Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-19T11:47:20.592Z Has data issue: false hasContentIssue false
  • English
  • Français

Free-surface flow past oscillating singularities at resonant frequency

Published online by Cambridge University Press:  20 April 2006

G. Dagan  and
T. Miloh
G. Dagan
Affiliation:
School of Engineering, Tel-Aviv University, Israel
T. Miloh
Affiliation:
School of Engineering, Tel-Aviv University, Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper analyses the problem of a flow past an oscillating body moving with constant velocity, below and parallel to a free surface. Special attention is given to frequencies of oscillation in the neighbourhood of the critical frequency ωc= 0.25 g/U, where the classical linearized solution yields infinitely large wave amplitude. As a result both the lift and drag forces acting on the oscillating body at the resonant frequency are singular. It is demonstrated in the paper how this resonance is elimi- nated by considering higher-order free-surface effects, in particular the interaction between the first- and third-order terms. The resulting generalized solution yields finite wave amplitudes at the resonant frequency which are O(ε½) and O(εlogε) for 2 and 3 dimensions respectively. Here 6 is a measure of the singularity strength. It is also shown that inclusion of third-order terms causes a shift in the wavenumber and group velocity which eliminates the singularity in the lift and drag expressions at the resonant frequency. These results are illustrated by computing the lift and drag experienced by a submerged oscillating horizontal doublet in a uniform flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 120 , July 1982 , pp. 139 - 154
Copyright
© 1982 Cambridge University Press

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

Becker, T. 1958 Das Wellenbild einer unter der oberflache eines stromes schwerer flussigkiet pulsierender quelle. Z. angew. Math. Mech. 38, 391–399.Google Scholar
Dagan, G. & Miloh, T. 1981 Flow past oscillating bodies at resonant frequency. In Proc. 13th Symp. on Naval Hydrodynamics, Tokyo, pp. 355–369.
Debnath, L. & Rosenblat, S. 1969 The ultimate approach to the steady state in the generation of waves on a running stream. Quart. J. Mech. Appl. Math. 22, 221–233.Google Scholar
Doctors, L. J. 1978 Hydrodynamic power radiated by a heaving and pitching air-cushion vehicle. J. Ship Res. 22, 67–79.Google Scholar
Eggers, K. 1957 Uber das Wellenbild einer pulsierenden Storung in Translation. Schiff und Hafen 11, 874–878.Google Scholar
Euvrand, D., Jami, A., Morice, C. & Ousset, Y. 1977 Calcul numerique des oscillations d'un navire engendrees par la houle. J. Méc. 16, 281–326.Google Scholar
Hanaoka, T. 1957 Theoretical investigation concerning ship motion in regular waves. In Proc. Symp. on the Behaviour of Ships in a Seaway, Netherland Ship Model Basin.
Haskind, M. D. 1954 On the motion with waves of heavy fluid (in Russian). Prikl. Mat. Mekh. 18, 15–26.Google Scholar
Lighthill, M. J. 1960 Studies on magneto-hydrodynamic waves and other anisotropic wave motions. Phil. Trans. R. Soc. Lond. A 252, 397–430.Google Scholar
Newman, J. N. 1959 The damping and wave resistance of a pitching and heaving ship. J. Ship Res. 3, 1–19.Google Scholar
Newman, J. N. 1971 Third-order interaction in Kelvin ship—waves systems. J. Ship Res. 15, pp. 1–10.Google Scholar
Phillips, O. M. 1969 The Dynamics of the Upper Ocean, 2nd edn. Cambridge University Press.
Tayler, A. B. & Van den Driessche, P. 1974 Small amplitude surface waves due to a moving source. Quart. J. Mech. Appl. Math. 27, 317–345.Google Scholar
Wehausen, J. V. & Laitone, E. V. 1960 Surface waves. In Handbuch der Physik (ed. S. Flugge), vol. 9, pp. 446–778. Springer.
Wu, T. Y. 1957 Water waves generated by the translatory and oscillatory surface disturbance. Calif. Inst. of Tech. Engng Div. Rep. no. 85–3.Google Scholar