Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 409
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Adib, M R M Amirza, A R M Wardah, T and Junaidah, A 2016. Effectiveness Using Circular Fibre Steel Flap Gate As a Control Structure Towards the Hydraulic Characteristics in Open Channel. IOP Conference Series: Materials Science and Engineering, Vol. 136, p. 012075.

    Akrish, Gal Schwartz, Rafael Rabinovitch, Oded and Agnon, Yehuda 2016. Impact of extreme waves on a vertical wall. Natural Hazards,

    Beji, S. 2016. Improved Korteweg & de Vries type equation with consistent shoaling characteristics. Coastal Engineering, Vol. 109, p. 128.

    Coclite, Giuseppe Maria and di Ruvo, Lorenzo 2016. On the convergence of the modified Rosenau and the modified Benjamin–Bona–Mahony equations. Computers & Mathematics with Applications,

    El, Gennady A. Hoefer, Mark A. and Shearer, Michael 2016. Expansion shock waves in regularized shallow-water theory. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Vol. 472, Issue. 2189, p. 20160141.

    Ghiloufi, Ahlem and Kadri, Tlili 2016. Analysis of new conservative difference scheme for two-dimensional Rosenau-RLW equation. Applicable Analysis, p. 1.

    Hammad, D.A. and El-Azab, M.S. 2016. Chebyshev–Chebyshev spectral collocation method for solving the generalized regularized long wave (GRLW) equation. Applied Mathematics and Computation, Vol. 285, p. 228.

    He, Dongdong 2016. Exact solitary solution and a three-level linearly implicit conservative finite difference method for the generalized Rosenau–Kawahara-RLW equation with generalized Novikov type perturbation. Nonlinear Dynamics, Vol. 85, Issue. 1, p. 479.

    Hoitink, A. J. F. and Jay, D. A. 2016. Tidal river dynamics: Implications for deltas. Reviews of Geophysics, Vol. 54, Issue. 1, p. 240.

    Hosseini, M.M. Ghaneai, H. Mohyud-Din, Syed Tauseef and Usman, Muhammad 2016. Tri-prong scheme for regularized long wave equation. Journal of the Association of Arab Universities for Basic and Applied Sciences, Vol. 20, p. 68.

    Karakoç, S. Battal Gazi and Zeybek, Halil 2016. Solitary-wave solutions of the GRLW equation using septic B-spline collocation method. Applied Mathematics and Computation, Vol. 289, p. 159.

    Korkmaz, Bahar and Dereli, Yilmaz 2016. Numerical solution of the Rosenau-KdV-RLW equation by using RBFs collocation method. International Journal of Modern Physics C, p. 1650117.

    Kumar, Rakesh and Baskar, S. 2016. B-spline quasi-interpolation based numerical methods for some Sobolev type equations. Journal of Computational and Applied Mathematics, Vol. 292, p. 41.

    Leng, Xinqian and Chanson, Hubert 2016. Coupling between free-surface fluctuations, velocity fluctuations and turbulent Reynolds stresses during the upstream propagation of positive surges, bores and compression waves. Environmental Fluid Mechanics, Vol. 16, Issue. 4, p. 695.

    Oruç, Ö. Bulut, F. and Esen, A. 2016. Numerical Solutions of Regularized Long Wave Equation By Haar Wavelet Method. Mediterranean Journal of Mathematics,

    Pan, Xintian and Zhang, Luming 2016. On the convergence of a high-accuracy compact conservative scheme for the modified regularized long-wave equation. SpringerPlus, Vol. 5, Issue. 1,

    Ramos, J I 2016. On the accuracy of some explicit and implicit methods for the inviscid GRLW equation subject to initial Gaussian conditions. International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26, Issue. 3/4, p. 698.

    Reyes, M. A. Gutiérrez-Ruiz, D. Mancas, S. C. and Rosu, H. C. 2016. Nongauge bright soliton of the nonlinear Schrödinger (NLS) equation and a family of generalized NLS equations. Modern Physics Letters A, Vol. 31, Issue. 03, p. 1650020.

    Trillo, S. Klein, M. Clauss, G.F. and Onorato, M. 2016. Observation of dispersive shock waves developing from initial depressions in shallow water. Physica D: Nonlinear Phenomena, Vol. 333, p. 276.

    Xu, G. Garnier, J. Faccio, D. Trillo, S. and Picozzi, A. 2016. Incoherent shock waves in long-range optical turbulence. Physica D: Nonlinear Phenomena, Vol. 333, p. 310.


Calculations of the development of an undular bore

  • D. H. Peregrine (a1)
  • DOI:
  • Published online: 01 March 2006

If a long wave of elevation travels in shallow water it steepens and forms a bore. The bore is undular if the change in surface elevation of the wave is less than 0·28 of the original depth of water. This paper describes the growth of an undular bore from a long wave which forms a gentle transition between a uniform flow and still water. A physical account of its development is followed by the results of numerical calculations. These use finite-difference approximations to the partial differential equations of motion. The equations of motion are of the same order of approximation as is necessary to derive the solitary wave. The results are in general agreement with the available experimental measurements.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *