Relationships between a roller and a dynamic pressure distribution in circular hydraulic jumps

Kensuke Yokoi; Feng Xiao

doi:10.1103/PhysRevE.61.R1016

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Relationships between a roller and a dynamic pressure distribution in circular hydraulic jumps

Kensuke Yokoi^1,2 and Feng Xiao³

¹Division of Mathematics and Research Institute for Electronic Science, Hokkaido University, Sapporo 060-0812, Japan
²Computational Science Division, RIKEN (The Institute of Physical and Chemical Research), Wako 351-0198, Japan
³Department of Energy Sciences, Tokyo Institute of Technology, Yokohama 226-8502, Japan

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Phys. Rev. E 61, R1016(R) – Published 1 February, 2000

DOI: https://doi.org/10.1103/PhysRevE.61.R1016

Abstract

We investigated numerically the relation between a roller and the pressure distribution to clarify the dynamics of the roller in circular hydraulic jumps. We found that a roller which characterizes a type II jump is associated with two high pressure regions after the jump, while a type I jump (without the roller) is associated with only one high pressure region. Our numerical results show that building up an appropriate pressure field is essential for a roller.

References (16)

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V.T. Chow, Open Channel Hydraulic (McGraw-Hill, New York, 1959).
E.J. Watson, J. Fluid Mech. 20, 481 (1964).
A.D.D. Craik et al., J. Fluid Mech. 112, 347 (1981).
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C. Ellegaard et al., Nature (London) 392, 767 (1998).
C. Ellegaard et al., Nonlinearity 12, 1 (1999).
K. Yokoi and F. Xiao, Phys. Lett. A 257, 153 (1999).
T. Yabe and P.Y. Wang, J. Phys. Soc. Jpn. 60, 2105 (1991).
S. Osher and J.A. Sethian, J. Comput. Phys. 79, 12 (1988).
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[c1] Lord Rayleigh, Proc. R. Soc. London, Ser. A 90, 324 (1914).

[c2] I. Tani, J. Phys. Soc. Jpn. 4, 212 (1949).

[c3] V.T. Chow, Open Channel Hydraulic (McGraw-Hill, New York, 1959).

[c4] E.J. Watson, J. Fluid Mech. 20, 481 (1964).

[c5] A.D.D. Craik et al., J. Fluid Mech. 112, 347 (1981).

[c6] T. Bohr, P. Dimon, and V. Putkaradze, J. Fluid Mech. 254, 635 (1993).

[c7] T. Bohr et al., Physica B 228, 1 (1996).

[c8] T. Bohr, V. Putkaradze, and S. Watanabe, Phys. Rev. Lett. 79, 1038 (1997).

[c9] C. Ellegaard et al., Nature (London) 392, 767 (1998).

[c10] C. Ellegaard et al., Nonlinearity 12, 1 (1999).

[c11] K. Yokoi and F. Xiao, Phys. Lett. A 257, 153 (1999).

[c12] T. Yabe and P.Y. Wang, J. Phys. Soc. Jpn. 60, 2105 (1991).

[c13] S. Osher and J.A. Sethian, J. Comput. Phys. 79, 12 (1988).

[c14] M. Sussman, P. Smereka, and S. Osher, J. Comput. Phys. 114, 146 (1994).

[c15] J.U. Brackbill, D.B. Kothe, and C. Zemach, J. Comput. Phys. 100, 335 (1992).

[c16] T. Yabe et al., Comput. Phys. Commun. 66, 233 (1991).

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Relationships between a roller and a dynamic pressure distribution in circular hydraulic jumps

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References (16)

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