메뉴 건너뛰기




Volumn 506, Issue , 2004, Pages 331-355

Self-similar solutions of the axisymmetric shallow-water equations governing converging inviscid gravity currents

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF STATE OF LIQUIDS; GRAVITATION; INTEGRATION; WAVE PROPAGATION;

EID: 2442656296     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112004008638     Document Type: Article
Times cited : (17)

References (35)
  • 1
    • 0002674883 scopus 로고
    • A selfsimilar solution to the focusing problem for the porous medium equation
    • ARONSON, D. G. & GRAVELEAU, J. 1993 A selfsimilar solution to the focusing problem for the porous medium equation. Eur. J. Appl. Maths 4, 65-81.
    • (1993) Eur. J. Appl. Maths , vol.4 , pp. 65-81
    • Aronson, D.G.1    Graveleau, J.2
  • 3
    • 84974486810 scopus 로고
    • Gravity currents and related phenomena
    • BENJAMIN, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31, 209-248.
    • (1968) J. Fluid Mech. , vol.31 , pp. 209-248
    • Benjamin, T.B.1
  • 4
    • 39249084144 scopus 로고    scopus 로고
    • Focusing of noncircular self-similar shock waves
    • art., no. 074501
    • BETELÚ, S. I. & ARONSON, D. G. 2001 Focusing of noncircular self-similar shock waves. Phys. Rev. Lett. 87, art. no. 074501.
    • (2001) Phys. Rev. Lett. , vol.87
    • Betelú, S.I.1    Aronson, D.G.2
  • 5
    • 0004357097 scopus 로고    scopus 로고
    • Spherical and cylindrical convergent shocks
    • BILBAO, L. E. & GRATTON, J. 1996 Spherical and cylindrical convergent shocks. Nuovo Cimento 18D, 1041-1060.
    • (1996) Nuovo Cimento , vol.18 D , pp. 1041-1060
    • Bilbao, L.E.1    Gratton, J.2
  • 6
    • 0642265419 scopus 로고
    • On auto-models in the solution of certain problems of gas dynamics
    • BRUSHLINSKII, K. V. & KAZHDAN, J. M. 1963 On auto-models in the solution of certain problems of gas dynamics. Russ. Math. Surv. 18 (2), 1-22.
    • (1963) Russ. Math. Surv. , vol.18 , Issue.2 , pp. 1-22
    • Brushlinskii, K.V.1    Kazhdan, J.M.2
  • 7
    • 0012163533 scopus 로고
    • Numerical renormalization-group calculations for similarity solutions and traveling waves
    • CHEN, L.-Y. & GOLDENFELD, N. 1995 Numerical renormalization-group calculations for similarity solutions and traveling waves. Phys. Rev. E 51, 5577-5581.
    • (1995) Phys. Rev. E , vol.51 , pp. 5577-5581
    • Chen, L.-Y.1    Goldenfeld, N.2
  • 8
    • 0343038242 scopus 로고
    • Self-similar solutions of the second kind of nonlinear diffusion-type equations
    • DIEZ, J. A., GRATTON, J. & MINOTTI, F. 1992a Self-similar solutions of the second kind of nonlinear diffusion-type equations. Q. Appl. Maths L (3), 401-414.
    • (1992) Q. Appl. Maths L , vol.3 , pp. 401-414
    • Diez, J.A.1    Gratton, J.2    Minotti, F.3
  • 9
    • 0004803539 scopus 로고
    • Self-similar solution of the second-kind for a convergent viscous gravity current
    • DIEZ, J. A., GRATTON, R. & GRATTON, J. 1992b Self-similar solution of the second-kind for a convergent viscous gravity current. Phys. Fluids A 4, 1148-1155.
    • (1992) Phys. Fluids A , vol.4 , pp. 1148-1155
    • Diez, J.A.1    Gratton, R.2    Gratton, J.3
  • 13
    • 2442709481 scopus 로고
    • Similarity and self similarity in fluid dynamics
    • GRATTON, J. 1991 Similarity and self similarity in fluid dynamics. Fundam. Cosmic Phys. 15, 1-106.
    • (1991) Fundam. Cosmic Phys. , vol.15 , pp. 1-106
    • Gratton, J.1
  • 14
    • 0025240137 scopus 로고
    • Self-similar viscous gravity currents: Phase-plane formalism
    • GRATTON, J. & MINOTTI, F. 1990 Self-similar viscous gravity currents: phase-plane formalism. J. Fluid Mech. 210, 155-182.
    • (1990) J. Fluid Mech. , vol.210 , pp. 155-182
    • Gratton, J.1    Minotti, F.2
  • 15
    • 0028160281 scopus 로고
    • Self-similar gravity currents with variable inflow revisited: Plane currents
    • GRATTON, J. & VIGO, C. 1994 Self-similar gravity currents with variable inflow revisited: plane currents. J. Fluid Mech. 258, 77-104.
    • (1994) J. Fluid Mech. , vol.258 , pp. 77-104
    • Gratton, J.1    Vigo, C.2
  • 16
    • 0032336842 scopus 로고    scopus 로고
    • Self-similar solution to equations describing shallow flows in large-scale water areas
    • GRIGORYAN, S. S. & BABKIN, Y. V. 1998 Self-similar solution to equations describing shallow flows in large-scale water areas. Dokl. Phys. 43 (6), 373-377.
    • (1998) Dokl. Phys. , vol.43 , Issue.6 , pp. 373-377
    • Grigoryan, S.S.1    Babkin, Y.V.2
  • 17
    • 0027798865 scopus 로고
    • The propagation of intrusion fronts of high density ratios
    • GRÖBELBAUER, H. P., FANNELOP, T. K. & BRITTER, R. E. 1993 The propagation of intrusion fronts of high density ratios. J. Fluid Mech. 250, 669-687.
    • (1993) J. Fluid Mech. , vol.250 , pp. 669-687
    • Gröbelbauer, H.P.1    Fannelop, T.K.2    Britter, R.E.3
  • 18
    • 0000318144 scopus 로고
    • Self-similar solutions of the shallow-water equations representing gravity currents with variable inflow
    • GRUNDY, R. E. & ROTTMAN, J. W. 1986 Self-similar solutions of the shallow-water equations representing gravity currents with variable inflow. J. Fluid Mech. 169, 337-351.
    • (1986) J. Fluid Mech. , vol.169 , pp. 337-351
    • Grundy, R.E.1    Rottman, J.W.2
  • 19
    • 0001173534 scopus 로고
    • Starke kugelige und zylindrische Verdichtungsstöße in der Nähe des Kugelmittelpunktes bzw. der Zylinderachse
    • GUDERLEY, G. 1942 Starke kugelige und zylindrische Verdichtungsstöße in der Nähe des Kugelmittelpunktes bzw. der Zylinderachse. Luftfahrtforschung 19, 302-312.
    • (1942) Luftfahrtforschung , vol.19 , pp. 302-312
    • Guderley, G.1
  • 20
    • 0344236352 scopus 로고    scopus 로고
    • On inwardly propagating high-Reynolds-number axisymmetric gravity currents
    • HALLWORTH, M. A., HUPPERT, H. E. & UNGARISH, M. 2003 On inwardly propagating high-Reynolds-number axisymmetric gravity currents. J. Fluid Mech. 494, 255-274.
    • (2003) J. Fluid Mech. , vol.494 , pp. 255-274
    • Hallworth, M.A.1    Huppert, H.E.2    Ungarish, M.3
  • 21
    • 84931406930 scopus 로고
    • On the collapse of an empty cavity in water
    • HUNTER, C. 1960 On the collapse of an empty cavity in water. J. Fluid Mech. 8, 241-263.
    • (1960) J. Fluid Mech. , vol.8 , pp. 241-263
    • Hunter, C.1
  • 22
    • 2442710698 scopus 로고
    • Similarity solutions for the flow into a cavity
    • HUNTER, C. 1963 Similarity solutions for the flow into a cavity. J. Fluid Mech. 15, 289-305.
    • (1963) J. Fluid Mech. , vol.15 , pp. 289-305
    • Hunter, C.1
  • 23
    • 0002652043 scopus 로고    scopus 로고
    • Geological fluid mechanics
    • (ed. G. K. Batchelor, H. K. Moffatt and M. G. Worster), Cambridge University Press
    • HUPPERT, H. E. 2000 Geological fluid mechanics. In Perspectives in Fluid Dynamics: A Collective Introduction to Current Research (ed. G. K. Batchelor, H. K. Moffatt & M. G. Worster), pp. 447-506. Cambridge University Press.
    • (2000) Perspectives in Fluid Dynamics: A Collective Introduction to Current Research , pp. 447-506
    • Huppert, H.E.1
  • 24
    • 0019047788 scopus 로고
    • The slumping of gravity currents
    • HUPPERT, H. E. & SIMPSON, J. E. 1980 The slumping of gravity currents. J. Fluid Mech. 99, 785-799.
    • (1980) J. Fluid Mech. , vol.99 , pp. 785-799
    • Huppert, H.E.1    Simpson, J.E.2
  • 25
    • 0027948779 scopus 로고
    • Self-similar, surfactant-driven flows
    • JENSEN, O. E. 1994 Self-similar, surfactant-driven flows. Phys. Fluids 6, 1084-1094.
    • (1994) Phys. Fluids , vol.6 , pp. 1084-1094
    • Jensen, O.E.1
  • 26
    • 84968484162 scopus 로고
    • The engineer grapples with nonlinear problems
    • VON KÁRMÁN, T. 1940 The engineer grapples with nonlinear problems. B. Am. Math. Soc. 46, 615-683.
    • (1940) B. Am. Math. Soc. , vol.46 , pp. 615-683
    • Von Kármán, T.1
  • 27
    • 0001326333 scopus 로고
    • The dispersion, under gravity, of a column of fluid supported on a rigid horizontal plane
    • PENNEY, W. G. & THORNHILL, C. K. 1952 The dispersion, under gravity, of a column of fluid supported on a rigid horizontal plane. Phil. Trans. R. Soc. Lond. A 244, 285-311.
    • (1952) Phil. Trans. R. Soc. Lond. A , vol.244 , pp. 285-311
    • Penney, W.G.1    Thornhill, C.K.2
  • 32
    • 0037431348 scopus 로고    scopus 로고
    • Integral methods for shallow free-surface flows with separation
    • WATANABE, S., PUTKARADZE, V. & BOHR, T. 2003 Integral methods for shallow free-surface flows with separation. J. Fluid Mech. 480, 233-265.
    • (2003) J. Fluid Mech. , vol.480 , pp. 233-265
    • Watanabe, S.1    Putkaradze, V.2    Bohr, T.3
  • 33
    • 84958442335 scopus 로고
    • A new approach to problems of shock dynamics. Part I: Two-dimensional problems
    • WHITHAM, G. B. 1956 A new approach to problems of shock dynamics. Part I: Two-dimensional problems. J. Fluid Mech. 2, 145-171.
    • (1956) J. Fluid Mech. , vol.2 , pp. 145-171
    • Whitham, G.B.1
  • 35
    • 0000770428 scopus 로고
    • Hydraulic jumps in a fluid system of two layers
    • YIH, C.-S. & GUHA, C. R. 1955 Hydraulic jumps in a fluid system of two layers. Tellus 7, 358-366.
    • (1955) Tellus , vol.7 , pp. 358-366
    • Yih, C.-S.1    Guha, C.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.