Hydraulic Jump for Planar and Axisymmetric Flow of a Fluid Layer

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Abstract

We consider fluid flow with a free boundary, which is defined as a function of height from coordinate x with two asymptotes at positive and negative infinities (hydraulic jump). The Boussinesq approximation is used to describe the phenomenon, and an additional force is introduced. The force is chosen to depend only on the height of the surface. The problem is solved analytically without using numerical schemes. This technique is used to determine the jump surface and the acting force depending on the wave propagation coordinate.

About the authors

A. D. Sukhov

Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences; Moscow Institute of Physics and Technology

Email: sukhov.ad@phystech.edu
Moscow, Russia; Moscow, Russia

A. G. Petrov

Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences

Author for correspondence.
Email: petrovipmech@gmail.com
Moscow, Russia

References

  1. И.И. Агроскин, Гидравлика, Энергия, Москва (1964).
  2. W. H. Hager, Critical Fow Condition in Open Channel Hydraulics, Acta Mechanica 54, 157 (1985).
  3. J.B. Belanger, Essay on the Numerical Solution of Some Problems Relative to Steady Flow of Water, Chez Carilian-Goeury libraire, Paris (1828).
  4. Lord Rayleigh, On the Theory of Long Waves and Bore, Proc. Roy. Soc. A 90, 324 (1914).
  5. W. H. Hager and K.Hutter, Approximate Treatment of the Plane Hydraulic Jump with Separation Approximate Treatment of the Plane Hydraulic Jump with Separation Zone Above the Flow Zone, J. Hydraulic Res. 21, 195 (1983).
  6. R. Schr¨oder, A Contribution to the Question of Energy Dissipation and the Turbulence of Discontinuous Water Flow, Institute of Hydraulic Engineering and Water Resources Management, Berlin (1957).
  7. R. Schr¨oder, The Turbulent Flow in the Free Alternating Jump, Institute of Hydraulic Engineering and Water Resources Management, Berlin (1963).
  8. F. Murzyn and H. Chanson, Free Surface, Bubbly Flow and Turbulence Measurements in Hydraulic Jumps, The University of Queensland, Brisbane (2007).
  9. K. Woycicki, Water Jump, Cover Roller and Discharge under a Contactor, ETH Zurich, Zurich (1931).
  10. H. Lamb, Hydrodynamics, Cambridge Univ. Press, Cambridge (1932).
  11. R.M. Khatsuria, Hydraulics of Spillways and Energy Dissipators, CRC Press, Atlanta (2004).
  12. J.J. Bloomer, Practical Fluid Mechanics for Engineering Applications, Marcel Dekker, New York (2000).
  13. T. B. Benjamin and M. J. Lighthill, On Cnoidal Waves and Bores, Proc. Roy. Soc. London, Ser. A, Math. Phys. Sci. 224, 448 (1954).
  14. A.G. Petrov, Integrating the Long Wave Equations in Kulikovskii-Drozdova Form, Dokl. Ross. Akad. Nauk 373, 762 (2000).
  15. A.G. Petrov, Integration of the Boussinesq Equations for Steady Channel and Jet Flows, Fluid Dynamics 42, 966 (2007).
  16. Yu.A. Drozdova and A.G. Kulikovskii, Concerning the Description of Long Nonlinear Waves in Channels, Fluid Dynamics 31, 739 (1996).
  17. G. L. Richard and S. L. Gavrilyuk, The Classical Hydraulic Jump in a Model of Shear Shallow-water Flows, J. Fluid Mech. 725, 492 (2013).
  18. S. Watanabe, Integral Methods for Shallow Freesurface Flows with Separation, J. Fluid Mech. 480, 233 (2003).
  19. O. Castro-Orgaz and W. H. Hager, Classical Hydraulic Jump: Basic Flow Features, J. Hydraulic Res. 47, 744 (2009).
  20. A. D. Craik, R. C. Latham, M.J. Fawkes, and P. W. F. Gribbon, The Circular Hydraulic Jump, J. Fluid Mech. 112, 347 (1981).
  21. R. K. Bhagat and P. F. Linden, The Circular Hydraulic Jump; the In uence of Downstream Flow on the Jump Radius, Phys. Fluids 34, 72 (2022).
  22. T. Bohr, C. Ellegaard, A. E. Hansen, and A. Haaning, Hydraulic Jumps, Flow Separation and Wave Breaking: An Experimental Study, Physica B 228, 1 (1996).
  23. Л.Г. Лойцянский, Механика жидкости и газа, Наука, Москва (1973)
  24. L. G. Loitsyanskii, Mechanics of Liquids and Gases, Nauka, Moscow (1973), Begell House, New York (1996).
  25. А.Г. Петров, Аналитическая гидродинамика, Физматлит, Москва (2009).
  26. A. G. Petrov, Saturation Free Numerical Scheme for Computing the Flow Past a Lattice of Airfoils and the Determination of Separation Points in a Viscous Fluid, Comp. Math. Math. Phys. 51, 1239 (2011).
  27. A. M. Elizarov, A. R. Kasimov, and D. V. Maklakov, Shape Optimization in Aerodynamics, Fizmatlit, Moscow (2009).
  28. A. G. Petrov, A. D. Sukhov, and I. N. Sibgatullin, Laminar Flow of Viscous Fluid around Elliptical Contours at an Angle of Attack, Lobachevskii J. Math. 43, 1184 (2022).

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