.” J. Comput. Phys., 32(1), 101–136.
Vinje, T., and Brevig, P. (1981). “Numerical simulation of breaking waves.” Adv. Water Resour., 4(2), 77–82.
Wei, G., Kirby, J. T., Grilli, S. T., and Subramanya, R. (1995). “A fully nonlinear Boussinesq model for surface waves. Part 1: Highly nonlinear unsteady waves.” J. Fluid Mech., 294(1), 71–92.
Witting, J. M. (1984). “A unified model for the evolution of nonlinear water waves.” J. Comput. Phys., 56, 203–236.
Yakhot, V., Orszag, S. A., Thangam, S., Gatski, T. B., and Speziale, C. G. (1992). “Development of turbulence models for shear flows by a double expansion technique.” Phys. Fluids A, 4(7), 1510–1520.
Zelt, J. A. (1991). “The run-up of nonbreaking and breaking solitary waves.” Coastal Eng., 15(3), 205–246.
Zhao, Q., Armfield, S., and Tanimoto, K. (2004). “Numerical simulation of breaking waves by a multi-scale turbulence model.” Coastal Eng., 51(1), 53–80.
Zijlema, M., and Stelling, G. S. (2008). “Efficient computation of surf zone waves using the nonlinear shallow water equations with non-hydrostatic pressure.” Coastal Eng., 55(10), 780–790.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 137 • Issue 4 • July 2011
Pages: 163 - 174
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Nov 19, 2009
Accepted: Oct 26, 2010
Published online: Oct 30, 2010
Published in print: Jul 1, 2011
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