Skip to main content
SpringerLink
Log in

Peaked sloshing in a wedge container

  • Published:
Journal of Engineering Mathematics Aims and scope Submit manuscript

Abstract

Finite-amplitude free-surface flow in a wedge container is investigated analytically. We study a motionless standing wave of pure potential-flow acceleration with maximal amplitude where its right-angle surface peak falls from rest. The nonlinear free-surface conditions are satisfied by a family of flows where the chosen initial acceleration field is governed by one single dipole plus its three image dipoles. Streamlines and isobars are plotted, with the free surface as the zero-pressure isobar. The key geometric parameters are tabulated for each case, supplied with force calculations for an upright wedge container. The present approach is assessed against established eigenfunctions for linearized standing waves in a wedge container. The present dipole flows constitute a much richer family of peaked free sloshing shapes than the classical Fourier modes of free oscillation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Rayleigh JWS (1915) Deep water waves, progressive or stationary, to the third order of approximation. Proc R Soc Lond A 91:345–353

    Article  Google Scholar 

  2. Penney WG, Price AT (1952) Some gravity wave problems in the motion of perfect liquids. Part II. Finite periodic stationary gravity waves in a perfect liquid. Philos Trans A 244:254–284

    Google Scholar 

  3. Taylor GI (1953) An experimental study of standing waves. Proc R Soc Lond A 218:44–59

    Article  Google Scholar 

  4. Fultz D (1962) An experimental note on finite amplitude standing gravity waves. J Fluid Mech 13:193–212

    Article  Google Scholar 

  5. Edge RD, Walters G (1964) The period of standing gravity waves of largest amplitude on water. J Geophys Res 69:1674–1675

    Article  Google Scholar 

  6. Tadjbakhsh I, Keller JB (1960) Standing surface waves of finite amplitude. J Fluid Mech 8:442–451

    Article  MathSciNet  Google Scholar 

  7. Longuet-Higgins MS, Cokelet ED (1976) The deformation of steep surface waves on water—I. A numerical method of computation. Proc R Soc Lond A 350:1–26

    Article  MathSciNet  Google Scholar 

  8. Saffman PG, Yuen HC (1979) A note on numerical computations of large amplitude standing waves. J Fluid Mech 95:707–715

    Article  MathSciNet  Google Scholar 

  9. Schwartz LW, Whitney AK (1981) A semi-analytic solution for nonlinear standing waves in deep water. J Fluid Mech 107:147–171

    Article  MathSciNet  Google Scholar 

  10. Vanden-Broeck JM, Schwartz LW (1981) Numerical calculation of standing waves of arbitrary uniform depth. Phys Fluids 24:812–815

    Article  Google Scholar 

  11. Mercer GN, Roberts AJ (1992) Standing waves in deep water: their stability and extreme form. Phys Fluids A 4:259–269

    Article  MathSciNet  Google Scholar 

  12. Mercer GN, Roberts AJ (1994) The form of standing waves on finite depth water. Wave Motion 19:233–244

    Article  MathSciNet  Google Scholar 

  13. Longuet-Higgins MS (2001) Vertical jets from standing waves. Proc R Soc Lond A 457:495–510

    Article  MathSciNet  Google Scholar 

  14. Longuet-Higgins MS, Dommermuth DG (2001) Vertical jets from standing waves II. Proc R Soc Lond A 457:2137–2149

    Article  Google Scholar 

  15. Tyvand PA (2020) Initial stage of the finite-amplitude Cauchy–Poisson problem. Water Waves 2:145–168

    Article  MathSciNet  Google Scholar 

  16. Lamb H (1932) Hydrodynamics. Cambridge Univ Press, Cambridge

    MATH  Google Scholar 

  17. Faltinsen OM, Timokha AN (2009) Sloshing. Cambridge Univ Press, Cambridge

    MATH  Google Scholar 

  18. Grant MA (1973) Standing Stokes waves of maximum height. J Fluid Mech 60:593–604

    Article  Google Scholar 

  19. Tyvand PA, Miloh T (2012) Incompressible impulsive sloshing. J Fluid Mech 708:279–302

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematical Sciences and Technology, Norwegian University of Life Sciences, 1432, Ås, Norway

    Peder A. Tyvand

  2. Faculty of Information Technology and Electrical Engineering, Norwegian University of Science and Technology, 7034, Trondheim, Norway

    Jonas Kristiansen Nøland

Authors
  1. Peder A. Tyvand
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jonas Kristiansen Nøland
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jonas Kristiansen Nøland.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tyvand, P.A., Nøland, J.K. Peaked sloshing in a wedge container. J Eng Math 126, 3 (2021). https://doi.org/10.1007/s10665-020-10078-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10665-020-10078-z

Keywords

Search

Navigation