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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Abd-el-Malek, Mina B. and Amin, Amr M. 2014. Lie group analysis of nonlinear inviscid flows with a free surface under gravity. Journal of Computational and Applied Mathematics, Vol. 258, p. 17.


    Chesnokov, A. A. 2008. Symmetries and exact solutions of the shallow water equations for a two-dimensional shear flow. Journal of Applied Mechanics and Technical Physics, Vol. 49, Issue. 5, p. 737.


    Ancey, C. Cochard, S. Rentschler, M. and Wiederseiner, S. 2007. Existence and features of similarity solutions for non-Boussinesq gravity currents. Physica D: Nonlinear Phenomena, Vol. 226, Issue. 1, p. 32.


    Abd-el-Malek, Mina B. and Helal, Medhat M. 2006. The characteristic function method and exact solutions of nonlinear sheared flows with free surface under gravity. Journal of Computational and Applied Mathematics, Vol. 189, Issue. 1-2, p. 2.


    Teshukov, V. M. and Gavrilyuk, S. L. 2006. Three-Dimensional Nonlinear Dispersive Waves on Shear Flows. Studies in Applied Mathematics, Vol. 116, Issue. 3, p. 241.


    TESHUKOV, VLADIMIR RUSSO, GIOVANNI and CHESNOKOV, ALEXANDER 2004. ANALYTICAL AND NUMERICAL SOLUTIONS OF THE SHALLOW WATER EQUATIONS FOR 2D ROTATIONAL FLOWS. Mathematical Models and Methods in Applied Sciences, Vol. 14, Issue. 10, p. 1451.


    Chesnokov, A. A. 1997. Exact solutions of the equations of vortex shallow water. Journal of Applied Mechanics and Technical Physics, Vol. 38, Issue. 5, p. 692.


    Sachdev, P. L. and Vaganan, B. Mayil 1995. Exact Free Surface Flows for Shallow Water Equations II: The Compressible Case. Studies in Applied Mathematics, Vol. 94, Issue. 1, p. 57.


    Sachdev, P. L. and Vaganan, B. Mayil 1994. Exact Free Surface Flows for Shallow Water Equations I: The Incompressible Case. Studies in Applied Mathematics, Vol. 93, Issue. 3, p. 251.


    Currò, Carmela 1989. Some new exact solutions to the nonlinear shallow-water wave equations via group analysis. Meccanica, Vol. 24, Issue. 1, p. 26.


    1989. Nonlinear Boundary Value Problems in Science and Engineering.


    Sachdev, P. L. and Philip, Varughese 1988. Exact Simple Waves on Shear Flows in a Compressible Barotropic Medium. Studies in Applied Mathematics, Vol. 79, Issue. 3, p. 193.


    Sachdev, P.L. 1984. Wave Phenomena: Modern Theory and Applications.


    Thacker, William Carlisle 1981. Some exact solutions to the nonlinear shallow-water wave equations. Journal of Fluid Mechanics, Vol. 107, Issue. -1, p. 499.


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Exact, self-similar, time-dependent free surface flows under gravity

  • P. L. Sachdev (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112080002364
  • Published online: 01 April 2006
Abstract

A class of exact, self-similar, time-dependent solutions describing free surface flows under gravity is found which extends the self-propagating class of solutions discovered earlier by Freeman (1972) to those which decay with time.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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