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Impulsive acceleration of a circular cylinder under free surface

Published online by Cambridge University Press:  14 August 2023

Peder A. Tyvand Open the ORCID record for Peder A. Tyvand [Opens in a new window]  and
Vasily K. Kostikov Open the ORCID record for Vasily K. Kostikov [Opens in a new window]
Peder A. Tyvand
Affiliation:
Faculty of Mathematical Sciences and Technology, Norwegian University of Life Sciences, 1432 Ås, Norway
Vasily K. Kostikov*
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin, PR China
*
†Email address for correspondence: kostikov@hrbeu.edu.cn
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Abstract

A present paper generalizes the work of Tyvand & Miloh (J. Fluid Mech., vol. 286, 1995, pp. 67–101) on the problem of the free surface flow generated by a submerged circular cylinder moving impulsively with constant velocity to the case of a cylinder moving with both initial velocity and acceleration. The nonlinear small-time asymptotic solution for the velocity potential, free surface elevation and hydrodynamic pressure force is calculated analytically in bipolar coordinates for a cylinder of arbitrary radius. The analytical solution is obtained to the leading order of nonlinear interaction between initial impulsive velocity and initial impulsive acceleration directed at arbitrary angles. In the special case of the motion with constant acceleration, the complete fourth-order free-surface flow problem is solved and the associated second-order hydrodynamic force is computed. The leading-order contributions to the free surface elevation due to the constant velocity and constant acceleration are compared for finite rectilinear cylinder displacements. The role of constant acceleration consists of two contributions to the leading nonlinear terms, where the amplitude of the first one is 25 % below the case of constant velocity while the amplitude of the other exceeds it by 50 %.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave-structure interactions Mathematical Foundations: General fluid mechanics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 969 , 25 August 2023 , A12
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Dean, W.R. 1948 On the reflection of surface waves by a submerged cylinder. Proc. Camb. Phil. Soc. 44, 483–491.CrossRefGoogle Scholar
Greenhow, M. & Li, Y. 1987 Added masses for circular cylinders near or penetrating fluid boundaries – review, extension and application to water-entry, -exit and slamming. Ocean Engng 14, 325–348.CrossRefGoogle Scholar
Greenhow, M. & Lin, W.-M. 1983 Nonlinear free surface effects: experiments and theory. Tech. Rep. 83-19. MIT, Dept. of Ocean Engineering.Google Scholar
Greenhow, M. & Moyo, S. 1997 Water entry and exit of horizontal circular cylinders. Phil. Trans. R. Soc. Lond. A 355, 551–563.CrossRefGoogle Scholar
Haussling, H.J. & Coleman, R.M. 1979 Nonlinear water waves generated by an accelerated circular cylinder. J. Fluid Mech. 92, 767–781.CrossRefGoogle Scholar
Havelock, T.H. 1936 The forces on a circular cylinder submerged in a uniform stream. Proc. R. Soc. Lond. A 157, 526–534.Google Scholar
Havelock, T.H. 1949 The resistance of a submerged cylinder in accelerated motion. Q. J. Mech. Appl. Maths 2, 419–427.CrossRefGoogle Scholar
King, A. & Needham, D. 1994 The initial development of a jet caused by fluid, body and free-surface interaction. Part 1. A uniformly accelerating plate. J. Fluid Mech. 268, 89–101.CrossRefGoogle Scholar
Kostikov, V.K. & Makarenko, N.I. 2016 The motion of elliptic cylinder under free surface. J. Phys.: Conf. Ser. 722, 012021.Google Scholar
Kostikov, V.K. & Makarenko, N.I. 2018 Unsteady free surface flow above a moving circular cylinder. J. Engng Maths 112, 1–16.CrossRefGoogle Scholar
Lamb, H. 1913 On some cases of wave-motion on deep water. Ann. Mat. Pur. Appl. 21 (1), 237–250.CrossRefGoogle Scholar
Liao, S. 2004 Beyond perturbation: introduction to the homotopy analysis method. Appl. Mech. Rev. 57 (5), B25–B26.CrossRefGoogle Scholar
Makarenko, N.I. 2003 Nonlinear interaction of submerged cylinder with free surface. Trans. ASME J. Offshore Mech. Arctic Engng 125 (1), 72–75.CrossRefGoogle Scholar
Moreira, R.M. & Peregrine, D.H. 2010 Nonlinear interactions between a free-surface flow with surface tension and a submerged cylinder. J. Fluid. Mech. 648, 485–507.CrossRefGoogle Scholar
Morse, P.M. & Feshbach, H. 1953 Methods of Theoretical Physics. McGraw-Hill.Google Scholar
Moyo, S. & Greenhow, M. 2000 Free motion of a cylinder moving below and through a free surface. Appl. Ocean Res. 22, 31–44.CrossRefGoogle Scholar
Needham, D., Billingham, J. & King, A. 2007 The initial development of a jet caused by fluid, body and free-surface interaction. Part 2. An impulsively moved plate. J. Fluid Mech. 578, 67–84.CrossRefGoogle Scholar
Ogilvie, T.F. 1963 First- and second-order forces on a cylinder submerged under a free surface. J. Fluid Mech. 16 (3), 451–472.CrossRefGoogle Scholar
Ovsyannikov, L.V., Makarenko, N.I., Nalimov, V.I., Liapidevskii, V.Y., Plotnikov, P.I., Sturova, I.V., Bukreev, V.I. & Vladimirov, V.A. 1985 Nonlinear Problems of the Theory of Surface and Internal Waves. Nauka.Google Scholar
Pardo, R.M., Barua, N., Lisak, D. & Nedić, J. 2022 Jetting onset on a liquid surface accelerated past a submerged cylinder. Flow 2, E36.CrossRefGoogle Scholar
Pardo, R.M. & Nedić, J. 2021 Free-surface disturbances due to the submersion of a cylindrical obstacle. J. Fluid Mech. 926, A1.CrossRefGoogle Scholar
Peregrine, H. 1972 Flow due to a vertical plate moving in a channel (unpublished note).Google Scholar
Semenov, Y.A., Savchenko, Y.N. & Savchenko, G.Y. 2021 Impulsive impact of submerged body. J. Fluid Mech. 919, R4.CrossRefGoogle Scholar
Sretensky, L.N. 1937 A theoretical study of wave resistance. Joukovsky Cent. Inst. Rep. 319, 1–55.Google Scholar
Telste, J.G. 1987 Inviscid flow about a cylinder rising to a free surface. J. Fluid Mech. 182, 149–168.CrossRefGoogle Scholar
Terent'ev, A.G. 1991 Nonstationary motion of bodies in a fluid. Proc. Steklov Inst. Maths 186, 211–221.Google Scholar
Tuck, E.O. 1965 The effect of non-linearity at the free surface on flow past a submerged cylinder. J. Fluid Mech. 22 (2), 401–414.CrossRefGoogle Scholar
Tyvand, P.A. & Miloh, T. 1995 Free surface flow due to impulsive motion of a submerged circular cylinder. J. Fluid Mech. 286, 67–101.CrossRefGoogle Scholar
Tyvand, P.A., Mulstad, C. & Bestehorn, M. 2021 a A nonlinear impulsive Cauchy–Poisson problem. Part 1. Eulerian description. J. Fluid Mech. 906, A24.CrossRefGoogle Scholar
Tyvand, P.A., Mulstad, C. & Bestehorn, M. 2021 b A nonlinear impulsive Cauchy–Poisson problem. Part 2. Lagrangian description. J. Fluid Mech. 906, A25.CrossRefGoogle Scholar
Ursell, F. 1950 Surface waves on deep water in the presence of a submerged circular cylinder. Proc. Camb. Phil. Soc. 46 (1), 141–152.CrossRefGoogle Scholar
Venkatesan, S.K. 1985 Added mass of two cylinders. J. Ship Res. 29 (04), 234–240.CrossRefGoogle Scholar
Wehausen, J.V. & Laitone, E.V. 1960 Surface waves. Handbuch der Physik 9, 446–779.Google Scholar
Zhong, X. & Liao, S. 2018 On the limiting Stokes wave of extreme height in arbitrary water depth. J. Fluid Mech. 843, 653–679.CrossRefGoogle Scholar