El modelado matemático de la propagación del oleaje en ingeniería de costas

Philip L.-F. Liu, Iñígo J. Losada

Resumen

Este artículo presenta un resumen de la evolución de los modelos matemáticos utilizados para el estudio de la propagación del oleaje, concentrándose especialmente en los últimos avances alcanzados. Se presenta, por tanto, un pequeño resumen de los progresos realizados en las dos últimas décadas para luego desarrollar más detalladamente las últimas investigaciones relativas a modelos unificados o modelos basados en las ecuaciones de Navier-Stokes. Es necesario hacer énfasis en el hecho de que el modelado matemático es tan sólo uno de los aspectos que abarca el estudio de la propagación del oleaje en el campo de la Ingeniería de Costas, dado que otras consideraciones tales como la definición de la batimetría, selección de los datos de partida relativos al clima marítimo, tratamiento de los contornos, etc. condicionan completamente el resultado final. Estos últimos aspectos, muy ligados al binomio modelo-modelador, quedan fuera del alcance de este artículo aunque no deben ser olvidados.

Palabras clave

Oleaje; Modelos numéricos; Navier-Stokes; Boussinesq; Mild-slope

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Referencias

Berkhoff, J. C. W. 1972 “Computation of combined refraction and diffraction”, Proceedings of the 13th International Coastal Engineering Conference, ASCE, 471-490. https://doi.org/10.1061/9780872620490.027

Berkhoff, J. C. W. 1976 Mathematical models for simple harmonic linear water waves; wave refraction and diffraction. PhD thesis, Delft Technical University of Technology.

Brocchini, M., Drago, M. and Ivoenitti, L. 1992. “The modeling of short waves in shallow water: Comparison of numerical model based on Boussinesq and Serre equations.” Proc. 23rd Intnl. Conf. Coastal Engng. ASCE. 76-88.

Chen, Q., Madsen, P. A., Schaffer, H. A. and Basco, D. R., 1998 Wave-current interaction based on an enhanced Boussinesq approach”, Coastal Engng., 33, 11-39. https://doi.org/10.1016/S0378-3839(97)00034-3

Chen, Y. and Liu, P. L.-F. 1994 "A Pseudo-Spectral Approach for Scattering of Water Waves", Proc. Roy. Soc. London, A, 445, 619-636. https://doi.org/10.1098/rspa.1994.0081

Chen, Y. and Liu, P. L.-F. 1995b “Modified Boussinesq equations and associated parabolic models for water wave propagation,” J. Fluid Mech., 288, 351-381. https://doi.org/10.1017/S0022112095001170

Chorin, A.J. 1968 “Numerical solution of the Navier-Stokes equations.” Math. Comput. 22, 745-762. https://doi.org/10.2307/2004575

Dalrymple, R.A., Kirby, R.T. and Hwang, P.A. 1984. “Wave diffraction due to area of energy dissipation.” J. of Waterway, Port, Coastal, and Ocean Engineering, ASCE., 110, No. 1., 67-79. https://doi.org/10.1061/(ASCE)0733-950X(1984)110:1(67)

Eckart, C. 1952 “The propagation of gravity waves from deep to shallow water”. Circular 20, National Bureau of Standards, 165-173.

Elgar, S. and Guza, R. T. 1985 “Shoaling gravity waves: comparisons between field observations, linear theory and a nonlinear model”, J. Fluid Mech., 158, 47-70. https://doi.org/10.1017/S0022112085002543

Goring, D. G. 1978 “Tsunamis - the propagation of long waves onto a shelf”, Ph.D. dissertation, California Institute of Technology, Pasadena, CA.

Hodges, B.R. 1997, Numerical simulation of nonlinear free Surface waves on a turbulent open-channel flow, PhD Dissertation, Department of Civil Engineering, Stanford University.

Jaw, S.Y. & Chen, C.J. 1998 “Present status of second-order closure turbulence model. I: overview.” J. Engineering Mechanics, 124, pp. 485-501. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:5(485)

Jaw, S.Y. & Chen, C.J. 1998 “Present status of second-order closure turbulence models. II: application.” J. Engineering Mechanics, 124, 502-512. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:5(502)

Johnson, D.B., Raad, P.E. & Chen, S. 1994, “Simulation of impacts of fluid free surface with solid boundary,” Int. J. Numer. Meth. Fluids, 19, 153-174. https://doi.org/10.1002/fld.1650190205

Karambas, Th. V. and Koutitas, C. 1992. “A breaking wave propagation model based on the Boussinesq equations.” Coastal Engineering, ELSEVIER, 18, 1-19. https://doi.org/10.1016/0378-3839(92)90002-C

Kawamura, T. 1998 “Numerical simulation of 3D turbulent free-surface flows”, International Research Center for Computational Hydrodynamics (ICCH), Denmark.

Kennedy, A.B., Chen, Q., Kirby, J.T. and Dalrymple, R.A. 2000. “Boussinesq modeling of wave transformation, breaking and runup, I: 1D.” J. of Waterway, Port, Coastal, and Ocean Engineering, ASCE., 126, No. 1., 39-48. https://doi.org/10.1061/(ASCE)0733-950X(2000)126:1(39)

Kirby, J.T. and Dalrymple, R.A. 1983. “A parabolic equation for combined refraction-diffraction if Stokes waves by a mildly varying topography.” J. Fluid Mech., 136, 453-466. https://doi.org/10.1017/S0022112083002232

Kothe, D.B., Mjolsness, R.C. & Torrey, M.D. 1991 “RIPPLE: a computer program for incompressible flows with free surfaces.” Los Alamos National Laboratory, LA-12007-MS. https://doi.org/10.2514/6.1991-3548

Lin, P. and Liu, P. L.-F. 1998a "A Numerical Study of Breaking Waves in the Surf Zone", J. Fluid Mech., 359, 239-264. https://doi.org/10.1017/S002211209700846X

Lin, P. and Liu, P. L.-F. 1998b “Turbulence Transport, Vorticity Dynamics, and Solute Mixing Under Plunging Breaking Waves in Surf Zone,” J. Geophys. Res., 103, 15677-15694. https://doi.org/10.1029/98JC01360

Liu, P. L.-F. 1990 “Wave transformation”, in the Sea, Wiley-Interscience Publication. v. 9, 27-63.

Liu, P. L.-F. 1994 “Model equations for wave propagation from deep to shallow water”, in Advances in Coastal and Ocean Engineering, v.1, 125-158. https://doi.org/10.1142/9789812797582_0003

Liu, P. L.-F. and Tsay, T.-K. 1983. “On weak reflection of water waves.” J. Fluid Mech., 131, 59-71. https://doi.org/10.1017/S0022112083001238

Liu, P. L.-F. and Tsay, T.-K. 1984. “Refraction-diffraction model for weakly nonlinear water waves” J. Fluid Mech., 141, 265-274. https://doi.org/10.1017/S0022112084000835

Liu, P. L.-F., Yoon, S. B. and Kirby, J. T. 1985 “Nonlinear refraction-diffraction of waves in shallow water”, J. Fluid Mech., 153, 185-201. https://doi.org/10.1017/S0022112085001203

Liu, P. L.-F., Lin, P., Chang, K.-A., and Sakakiyama, T. 1999 "Wave interaction with porous structures", J. Waterway, Port, Coastal and Ocean Engrg., ASCE, 125, (6), 322-330. https://doi.org/10.1061/(ASCE)0733-950X(1999)125:6(322)

Liu P.L.-F, Lin, P., Hsu, T., Chang, K., Losada, I.J., Vidal, C. and Sakakiyama, T. 2000. A Reynolds averaged Navier-Stokes equation model for nonlinear water wave and structure interactions. Proceedings Coastal Structures 99. Ed. I.J. Losada, A.A. Balkema. Rotterdam.

Madsen, P. A., Murray, R. and Sorensen, O. R. 1991 “A new form of the Boussinesq equations with improved linear dispersión characteristics”, Coastal Engineering, 15, 371-388. https://doi.org/10.1016/0378-3839(91)90017-B

Miyata, H., Kanai, A., Kawamura, T. & Park, J-C. 1996 “Numerical simulation of three-dimensional breaking waves”, J. Mar. Sci. Technol., 1, pp.183-197. https://doi.org/10.1007/BF02390795

Ng, C. O. & Kot, S.C. 1992 “Computations of water impact on a two-dimensional flat-bottom body with a volume of fluid method”, Ocean Eng. 19, pp. 377-393. https://doi.org/10.1016/0029-8018(92)90036-4

Nwogu, O. 1993 “An alternative form of the Boussinesq equations for nearshore wave propagation”, J. Waterway. Port, Coast. Ocean Engng, ASCE, 119, 618-638. https://doi.org/10.1061/(ASCE)0733-950X(1993)119:6(618)

Peregrine, D. H. 1967 “Long waves on a beach” J. Fluid Mech., 27, 815-882. https://doi.org/10.1017/S0022112067002605

Rodi, W. 1980. “Turbulence models and their application in hydraulics - a state-of-the-art review.” IAHR Publication.

Schäffer, H.A., Madsen, P.A. and Deigaard, R.A. (1993). “A Boussinesq model for waves breaking in shallow water.” Coastal Engineering, 20, 185-202. https://doi.org/10.1016/0378-3839(93)90001-O

Shih, T.-H., Zhu, J. & Lumley, J.L. 1996. “Calculation of wall-bounded complex flows and free shear flows.” Intl J. Numer. Meth. Fluids, 23, 1133-1144. https://doi.org/10.1002/(SICI)1097-0363(19961215)23:11<1133::AID-FLD456>3.0.CO;2-A

Smith, R. and Sprinks, T. 1995. “Scattering of surface waves by a conical island.” J. Fluid. Mech., 72, 373-384. https://doi.org/10.1017/S0022112075003424

Ting, F.C.K. and Kirby, J.T. 1995, “Dynamics of surf-zone turbulence in a strong plunging breaker.” Coastal Engng, 24, 177-204. https://doi.org/10.1016/0378-3839(94)00036-W

Ting, F.C.K. and Kirby, J.T. 1994, “Observation of undertow and turbulence in a laboratory surf zone.” Coastal Engng, 24, 51-80. https://doi.org/10.1016/0378-3839(94)90026-4

Witting, J. M. 1984 “A unified model for the evolution of nonlinear water waves”, J. Comp. Phys., 56, 203-236. https://doi.org/10.1016/0021-9991(84)90092-5

Zelt, J. L. 1991 “The run-up of nonbreaking and breaking solitary waves”, Coastal Engng, 15, 205-246. https://doi.org/10.1016/0378-3839(91)90003-Y

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