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Turbulent bores and hydraulic jumps

Published online by Cambridge University Press:  20 April 2006

P. A. Madsen  and
I. A. Svendsen
P. A. Madsen
Affiliation:
Institute of Hydrodynamics and Hydraulic Engineering (ISVA), Technical University of Denmark, Building 115, DK 2800 Lyngby, Denmark Present address: Danish Hydraulic Institute, Horsholm, Denmark.
I. A. Svendsen
Affiliation:
Institute of Hydrodynamics and Hydraulic Engineering (ISVA), Technical University of Denmark, Building 115, DK 2800 Lyngby, Denmark
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Abstract

A theoretical model for the velocity field and the surface profile of bores and hydraulic jumps is developed. The turbulence is assumed to be concentrated in a wedge that originates at the toe of the front and spreads towards the bottom, and the turbulent closure used is a simplified k-ε model allowing for non-equilibrium in the turbulent kinetic energy. The flow equations are satisfied in depth-integrated form (method of weighted residuals), and measured deviations from static pressure are analysed and shown to have a negligible effect on the results. Comparison with measurements shows good agreement, but there is a clear need for further experimental results in the highly turbulent region near the free surface. Some basic mechanisms of the flow are discussed and explained from the theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 129 , April 1983 , pp. 1 - 25
Copyright
© 1983 Cambridge University Press

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References

Abramovich, G. N. 1963 The Theory of Turbulent Jets. MIT Press.
Bakhmeteff, B. A. & Matzke, A. E. 1936 The hydraulic jump in terms of dynamic similarity Trans. ASCE 101, 630–647.Google Scholar
Battjes, J. A. & Sakai, T. 1981 Velocity fields in a steady breaker J. Fluid Mech. 111, 421–437.Google Scholar
Bélanger, J. M. 1828 Essai sur la Solution Numérique de Quelques Problèmes, Relatives au Mouvement Permanent des Eaux Courantes. Paris.
Falkner, V. M. & Scan, S. W. 1930 Some approximate solutions of the boundary layer equations. ARC R. & M. no. 1314.Google Scholar
Finlayson, B. A. 1972 The method of weighted residuals and variational principles. Maths in Sci. and Engng 87.Google Scholar
Harleman, D. R. F. 1958 Discussion on Rouse et al. (1958). J. Hydraul. Div. ASCE 84 (HY6), 1856-52–55.Google Scholar
Hibberd, S. & Peregrine, D. H. 1979 Surf and run-up on a beach: a uniform bore. J. Fluid Mech. 95, 323–345.Google Scholar
Johns, B. 1980 The modelling of the approach of bores to a shoreline Coastal Engng 3, 207–219.Google Scholar
Kááan, T. Von 1930 Mechanische Ähnlichkeit und Turbulenz. Nachr. Ges. Wiss. Göttingen, Math. Phys. Kl.
Keller, H. B., Levine, D. A. & Whitham, G. B. 1969 Motion of a bore over a sloping beach J. Fluid Mech. 7, 302–316.Google Scholar
Launder, B. E. & Spalding, D. B. 1972 Mathematical Models of Turbulence. Academic.
Longuet-Higgins, M. S. & Turner, J. S. 1974 An entraining plume model of a spilling breaker J. Fluid Mech. 63, 1–20.Google Scholar
Madsen, P. A. 1981 A model for a turbulent bore. Series Paper 28, Inst. Hydrodyn. and Hydraul. Engng, Tech. Univ. Denmark.
Madsen, P. A. & Svendsen, I. A. 1979 On the form of the integrated conservation equations for waves in the surf zone. Prog. Rep. 48, Inst. Hydrodyn. and Hydraul. Engng, Tech. Univ. Denmark, 31–39.Google Scholar
Mavis, F. T. & Luksch, A. 1936 Discussion of Bakhmeteff & Matzke (1936) Trans. ASCE 101, 669–672.Google Scholar
Narayanan, R. 1975 Wall jet analogy to hydraulic jump. J. Hydraul. Div. ASCE 101 (HY3), 347–359.Google Scholar
Peregrine, D. H. 1972 Equations for water waves and the approximations behind them. In Waves on Beaches (ed. R. E. Meyer). Academic.
Peregrine, D. H. 1974 Water wave interaction in the surf zone. In Proc. 14th Conf. on Coastal Engng, pp. 500–517.
Peregrine, D. H. & Svendsen, I. A. 1978 Spilling breakers, bores, and hydraulic jumps. In Proc. 16th Coastal Engng Conf., chap. 30, pp. 540–550.
Rajaratnam, N. 1965 The hydraulic jump as a wall jet. J. Hydraul. Div. ASCE 91 (HY5), 107–131.Google Scholar
Rajaratnam, N. 1967 Hydraulic jumps Adv. Hydrosci. 4, 197–280.Google Scholar
Rajaratnam, N. 1976 Turbulent Jets. Elsevier.
Resch, F. J. & Leutheusser, H. J. 1972a Reynold stress measurements in hydraulic jumps J. Hydraul. Res. 10, 409–430.Google Scholar
Resch, F. J. & Leutheusser, H. J. 1972b Le ressaut hydraulique; mesure de turbulence dans la région diaphasique Houille Blanche 4, 279–293.Google Scholar
Resch, F. J., Leutheusser, H. J. & Coantic, M. 1976 Étude de la structure cinématique et dynamique du ressaut hydraulique J. Hydraul. Res. 14, 293–319.Google Scholar
Rouse, H., Siao, T. T. & Nagaratnam, S. 1958 Turbulence characteristics of the hydraulic jump. J. Hydraul. Div. ASCE 84 (HY1), 1528-1–30.Google Scholar
Sarma, K. V. N. & Newham, D. A. 1973 Surface profiles of hydraulic jump for Froude numbers less than four Water Power 25, 139–142.Google Scholar
Svendsen, I. A. & Jonsson, I. G. 1976 Hydrodynamics of coastal regions. Den Private Ingeniørfond, Tech. Univ. Denmark.Google Scholar
Svendsen, I. A., Madsen, P. A. & BUHR HANSEN, J. 1978 Wave characteristics in the surf zone. In Proc. 16th Coastal Engng Conf., Hamburg, chap. 29, pp. 520–539.
Tsubaki, T. 1950 Theory of hydraulic jump Rep. Res. Inst. for Fluid Engng, Kyushu Univ., Fukuoka, Japan 6, 2.Google Scholar