Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-12-02T21:53:51.815Z Has data issue: false hasContentIssue false
  • English
  • Français

Higher harmonic wave loads on a vertical cylinder in finite water depth

Published online by Cambridge University Press:  14 November 2017

T. Kristiansen Open the ORCID record for T. Kristiansen [Opens in a new window]  and
O. M. Faltinsen Open the ORCID record for O. M. Faltinsen [Opens in a new window]
T. Kristiansen
Affiliation:
Department of Marine Technology, Norwegian University of Science and Technology, 7491 Trondheim, Norway
O. M. Faltinsen
Affiliation:
Department of Marine Technology, Norwegian University of Science and Technology, 7491 Trondheim, Norway Centre of Autonomous Marine Operations and Systems (AMOS), Norwegian University of Science and Technology, Trondheim, Norway
Get access Rights & Permissions [Opens in a new window]

Abstract

The theory of Faltinsen et al. (J. Fluid Mech., vol. 289, 1995, pp. 179–198; FNV) for calculation of higher-order wave loads in deep water on a vertical free-surface-piercing circular bottom-mounted non-moving cylinder, based on potential flow of an incompressible fluid, is generalized to finite water depth. Systematic regular wave experiments are carried out, and the harmonics of the horizontal wave loads are compared with the generalized FNV theory. The horizontal force and mudline overturning moment are studied. The main focus is on the third harmonic of the loads, although all harmonics from one to five are considered. The theoretically predicted third harmonic loads are shown to agree well with the experiments for small to medium wave steepnesses, up to a rather distinct limiting wave steepness. Above this limit, the theory overpredicts, and the discrepancy in general increases monotonically with increasing wave steepness. The local Keulegan–Carpenter ($KC$) number along the axis of the cylinder indicates that flow separation will occur for the wave conditions where there are discrepancies. The assumption of $KC$-dependent added mass coefficients and the addition of a drag term in the FNV model, as is done in Morison’s equation, do not explain the discrepancies. A distinct run-up at the rear of the cylinder is observed in the experiments. A 2D Navier–Stokes simulation is carried out, and the resulting pressure, due to flow separation, is shown to qualitatively explain the local rear run-up.

JFM classification

Wakes/Jets: Separated flows Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 833 , 25 December 2017 , pp. 773 - 805
Copyright
© 2017 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

Chaplin, J. R., Rainey, R. C. T. & Yemm, R. W. 1997 Ringing of a vertical cylinder in waves. J. Fluid Mech. 350, 119–147.CrossRefGoogle Scholar
Faltinsen, O. M. 1999 Ringing loads on a slender vertical cylinder of general cross-section. J. Engng Math. 35 (1–2), 199–217.CrossRefGoogle Scholar
Faltinsen, O. M., Newman, J. N. & Vinje, T. 1995 Nonlinear wave loads on a slender vertical cylinder. J. Fluid Mech. 289, 179–198.Google Scholar
Fenton, J. D. 1985 A fifth-order Stokes theory for steady waves. J. Waterway Port Coastal Ocean Engng 111 (2), 216–234.Google Scholar
Fenton, J. D. 1990 Nonlinear Wave Theories, The Sea, vol. 9. Wiley.Google Scholar
Grue, J., Bjorshol, G. & Strand, O. 1994 Nonlinear wave loads which may generate ‘ringing’ responses of offshore structures. In International Workshop on Water Waves and Floating Bodies (IWWWFB), Japan.Google Scholar
Hughes, S. A. 1993 Physical Models and Laboratory Techniques in Coastal Engineering, Advanced Series on Ocean Engineering, vol. 7. World Scientific.Google Scholar
Huseby, M. & Grue, J. 2000 An experimental investigation of higher-harmonic wave forces on a vertical cylinder. J. Fluid Mech. 414, 75–103.Google Scholar
Kristiansen, T.2009 Two-dimensional numerical and experimental studies of piston-mode resonance. PhD thesis, Norwegian University of Science and Technology.Google Scholar
Malenica, Š. & Molin, B. 1995 Third-harmonic wave diffraction by a vertical cylinder. J. Fluid Mech. 302, 203–229.Google Scholar
Manners, W. & Rainey, R. C. T.1992 Hydrodynamic forces on fixed submerged cylinders. 436, 13–32.Google Scholar
Nelson, R. C. 1994 Depth limited design wave heights in very flat regions. Coast. Engng 23 (1), 43–59.Google Scholar
Newman, J. N. 1996 Nonlinear scattering of long waves by a vertical cylinder. In Fluid Mechanics and Its Applications (ed. Grue, J., Gjevik, B. & Weber, J. E.), vol. 34, pp. 91–102. Springer.Google Scholar
Paulsen, B. T., Bredmose, H., Bingham, H. B. & Jacobsen, N. G. 2014 Forcing of a bottom-mounted circular cylinder by steep regular water waves at finite depth. J. Fluid Mech. 755, 1–34.Google Scholar
Sarpkaya, T. 1986 Force on a circular cylinder in viscous oscillatory flow at low Keulegan–Carpenter numbers. J. Fluid Mech. 165, 61–71.Google Scholar
Schäffer, H. A. 1996 Second-order wavemaker theory for irregular waves. Ocean Engng 23, 47–88.Google Scholar
Shao, Y.-L. & Faltinsen, O. M. 2014 A harmonic polynomial cell (HPC) method for 3D Laplace equation with application in marine hydrodynamics. J. Comp. Phys. 274, 312–332.Google Scholar
Skjelbreia, L. & Hendrickson, J. 1960 Fifth order gravity wave theory. Coastal Engng Proc. 1 (7), 184–196.Google Scholar
Sortland, B.1986 Force measurements in oscillating flow on ship sections and circular cylinders in a U-tube water tank. PhD thesis, NTH, Trondheim, Norway.Google Scholar
Ursell, F. 1963 The decay of the free motion of a floating body. J. Fluid Mech. 19 (2), 305–319.CrossRefGoogle Scholar

Kristiansen supplementary movie 1

Regular wave condition T=12s, H_1/\lambda = 1/25, h/a=7.83

Download Kristiansen supplementary movie 1(Video)
Video 117 MB