Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-05-17T06:52:48.850Z Has data issue: false hasContentIssue false
  • English
  • Français

On sloshing modes in a circular tank

Published online by Cambridge University Press:  16 February 2012

Odd M. Faltinsen  and
Alexander N. Timokha
Odd M. Faltinsen*
Affiliation:
Centre for Ships and Ocean Structures & Department of Marine Technology, Norwegian University of Science and Technology, NO-7091 Trondheim, Norway
Alexander N. Timokha
Affiliation:
Centre for Ships and Ocean Structures & Department of Marine Technology, Norwegian University of Science and Technology, NO-7091 Trondheim, Norway
*
†Email address for correspondence: oddfal@marin.ntnu.no
Get access Rights & Permissions [Opens in a new window]

Abstract

Employing the multipole-type functions given by Faltinsen & Timokha (J. Fluid Mech., vol. 665, 2010, pp. 457–479), we derive a Trefftz-type representation of the velocity potential for the liquid sloshing problem in a two-dimensional circular tank. This representation defines a continuation of the velocity potential into the ‘air’ area confined by the ‘dry’ tank surface. Its usage facilitates an effective approximation of the natural sloshing modes for all tank fillings.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Papers
Information
Journal of Fluid Mechanics , Volume 695 , 25 March 2012 , pp. 467 - 477
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Barkowiak, K., Gampert, B. & Siekmann, J. 1985 On liquid motion in a circular cylinder with horizontal axis. Acta Mechanica 54, 207–220.CrossRefGoogle Scholar
2. Barnyak, M., Gavrilyuk, I., Hermann, M. & Timokha, A. 2011 Analytical velocity potentials in cells with a rigid spherical wall. Z. Angew. Math. Mech. 91 (1), 38–45.CrossRefGoogle Scholar
3. Faltinsen, O. M. & Timokha, A. N. 2009 Sloshing. Cambridge University Press.Google Scholar
4. Faltinsen, O. M. & Timokha, A. N. 2010 A multimodal method for liquid sloshing in a two-dimensional circular tank. J. Fluid Mech. 665, 457–479.CrossRefGoogle Scholar
5. Ibrahim, R. 2005 Liquid Sloshing Dynamics. Cambridge University Press.CrossRefGoogle Scholar
6. Komarenko, A. 1980 Asymptotic expansion of eigenfunctions of a problem with a parameter in the boundary conditions in a neighbourhood of angular boundary points. Ukr. Math. J. 32 (5), 433–437.CrossRefGoogle Scholar
7. Kress, R. 1990 A Nyström method for boundary integral equations in domains with corners. Numer. Math. 58, 145–161.CrossRefGoogle Scholar
8. Kuznetsov, E. A., Spector, M. D. & Zakharov, V. E. 1994 Formation of singularities on the free surface of an ideal fluid. Phys. Rev. E 49, 1283–1290.CrossRefGoogle ScholarPubMed
9. McIver, P. 1989 Sloshing frequencies for cylindrical and spherical containers filled to an arbitrary depth. J. Fluid Mech. 201, 243–257.CrossRefGoogle Scholar
10. Miles, J. W. 1972 On the eigenvalue problem for fluid sloshing in a half-space. Z. Angew. Math. Mech. 23, 861–869.Google Scholar
11. Polyanin, A. D. 2001 Handbook of Linear Partial Differential Equations for Engineers and Scientists. Chapman and Hall/CRC.CrossRefGoogle Scholar
12. Timokha, A. N. 2005 Planimetry of vibrocapillary equilibria at small wavenumbers. Intl. J. Fluid Mech. Res. 32 (4), 454–487.CrossRefGoogle Scholar
13. Wigley, N. M. 1964 Asymptotic expansions at a corner of solutions of mixed boundary value problems (asymptotic expansions at corner of solutions of elliptic second order partial differential equations in two variables). J. Math. Mech. 13, 549–576.Google Scholar
14. Wigley, N. M. 1970 Mixed boundary value problems in plane domains with corners. Math. Z. 115, 33–52.CrossRefGoogle Scholar