A compendium of references on shallow water sloshing and dynamic coupling

  1. B.H. Adee & I. Caglayan. The effects of free water on deck on the motions and stability of vessels, In Proc. Second Inter. Conf. Stab. Ships and Ocean Vehicles, pp. 413-426. Berlin: Springer (1982).

  2. H. Alemi Ardakani. Rigid-body motion with interior shallow-water sloshing, PhD Thesis, University of Surrey (2010).

  3. H. Alemi Ardakani & T.J. Bridges. Dynamic coupling between shallow water sloshing and horizontal vehicle motion, Europ. J. Appl. Math. 21 479-517 (2010).

  4. H. Alemi Ardakani & T.J. Bridges. Shallow-water sloshing in rotating vessels undergoing prescribed rigid-body motion in three dimensions, J. Fluid Mech. 667 474-519 (2011).

  5. H. Alemi Ardakani & T.J. Bridges. Shallow-water sloshing in rotating vessels undergoing prescribed rigid-body motion in two dimensions, Preprint, submitted (2010).

  6. H. Alemi Ardakani & T.J. Bridges. Review of the Dillingham, Falzarano & Pantazopoulos three-dimensional shallow-water equations, Tech. Rep., Department of Mathematics, University of Surrey (2009).

  7. H. Alemi Ardakani & T.J. Bridges. Review of the Huang-Hsiung rotating three-dimensional shallow-water equations, Tech. Rep., Department of Mathematics, University of Surrey (2009).

  8. H. Alemi Ardakani & T.J. Bridges. Shallow water sloshing in rotating vessels: details of the numerical algorithm, Tech. Rep., Department of Mathematics, University of Surrey (2009).

  9. H. Alemi Ardakani & T.J. Bridges. The Euler equations in fluid mechanics relative to a rotating-translating reference frame Technical Report, Department of Mathematics, University of Surrey (2010).

  10. H. Alemi Ardakani & T.J. Bridges. Symplecticity of the Stormer-Verlet algorithm for coupling between the shallow water equations and horizontal vehicle motion, Technical report, University of Surrey (2010).

  11. V. Armenio & M. La Rocca. On the analysis of sloshing of water in rectangular containers: numerical study and experimental validation Ocean Eng. 23 705-739 (1996).

  12. J. Billingham. Nonlinear sloshing in zero gravity J. Fluid Mech. 464 365-391 (2002).

  13. T.J. Bridges. Cnoidal standing waves and the transition to the traveling hydraulic jump, Phys. Fluids 29 2819-2828 (1986).

  14. T.J. Bridges. Secondary bifurcation and change of type for three-dimensional standing waves in finite depth, J. Fluid Mech. 179 137-153 (1987).

  15. T.J. Bridges. Wave breaking and the surface velocity field for three-dimensional water waves Nonlinearity 22 947-953 (2009).

  16. I. Caglayan & R.L. Storch. Stability of fishing vessels with water on deck: a review, J. Ship Research 26 106-116 (1982).

  17. A. Cariou & G. Casella. Liquid sloshing in ship tanks: a comparitive study of numerical simulation, Marine Structures 12 183-198 (1999).

  18. B.-F. Chen. Viscous fluid in tank under coupled surge, heave and pitch motions, ASCE J. Waterways, Port, Coastal & Ocean Eng. 131 239-256 (2005).

  19. Y.G. Chen, K. Djidjeli & W.G. Price. Numerical simulation of liquid sloshing phenomena in partially filled containers, Computers & Fluids 38 830-842 (2009).

  20. Y.-H. Chen, W.-S. Hwang & C.-H. Ko. Numerical simulation of the three-dimensional sloshing problem by boundary element method J. Chinese Inst. Engin. 23 321-330 (2000).

  21. W. Chester. Resonant oscillations of water waves. I. theory, Proc. Royal Soc. London A 306 5-22 (1968).

  22. W. Chester & J.A. Bones. Resonant oscillations of water waves. II. experiment, Proc. Royal Soc. London A 306 23-39 (1968).

  23. M.J. Cooker. Water waves in a suspended container Wave Motion 20 385-395 (1994).

  24. E.A. Cox, J.P. Gleeson & M.P. Mortell. Nonlinear sloshing and passage through resonance in a shallow water tank, Z. angew. Math. Phys. 56 645-680 (2005).

  25. J. Dillingham. Motion studies of a vessel with water on deck Marine Technology 18 38-50 (1981).

  26. J.T. Dillingham & J.M. Falzarano. Three-dimensional numerical simulation of green water on deck, In the 3rd Inter. Conf. Stability of Ships and Ocean Vehicles. Gdansk, Poland (1986).

  27. P.J. Disimile, J.M. Pyles & N. Toy. Hydraulic jump formation in water sloshing within an oscillating tank, J. Aircraft 46 549-556 (2009).

  28. C.M. Edwards, S.D. Howison, H. Ockendon & J.R. Ockendon. Nonclassical shallow water flows, IMA J. Applied Math. 73 137-157 (2007).

  29. O.M. Faltinsen, O.F. Rognebakke, I.A. Lukovsky & A.N. Timokha. Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth, J. Fluid Mech. 407 201-234 (2000).

  30. O.M. Faltinsen & A.N. Timokha. Asymptotic modal approximation of nonlinear resonant sloshing in a rectangular tank with small fluid depth J. Fluid Mech. 470 319-357 (2002).

  31. O.M. Faltinsen, O.F. Rognebakke & A.N. Timokha. Resonant three-dimensional nonlinear sloshing in a square basin, J. Fluid Mech. 487 1-42 (2003).

  32. O.M. Faltinsen, O.F. Rognebakke & A.N. Timokha. Resonant three-dimensional nonlinear sloshing in a square-base basin. Part 3. base ratio perturbations, J. Fluid Mech. 551 359-397 (2006).

  33. O.M. Faltinsen, O.F. Rognebakke & A.N. Timokha. Transient and steady-state amplitudes of resonant three-dimensional sloshing in a square base tank with finite fluid depth Physics of Fluids 18 012103 (2006).

  34. O.M. Faltinsen & A.N. Timokha. An adaptive multimodal approach to nonlinear sloshing in a rectangular tank, J. Fluid Mech. 432 167-200 (2003).

  35. O.M. Faltinsen & A.N. Timokha. Sloshing, Cambridge University Press (2009).

  36. J.T. Feddema, C.R. Dohrmann, G.G. Parker, R.D. Robinett, V.J. Romero & D.J. Schmitt. Control for slosh-free motion of an open container, IEEE Control Systems Magazine 17 29-36 (1997).

  37. T. Gedeon, H. Kokubu, K. Mischaikow & H. Oka. Chaotic solutions in slowly-varying perturbations of hamiltonian systems with applications to shallow-water sloshing, J. Dyn. Diff. Eqns. 14 63-84 (2004).

  38. J. Gerrits. Dynamics of liquid-filled spacecraft, PhD thesis, University of Groningen, Netherlands (2001).

  39. M. Grundelius & B. Bernhardsson. Control of liquid slosh in an industrial packaging machine, IEEE Int. Conf. Control Appl., Kohala Coast, Hawaii, 6 pages (1999).

  40. S.P. Hastings & J.B. McLeod. On the periodic solutions of a forced second-order equation, J. Nonlinear Sci. 1 225-245 (1991).

  41. Z. Huang. Nonlinear shallow water flow on deck and its effect on ship motion PhD thesis, Technical University of Nova Scotia, Halifax, Canada (1995).

  42. Z.J. Huang & C.C. Hsiung. Application of the flux difference splitting method to compute nonlinear shallow water flow on deck, In the Proc. 9th Int. Workshop on Water Waves and Floating Bodies, Japan, 17-20 April 1994, pp. 83-87, IWWWFB (1994).

  43. Z.J. Huang & C.C. Hsiung. Nonlinear shallow water flow on deck J. Ship Research 40 303-315 (1996).

  44. Z.J. Huang & C.C. Hsiung. Nonlinear shallow-water flow on deck coupled with ship motion. In the Twenty-First Symposium on Naval Hydrodynamics, pp. 220-234, National Academies Press (1997).

  45. R.A. Ibrahim. Liquid Sloshing Dynamics Cambridge University Press (2005).

  46. T. Ikeda & N. Nakagawa. Non-linear vibrations of a structure caused by water sloshing in a rectangular tank, J. Sound & Vibration 201 23-41 (1997).

  47. R.S. Johnson. A Modern Introduction to the Mathematical Theory of Water Waves, Cambridge University Press (2001).

  48. A.F. Jones & A. Hulme. The hydrodynamics of water on deck J. Ship Research 31 125-135 (1987).

  49. T.J. Kaper & S. Wiggins. A commentary on ``The periodic solutions of a forced second-order equation'' by S.P. Hastings and J.B. MacLeod, J. Nonlinear Sci. 1 247-253 (1991).

  50. R. Kidambi & P.N. Shankar. The effects of the contact angle on sloshing in containers Proc. Royal Soc. London A 460 2251-2267 (2004).

  51. Y. Kim. Numerical simulation of sloshing flows with impact load Applied Ocean Research 23 53-62 (2001).

  52. J.J. Kobine. Nonlinear resonant characteristics of shallow fluid layers, Phil. Trans. Royal Soc. London A 366 1131-1346 (2008).

  53. M. La Rocca, P. Mele & V. Armenio. Variational approach to the problem of sloshing in a moving container, J. Theor. Appl. Fluid Mech. 1 280 (1997).

  54. M. La Rocca, G. Sciortino & M.A. Boniforti. A fully nonlinear model for sloshing in a rotating container, Fluid Dynamics Res. 27 23-52 (2000).

  55. J. Laranjinha, J.M. Falzarano & C.G. Soares. Analysis of the dynamical behaviour of an offshore supply vessel with water on deck In the Proc. 21st Inter. Conf. Offshore Mechanics and Arctic Eng. (OMAE02), Paper No. OMAE2002-OFT28177, ASME (2002).

  56. S.J. Lee, H.H. Kim, D.H. Lee, J.W. Kim & Y.H. Kim. The effects of LNG-tank sloshing on the global motions of LNG carriers, Ocean Engineering 34 10-20 (2007).

  57. S.K. Lee, S. Surendran & G. Lee. Roll performance of a small fishing vessel with live fish tank, Ocean Engineering 32 1873-1885 (2005).

  58. T.H. Lee, Z. Zhou & Y. Cao. Numerical simulations of hydraulic jumps in water sloshing and water impacting, ASME J. Fluids Eng. 124 215-226 (2002).

  59. D. Liu & P. Lin. A numerical study of three-dimensional liquid sloshing in tanks, J. Comp. Phys. 227 3921-3939 (2008).

  60. M.S. Longuet-Higgins. On the form of the highest progressive and standing waves in deep water, Proc. Royal Soc. London A 331 445-456 (1973).

  61. M.S. Longuet-Higgins. Vertical jets from standing waves Proc. Royal Soc. London A 457 495-510 (2001).

  62. Y.K. Lou, T.C. Su & J.E. Flipse. A nonlinear analysis of liquid sloshing in rigid containers, Tech. Rep. MA-79-SAC-B0018, Texas A&M University (1980).

  63. P.-C. Lui & Y.K. Lou. Dynamic coupling of a liquid-tank system under transient excitation, Ocean Engng. 17 263-277 (1990).

  64. M.E. McIntyre. Potential vorticity. In Encylopedia of Atmospheric Sciences (ed. J.R. Holton, J.A. Pyle & J.A. Curry), London, vol. 2. Academic/Elsevier (2003).

  65. J. Miles & D. Henderson. Parametrically forced surface waves, Ann. Rev. Fluid Mech. 22 143-165 (1990).

  66. J.R. Ockendon & H. Ockendon. Resonant surface waves, J. Fluid Mech. 59 397-413 (1973).

  67. H. Ockendon, J.R. Ockendon & A.D. Johnson. Resonant sloshing in shallow water, J. Fluid Mech. 167 465-479 (1986).

  68. M. Okamura. Standing gravity waves of large amplitude in deep water, Wave Motion 37 173-182 (2003).

  69. M.S. Pantazopoulos. Numerical solution of the general shallow water sloshing problem, PhD thesis, University of Washington, Seattle (1987).

  70. M.S. Pantazopoulos. Three-dimensional sloshing of water on decks, Marine Technology 25 253-261 (1988).

  71. M.S. Pantazopoulos & B.H. Adee. Three-dimensional shallow water waves in an oscillating tank, Proc. Amer. Soc. Civil. Eng. pp. 399-412 (1987).

  72. W.G. Penney & A.T. Price. Part II. finite periodic stationary gravity waves in a perfect fluid, Phil. Trans. Royal Soc. London A 244 254-284 (1952).

  73. D.H. Peregrine. Surf-zone currents, Theor. Compl. Fluid Dynamics 10 295-309 (1998).

  74. D.H. Peregrine. Large-scale vorticity generation by breakers in shallow and deep water, Eur. J. Mech. B/Fluids 18 403-408 (1999).

  75. L.J. Pratt. On internal flow over topography. Part 1. semigeostrophic adjustment to an obstacle, J. Fluid Mech. 131 195-218 (1983).

  76. C. Prieur & J. de Halleux. Stabilization of a 1-D tank containing a fluid modeled by the shallow water equations, Systems & Control Letters 52 167-178 (2004).

  77. S. Rebouillat & D. Liksonov. Fluid-structure interaction in partially filled liquid containders: A comparative review of numerical approaches, Computers & Fluids 39 739-746 (2010).

  78. A. Royon-Lebeaud, E.J. Hopfinger & A. Cartellier. Liquid sloshing and wave breaking in circular and square-based cylindrical coordinates, J. Fluid Mech. 577 467-494 (2007).

  79. P. Ruponen, J. Matusiak, J. Luukkonen & M. Ilus. Experimental study on the behavior of a swimming pool onboard a large passenger ship Marine Technology 46 27-33 (2009).

  80. P.G. Saffmann & H.C. Yuen. A note on the numerical computations of large amplitude standing waves, J. Fluid Mech. 95 707-715 (1979).

  81. B.R. Seymour & M.P. Mortell. Nonlinear resonant oscillations in open tubes, J. Fluid Mech. 60 733-749 (1973).

  82. G.I. Taylor. An experimental study of standing waves, Proc. Royal Soc. London A 218 44-59 (1953).

  83. M.P. Tzamtzi & N.D. Kouvakas. Sloshing control of tilting phases of the pouring process, Inter. J. Math. Phys. Eng. Sciences 1 175-182 (2007).

  84. M.P. Tzamtzi & N.D. Kouvakas. Robustness of a robot control scheme for liquid transfer, in Novel Algortithms and Techniques in Telecommunications, Automation and Industrial Electronics, Edited by T. Sobh et al., Springer-Verlag 154-161 (2008).

  85. A.E.P. Veldman, J. Gerrits, R. Luppes, J.A. Helder & J.P.B. Vreeburg. The numerical simulation of liquid sloshing on board spacecraft, J. Comp. Physics 224 82-99 (2007).

  86. J.H.G. Verhagen & L. van Wijngaarden. Non-linear oscillations of fluid in a container, J. Fluid Mech. 22 737-751 (1965).

  87. S. aus der Wiesche. Computational slosh dynamics: theory and industrial application, Comp. Mech. 30 374-387 (2003).

  88. C.-H. Wu & B.-F. Chen. Sloshing waves and resonance modes of fluid in a 3D tank by a time-independent finite difference method, Ocean Eng. 36 500-510 (2009).

  89. G.S. Wu, Q.W. Ma & R. Eatock Taylor. Numerical simulation of sloshing waves in a 3D tank based on a finite element method, Appl. Ocean Res. 20 337-355 (1998).

  90. Z. Zhou, J.O. Kat & B. Buchner. A nonlinear 3D approach to simulate green water dynamics on deck, In Proc. 7th Inter. Conf. Numer. Ship Hydro. (ed. J. Piquet), Nantes, vol. 7. DTIC (1999).

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