Resonant three-dimensional nonlinear sloshing in a square-base basin

Journal of Fluid Mechanics

Volumn 487, Issue , 2003, Pages 1-42

  Faltinsen, Odd M ^a   Rognebakke, Olav F ^b   Timokha, Alexander N ^c  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

^b SINTEF OCEAN   (Norway)

^c INSTITUTE OF MATHEMATICS   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

NATURAL FREQUENCIES; TANKS (CONTAINERS);

NONLINEAR SLOSHING;

LIQUID SLOSHING;

COMPUTATIONAL FLUID DYNAMICS; MATHEMATICAL ANALYSIS; MODEL; SLOSHING; THREE-DIMENSIONAL FLOW; TWO-DIMENSIONAL FLOW;

EID: 0042732021     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112003004816     Document Type: Article

References (57)

1. ABRAMSON, H. N. 1966 The dynamics of liquids in moving containers. NASA Rep. SP 106.
2. ABRAMSON, H. N., BASS, R. L., FALTINSEN, O. M. & OLSEN, H. A. 1974 Liquid slosh in LNG Carriers. In Tenth Symp. on Naval Hydrodynamics, June 24 28, 1974, Cambridge, Massachusetts. ACR-204, pp. 371 388.
3. ALIABADI, S., JOHNSON, A. & ABEDI, J. 2003 Comparison of finite element and pendulum models for simulation of sloshing. Computers Fluids, 23, 535 545.
4. ARAI, M., CHENG, L. Y. & INQUE, Y. 1992a 3D numerical simulation of impact load due to liquid cargo sloshing. J. Soc. Nav. Arch. Japan. 171, 177 185.
5. ARAI, M., CHENG, L. Y. & INQUE, Y. 1993 Numerical simulation of sloshing and swirling in cubic and cylindrical tank. J. Kansai Soc. Nav. Arch. Japan. 219, 97-101.
6. ARAI, M., CHENG, L. Y., INQUE, Y., SASAKI, H. & YAMAGISHI, N. 1992b Numerical analysis of liquid sloshing in tanks of FPSO. Proc. Second (1992) Intl Offshore and Polar Conf., San Francisco. USA, 14 19 June 1992, vol. 3, 383 390.
7. BADER, G. & ASCHER, U. 1987 A new basis implementation for a mixed order boundary value ODE solver. SIAM J. Sci. Statist. Comput. 8, 483 500.
8. BRIDGES, T. J. 1985 On secondary bifurcation of three dimensional standing waves. Tech. Summary Rep. Wisconsin Univ., Madison.
9. BRIDGES, T. J. 1986 On secondary bifurcation of three-dimensional standing waves. SIAM J. Appl. Maths 47, 40 59.
10. BRIDGES, T. J. 1987 Secondary bifurcation and change of type for three dimensional standing waves in finite depth. J. Fluid Mech. 179, 137 153.
11. 2 symmetry, and multiple periodic solutions. SIAM J. Math. Anal. 19, 1015-1031.
12. BRYANT, P. J. 1989 Nonlinear progressive waves in a circular basin. J. Fluid Mech. 205, 453-467.
13. BRYANT, P. J. & STIASSNIE, M. 1994 Different forms for nonlinear standing waves in deep water. J. Fluid Mech. 272, 135-156.
14. BRYANT, P. J. & STIASSNIE, M. 1995 Water waves in a deep square basin. J. Fluid Mech. 302, 65-90.
15. CELEBI, S. M. & AKYILDIZ, H. 2002 Nonlinear modelling of liquid sloshing in a moving rectangular tank. Ocean Engng 29, 1527-1553.
16. CHEN, L. Y. & ARAI, M. 1995 Liquid sloshing in a cubic and a cylindrical tank. Ninth Technical Exchange and Advisory Meeting, July 24-27, 1995, Hiroshima, Japan.
17. FALTINSEN, O. M. 1974 A nonlinear theory of sloshing in rectangular tanks. J. Ship. Res. 18, 224-241.
18. FALTINSEN, O. M. & ROGNEBAKKE, O. F. 2000 Sloshing. Keynote lecture. NAV 2000. Proc. Intl Conf. on Ship and Shipping Research, Venice, 19-22 September, 2000, Italy.
19. FALTINSEN, O. M., ROGNEBAKKE, O. F., LUKOVSKY, I. A. & TIMOKHA, A. N. 2000 Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth. J. Fluid Mech. 407, 201-234.
20. FALTINSEN, O. M. & TIMOKHA, A. N. 2001 Adaptive multimodal approach to nonlinear sloshing in a rectangular rank. J. Fluid Mech. 432, 167-200.
21. FALTINSEN, O. M. & TIMOKHA, A. N. 2002a Asymptotic modal approximation of nonlinear resonant sloshing in a rectangular tank with small fluid depth. J. Fluid Mech. 470, 319-357.
22. FALTINSEN, O. M. & TIMOKHA, A. N. 2002b Analytically-oriented approaches to two-dimensional fluid sloshing in a rectangular tank (survey). Proc. Insti. Maths Ukrainian Natl. Acad. Sci. "Problems of Analytical Mechanics and its Applications" 44, 321-345.
23. FENG, Z. C. & SENTHNA, P. R. 1989 Symmetry-breaking bifurcations in resonant surface waves. J. Fluid Mech. 199, 495-518.
24. FULTZ, D. 1962 An experimental note on finite-amplitude standing gravity waves. J. Fluid Mech. 13, 193-212.
25. GAVRILYUK, I., LUKOVSKY, I. A. & TIMOKHA, A. N. 2000 A multimodal approach to nonlinear sloshing in a circular cylindrical tank. Hybrid Meth. Engng 2, 463-483.
26. HENDERSON, D. M. & MILES, J. W. 1990 Single-mode Faraday waves in small cylinder. J. Fluid Mech. 213, 95-109.
27. HERMANN, M. & ULLRICH, K. 1992 RWPKV: a software package for continuation and bifurcation problems in two-point boundary value problems. Appl. Math. Lett. 5, 57-61.
28. IBRAHIM, R. A., PILIPCHUK, V. N. & IKEDA, T. 2001 Recent advances in liquid sloshing dynamics. Appl. Mech. Res. 54(2), 133-199.
29. ISSC 1997 Report of Committee 1.2 "Loads". In Proc. 13th Intl Ship and Offshore Structures Congress (ed. T. Moan & S. Berge) Vol. 1, pp. 59-122. Pergamon.
30. LA ROCCA, M., MELE, P. & ARMENIO, V. 1997 Variational approach to the problem of sloshing in a moving container. J. Theor. Appl. Fluid Mech. 1(4), 280-310.
31. LA ROCCA, M., SCIORTINO, G. & BONIFORTI, M. A. 2000 A fully nonlinear model for sloshing in a rotating container. Fluid Dyn. Res. 27, 23-52.
32. LUKOVSKY, I. A. 1990 Introduction to Nonlinear Dynamics of a Solid Body with a Cavity Including a Liquid. Kiev: Naukova dumka (in Russian).
33. MIKISHEV, G. I. 1978 Experimental Methods in the Dynamics of Spacecraft. Moscow: Mashinostroenie (in Russian).
34. MILES, J. W. 1984a Internally resonant surface waves in circular cylinder. J. Fluid Mech. 149, 1-14.
35. MILES, J. W. 1984b Resonantly forces surface waves in circular cylinder. J. Fluid Mech. 149, 15-31.
36. MILES, J. W. 1994 Faraday waves: rolls versus squares. J. Fluid Mech. 269, 353-371.
37. MOISEYEV, N. N. & RUMYANTSEV, V. V. 1968 Dynamic Stability of Bodies Containing Fluid. Springer.
38. NAGATA, M. 1991 Chaotic behaviour of parametrically excited surface waves in square geometry. Eur. J. Mech. B/ Fluids. 10, 61-66.
39. NARIMANOV, G. S. 1957 Movement of a tank partly filled by a fluid: the taking into account of non-smallness of amplitude. Prikl. Mat. Mekh. 21, 513-524 (in Russian).
40. NARIMANOV, G. S., DOKUCHAEV, L. V. & LUKOVSKY, I. A. 1977 Nonlinear Dynamics of Flying Apparatus with Liquid. Moscow: Mashinostroenie (in Russian).
41. NEVOLIN, V. G. 1984 Parametric excitation of surface waves (survey). Inzhenerno-phys. Z. 47, 1028 1042 (in Russian).
42. OCKENDON, J. R. & OCKENDON, H. 1973 Resonant surface waves. J. Fluid Mech. 59, 397 413.
43. OCKENDON, H., OCKENDON, J. R. & WATERHOUSE, D. D. 1996 Multi-mode resonance in fluids. J. Fluid Mech. 315, 317-344.
44. PERLIN, M. & SCHULTZ, W. W. 2000 Capillary effects on surface waves. Annu. Rev. Fluid Mech. 32, 241-274.
45. ROGNEBAKKE, O. F. & FALTINSEN, O. M. 2003 Coupling of sloshing and ship motions. J. Ship Res. (in press).
46. ROYON, A., GAUDIN, E., CAVELLIER, A. & HOPPINGER, E. J. 2002 Sloshing and drop formation conditions in cylindrical liquid propellant tanks. 4th Intl Conf. on Launcher Technology "Space Launcher Liquid Propulsion", Liege, Belgium. 3 6 December, 2002. Abstracts.
47. SAMES, P. C., MARCOULY, D. & SCHELLIN, T. 2002 Sloshing in rectangular and cylindrical tank. J. Ship Res. 46, 186 200.
48. SHANKAR, P. N. & KIDAMBI, R. 2002 A modal method for finite amplitude, nonlinear sloshing. Pramana J. Phy. 59, 631-651.
49. SIMONELLI, F. & GOLLUB, J. P. 1989 Surface wave mode interaction: effects of symmetry and degeneracy. J. Fluid Mech. 199, 471 494.
50. SOLAAS, F. 1995 Analytical and numerical studies of sloshing in tanks. PhD Thesis, The Norwegian Institute of Technology, Faculty of Marine Technology, Trondheim.
51. STOLBETSOV, V. I. 1967 On oscillations of a fluid in the tank having the shape of rectangular parallelepiped. Mech. Zhid. i Gaza (Fluid Dyn.) N 1, 67 76 (in Russian).
52. TOMAWA, S. & SUEOKA, H. 1989 Experimental and numerical studies on sloshing in partially filled tank. Proc. Fourth Intl Symp. on Practical Design of Ships and Mobile Units, pp. 57.1 57.8.
53. TSAI, W.-T., YUE, D, K.-P. & YIP, K. M. K. 1990 Resonantly excited regular and chaotic motions in a rectangular wave tank. J. Fluid Mech. 216, 343 380.
54. WATERHOUSE, D. D. 1994 Resonant sloshing near a critical depth. J. Fluid Mech. 281, 313 318.
55. WATERHOUSE, D. D. 1995 Resonant oscillations of gases and liquids in three dimensions. DPhil thesis, Oxford University.
56. WU, G. X., MA, Q. W. & TAYLOR, R. E. 1998 Numerical simulation of sloshing waves in 3D tank based on a finite element method. Appl. Ocean Res. 20, 337 355.
57. ZAKHAROV, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 2, 190 194.