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Forcing of a bottom-mounted circular cylinder by steep regular water waves at finite depth

Published online by Cambridge University Press:  14 August 2014

Bo T. Paulsen ,
H. Bredmose ,
H. B. Bingham  and
N. G. Jacobsen
Bo T. Paulsen*
Affiliation:
Department of Mechanical Engineering, Technical University of Denmark, Kgs. Lyngby, 2800, Denmark Deltares, Rotterdamseweg 185, 2629HD Delft, The Netherlands
H. Bredmose
Affiliation:
Department of Wind Energy, Technical University of Denmark, Kgs. Lyngby, 2800, Denmark
H. B. Bingham
Affiliation:
Department of Mechanical Engineering, Technical University of Denmark, Kgs. Lyngby, 2800, Denmark
N. G. Jacobsen
Affiliation:
Department of Mechanical Engineering, Technical University of Denmark, Kgs. Lyngby, 2800, Denmark Deltares, Rotterdamseweg 185, 2629HD Delft, The Netherlands
*
†Email address for correspondence: bo.paulsen@deltares.nl
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Abstract

Forcing by steep regular water waves on a vertical circular cylinder at finite depth was investigated numerically by solving the two-phase incompressible Navier–Stokes equations. Consistently with potential flow theory, boundary layer effects were neglected at the sea bed and at the cylinder surface, but the strong nonlinear motion of the free surface was included. The numerical model was verified and validated by grid convergence and by comparison to relevant experimental measurements. First-order convergence towards an analytical solution was demonstrated and an excellent agreement with the experimental data was found. Time-domain computations of the normalized inline force history on the cylinder were analysed as a function of dimensionless wave height, water depth and wavelength. Here the dependence on depth was weak, while an increase in wavelength or wave height both lead to the formation of secondary load cycles. Special attention was paid to this secondary load cycle and the flow features that cause it. By visual observation and a simplified analytical model it was shown that the secondary load cycle was caused by the strong nonlinear motion of the free surface which drives a return flow at the back of the cylinder following the passage of the wave crest. The numerical computations were further analysed in the frequency domain. For a representative example, the secondary load cycle was found to be associated with frequencies above the fifth- and sixth-harmonic force component. For the third-harmonic force, a good agreement with the perturbation theories of Faltinsen, Newman & Vinje (J. Fluid Mech., vol. 289, 1995, pp. 179–198) and Malenica & Molin (J. Fluid Mech., vol. 302, 1995, pp. 203–229) was found. It was shown that the third-harmonic forces were estimated well by a Morison force formulation in deep water but start to deviate at decreasing depth.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave breaking Waves/Free-surface Flows: Wave-structure interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 755 , 25 September 2014 , pp. 1 - 34
Copyright
© 2014 Cambridge University Press 

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