Run-up of dispersive and breaking waves on beaches

• Autorzy: Massel S.R. , Pelinovsky E.N.
• Języki publikacji: EN

Abstrakty

EN

Transformation of waves on sandy beaches, their breaking, set-up and run-up are the main factors contributing to fluctuations in the water table and groundwater flow. In this paper, the run-up mechanisms have been studied using analytical models. In contrast to the standard models, the waves approaching the shoreline are assumed to be dispersive and the equivalence of the non-linear and linear solutions for the extreme characteristics of wave run-up, such as the height of maximum run-up and the velocity of run-up, are used. A linear system of equations for the run-up of breaking waves is developed. This system is based on the application of the mild-slope equation in the deeper area, where waves are dispersive, while the linear equations of shallow water are applied close to the shoreline, where the water depth is a linear function of distance. The dissipation factor in the shallow water equation has been formulated using its resemblance to the mild-slope equation for a non-permeable sea bottom. Application of the method is illustrated for various bottom profiles and wave characteristics, and theoretical results compared well with experimental data. These solutions of the run-up phenomena will assist future studies on wave-induced beach groundwater flow.

Słowa kluczowe

EN

fluctuation; wave transformation; filtration; beach; sandy beach; mathematical model; dispersive wave; surface wave; breaking wave

• Wydawca: -
• Czasopismo: Oceanologia
• Rocznik: 2001
• Tom: 43
• Numer: 1
• Opis fizyczny: p.61-97,fig.,ref.

Twórcy

autor

Massel S.R.

• Polish Academy of Sciences, Powstancow Warszawy 55, 81-712 Sopot, Poland

autor

Pelinovsky E.N.

Bibliografia

• Abramowitz M., Stegun I.A., 1975, Handbook of mathematical functions, Dover Publ. Inc., New York, 1055 pp.
• Athanassoulis G.A., Belibassakis K.A., 1999, A consistent coupled-mode theory for the propagation of small-amplitude water waves over variable bathymetry regions, J. Fluid Mech., 389, 275–301.
• Battjes J.A., 1974, Computation of set-up, longshore currents, run-up and overtopping due to wind-generated waves, Comm. Hydraul., Delft Univ. Technol., Rep. 74 (2), 244 pp.
• Battjes J.A., Janssen J.P.F.M., 1978, Energy loss and set-up due to breaking of random waves, Proc. 16th Coast. Eng. Conf., Hamburg, 1, 563–587.
• Berkhoff J.C.W., 1973, Computation of combined refraction-diffraction, Proc. 13th Coast. Eng. Conf., Vancouver, 1, 471–490.
• Carrier, G. F., 1966, Gravity waves on water of variable depth, J. Fluid Mech., 24, 641–659.
• Carrier G. F. & Greenspan H.P., 1958, Water waves of finite amplitude on a sloping beach, J. Fluid Mech., 4, 97–109.
• Dingemans M.W., 1997, Water wave propagation over uneven bottoms. Part 1. Linear wave propagation, World Sci. Publ., Singapore, 471 pp.
• F¨uhrb¨oter A., 1984, Model and prototype tests for wave impact and run-up on a uniform slope 1:4, Proc. Conf. Water Wave Res., Theory, Lab. Field, Hannover, 1–51.
• Gourlay M.R., 1992, Wave set-up, wave run-up and beach water table: Interaction between surf zone hydraulics and groundwater hydraulics, Coast. Eng., 17, 93–144.
• Haggerty G.B., 1972, Elementary numerical analysis with programming, Allyn & Bacon, Boston, 476 pp.
• Hunt J.A., 1959, Design of seawalls and breakwaters, J. Waterway, Port, Coast. Ocean Eng., 85, 123–152.
• Kaystrenko V.M., Pelinovsky E.N., Simonov K.V., 1985, The run-up and transformation of tsunami in shallow water, Sov. Meteor. Hydrol., 10, 56–62.
• Kang H.Y., Nielsen P., 1996, Watertable dynamics in coastal areas, Proc. Coast. Eng. Conf., 3, 4601–4612.
• Keller J.B., Keller H.B., 1964, Water run-up on a beach, Serv. Bureau Corp. Res., Rep. prep. for Office Naval Res., Washington.
• Kobayashi N., Greenwald J.H., 1986, Prediction of wave run-up and riprap stability, Proc. 20th Coast. Eng. Conf., ASCE, 3, 1958–1971.
• Lamb H., 1932, Hydrodynamics, Dover Publ., New York, 738 pp.
• Le Mehaute B., Koh, R.C.Y., Hwang L., 1968, A synthesis on wave runup, Proc. Waterway Harbor Div., 94, 77–92.
• Li L., Barry D.A., 2000, Wave-induced beach groundwater flow, Adv. Water Res., 23, 325–337.
• Longuet-Higgins M. S., 1983, Wave set-up, percolation and undertow in the surf zone, Proc. R. Soc., A390, 283–291.
• Longuet-Higgins M. S., Stewart R.W., 1964, Radiation stress in water waves: a physical discussion with applications, Deep Sea Res., 11, 529–562.
• Massel S.R., 1989, Hydrodynamics of coastal zones, Elsevier Publ., Amsterdam, 336 pp.
• Massel S.R., 1993., Extended refraction-diffraction equations for surface waves, Coast. Eng., 19, 97–126.
• Massel S.R., 1996, Ocean surface waves: their physics and prediction, World Sci., Singapore–New Jersey, 491 pp.
• Massel S.R., 1999, Fluid mechanics for marine ecologists, Springer Verlag, Heidelberg–Berlin, 566 pp.
• Massel S.R., Belberova D. Z., 1990, Parameterization of the dissipation mechanisms in the surface waves induced by wind, Arch. Mech., 42, 515–530.
• Massel S.R., Gourlay M.R., 2000, On the modelling of wave breaking and set-up on coral reefs, Coast. Eng., 39, 1–27.
• Massel S.R., Pelinovsky E.N., Chybicki W., 1990, Run-up of dispersive waves on plane beach. In oscillations and waves in liquid and gas, Tech. Univ., Gorkiy, 6–19, (in Russian).
• Mazova R. K., Pelinovsky E.N., 1982, Linear theory of run-up of tsunami on a beach, Izv., Atm. Ocean Phys., 18, 124–128.
• McLachlan N.W., 1964, Bessel functions for engineers, PWN, Warszawa, 331 pp., (Polish edn.).
• McLachlan A., 1989, Water filtration by dissipative beaches, Limnol. Oceanogr., 34, 774–780.
• Pelinovsky E.N., 1982, Nonlinear dynamics of tsunami, Inst. Appl. Phys., Gorkiy, 226 pp., (in Russian).
• Pelinovsky E., Mazova R., 1992, Exact analytical solutions of nonlinear problems of tsunami wave run-up on slopes with different profiles, Natur. Hazards, 6, 227–249.
• Savage R.P., 1958, Wave runup on roughened and permeable slopes, J. Waterway Harbour Div., ASCE, 84, 1–38.
• Saville T., 1958, Wave runup on composite slopes, Proc. 6th Coast. Eng. Conf., ASCE, 691–699.
• Shore Protection Manual (SPM), 1984, Dept. Army, U. S. Army Corps Eng., Washington, I–III.
• Short A.D., 1991, Macro-mezo tidal beach morphodynamics – an overview, J. Coast. Res., 7, 417–436.
• Singamsetti S.R., Wind H.G., 1980, Breaking waves: characteristics of shoaling and breaking periodic waves normally incident to plane beaches of constant slope Delft Hydraul., Rep. M1371, 80 pp.
• Titov V.V., Synolakis C.E., 1995, Modeling of breaking and nonbreaking long-wave evolution and run-up using VTSC-2, Proc. ASCE, J. Waterway, Port, Coast. Ocean Eng., 121, 308–316.
• Turner I. L., 1995, Simulating the influence of groundwater seepage on sediment transported by the sweep of the swash zone across macro-tidal beaches, Mar. Geol., 125, 153–174.
• Voltzinger N. E., Klevanny K.A., Pelinovsky E.N., 1989, Long wave dynamics of the coastal zone, Gidrometeoizdat, 271 pp., (in Russian).
• Walton T. L., Ahrens J., 1989, Maximum periodic wave run-up on smooth slopes, J. Waterway, Port, Coast. Ocean Eng., 115, 703–708.
• Węsławski J.M., Malinga B., Kotwicki L., Opaliński K., Szymelfenig M., Dutkowski M., 2001, Sandy coastlines – are there conflicts between recreation and natural values?, Oceanol. Stud., (in press).