Hostname: page-component-546b4f848f-gfk6d Total loading time: 0 Render date: 2023-05-31T04:01:10.369Z Has data issue: false Feature Flags: { "useRatesEcommerce": true } hasContentIssue false

On the initiation and sustenance of flow-induced vibration of cylinders: insights from force partitioning

Published online by Cambridge University Press:  26 November 2020

Karthik Menon*
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD21218, USA
Rajat Mittal*
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD21218, USA
Email addresses for correspondence:,
Email addresses for correspondence:,


The focus of this work is to dissect the physical mechanisms that drive and sustain flow-induced, transverse vibrations of cylinders. The influence of different mechanisms is quantified by using a method to partition the fluid dynamic force on the cylinder into distinct, physically relevant components. In conjunction with this force partitioning, calculations of the energy extracted by the oscillating body from the flow are used to make a direct connection between the phenomena responsible for force generation and their effect on driving flow-induced oscillations. These tools are demonstrated in a study of the effect of cylinder shape on flow-induced vibrations. Relatively small increases in cylinder aspect ratio are found to have a significant influence on the amplitude of oscillation, resulting in a large drop in oscillation amplitude at reduced velocities that correspond to the upper range of the synchronization regime. By mapping out the energy transfer between the fluid and structure as a function of aspect ratio, we identify the existence of a low-amplitude stationary state as the cause of the drop in amplitude. Partitioning the fluid dynamic forces on cylinders of varying aspect ratio then allows us to uncover the physical mechanisms behind the appearance of the underlying bifurcation. The analysis also suggests that while vortex shedding in the wake is necessary to initiate oscillations, it is the vorticity associated with the boundary layer over the cylinder that is responsible for the sustenance of flow-induced vibrations.

JFM Papers
© The Author(s), 2020. Published by 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.)



Anagnostopoulos, P. & Bearman, P. W. 1992 Response characteristics of a vortex-excited cylinder at low Reynolds numbers. J. Fluids Struct. 6 (1), 3950.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Bearman, P. W. 2011 Circular cylinder wakes and vortex-induced vibrations. J. Fluids Struct. 27 (5–6), 648658.CrossRefGoogle Scholar
Bhat, S. S. & Govardhan, R. N. 2013 Stall flutter of NACA 0012 airfoil at low Reynolds numbers. J. Fluids Struct. 41, 166174.CrossRefGoogle Scholar
Bishop, R. E. D. & Hassan, A. Y. 1964 The lift and drag forces on a circular cylinder oscillating in a flowing fluid. Proc. R. Soc. Lond. A 277 (1368), 5175.Google Scholar
Blackburn, H. M. & Henderson, R. D. 1999 A study of two-dimensional flow past an oscillating cylinder. J. Fluid Mech. 385, 255286.CrossRefGoogle Scholar
Blackburn, H. M. & Karniadakis, G. E. 1993 Two- and three-dimensional simulations of vortex-induced vibration of a circular cylinder. In 3rd International Offshore and Polar Engineering Conference, Singapore, 1977, pp. 715–720.Google Scholar
Brika, D. & Laneville, A. 1993 Vortex-induced vibrations of a long flexible circular cylinder. J. Fluid Mech. 250, 481508.CrossRefGoogle Scholar
Carberry, J., Sheridan, J. & Rockwell, D. 2005 Controlled oscillations of a cylinder: forces and wake modes. J. Fluid Mech. 538, 3169.CrossRefGoogle Scholar
Chang, C. C. 1992 Potential flow and forces for incompressible viscous flow. Proc. R. Soc. Lond. A 437 (1901), 517525.Google Scholar
D'Alessio, S. J. D., Dennis, S. C. R. & Nguyen, P. 1999 Unsteady viscous flow past an impulsively started oscillating and translating elliptic cylinder. J. Engng Maths 35 (3), 339357.CrossRefGoogle Scholar
D'Alessio, S. J. D. & Kocabiyik, S. 2001 Numerical simulation of the flow induced by a transversely oscillating inclined elliptic cylinder. J. Fluids Struct. 15 (5), 691715.CrossRefGoogle Scholar
Davidson, B. J. & Riley, N. 1972 Jets induced by oscillatory motion. J. Fluid Mech. 53 (2), 287303.CrossRefGoogle Scholar
Feng, C. C. 1968 The measurement of vortex induced effects in flow past stationary and oscillating circular and D-section cylinders. Masters thesis, The University of British Columbia, Canada.Google Scholar
Franzini, G. R., Fujarra, A. L. C., Meneghini, J. R., Korkischko, I. & Franciss, R. 2009 Experimental investigation of vortex-induced vibration on rigid, smooth and inclined cylinders. J. Fluids Struct. 25 (4), 742750.CrossRefGoogle Scholar
Ghias, R., Mittal, R. & Dong, H. 2007 A sharp interface immersed boundary method for compressible viscous flows. J. Comput. Phys. 225 (1), 528553.CrossRefGoogle Scholar
Gopalakrishnan, R. 1993 Vortex-induced forces on oscillating bluff cylinders. PhD thesis, Massachusetts Institute of Technology.Google Scholar
Govardhan, R. & Williamson, C. H. K. 2000 Modes of vortex formation and frequency response of a freely vibrating cylinder. J. Fluid Mech. 420, 85130.CrossRefGoogle Scholar
Hall, P. 1984 On the stability of the unsteady boundary layer on a cylinder oscillating transversely in a viscous fluid. J. Fluid Mech. 146, 347367.CrossRefGoogle Scholar
Hasheminejad, S. M. & Jarrahi, M. 2015 Numerical simulation of two dimensional vortex-induced vibrations of an elliptic cylinder at low Reynolds numbers. Comput. Fluids 107, 2542.CrossRefGoogle Scholar
Hover, F. S., Techet, A. H. & Triantafyllou, M. S. 1998 Forces on oscillating uniform and tapered cylinders in crossflow. J. Fluid Mech. 363, 97114.CrossRefGoogle Scholar
Howe, M. S. 1995 On the force and moment on a body in an incompressible fluid, with application to rigid bodies and bubbles at high and low Reynolds numbers. Q. J. Mech. Appl. Maths 48 (3), 401426.CrossRefGoogle Scholar
Kanwal, R. P. 1955 Vibrations of an elliptic cylinder and a flat plate in a viscous fluid. Z. Angew. Math. Mech. 35 (1–2), 1722.CrossRefGoogle Scholar
Khalak, A. & Williamson, C. H. K. 1999 Motions, forces and mode transitions in vortex-induced vibrations at low mass-damping. J. Fluids Struct. 13 (7–8), 813851.CrossRefGoogle Scholar
Kocabiyik, S. & D'Alessio, S. J. D. 2004 Numerical study of flow around an inclined elliptic cylinder oscillating in line with an incident uniform flow. Eur. J. Mech. B/Fluids 23 (2), 279302.CrossRefGoogle Scholar
Kumar, S., Navrose, & Mittal, S. 2016 Lock-in in forced vibration of a circular cylinder. Phys. Fluids 28 (11), 113605.CrossRefGoogle Scholar
Lighthill, J. 1986 Fundamentals concerning wave loading on offshore structures. J. Fluid Mech. 173, 667681.CrossRefGoogle Scholar
Magnaudet, J. 2011 A ‘reciprocal’ theorem for the prediction of loads on a body moving in an inhomogeneous flow at arbitrary Reynolds number. J. Fluid Mech. 689, 564604.CrossRefGoogle Scholar
Martín-Alcántara, A., Fernandez-Feria, R. & Sanmiguel-Rojas, E. 2015 Vortex flow structures and interactions for the optimum thrust efficiency of a heaving airfoil at different mean angles of attack. Phys. Fluids 27 (7), 073602.CrossRefGoogle Scholar
Meneghini, J. R. & Bearman, P. W. 1995 Numerical simulation of high amplitude oscillatory flow about a circular cylinder. J. Fluids Struct. 9 (4), 435455.CrossRefGoogle Scholar
Menon, K. & Mittal, R. 2019 Flow physics and dynamics of flow-induced pitch oscillations of an airfoil. J. Fluid Mech. 877, 582613.CrossRefGoogle Scholar
Menon, K. & Mittal, R. 2020 Aeroelastic response of an airfoil to gusts: prediction and control strategies from computed energy maps. J. Fluids Struct. 97, 103078.CrossRefGoogle Scholar
Mittal, R., Dong, H., Bozkurttas, M., Najjar, F. M., Vargas, A. & von Loebbecke, A. 2008 A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries. J. Comput. Phys. 227 (10), 48254852.CrossRefGoogle ScholarPubMed
Moriche, M., Flores, O. & García-Villalba, M. 2018 On the aerodynamic forces on heaving and pitching airfoils at low Reynolds number. J. Fluid Mech. 828, 395423.CrossRefGoogle Scholar
Morison, J. R., Johnson, J. W. & Schaaf, S. A. 1950 The force exerted by surface waves on piles. J. Petrol. Tech. 2 (05), 149154.CrossRefGoogle Scholar
Morse, T. L. & Williamson, C. H. K. 2006 Employing controlled vibrations to predict fluid forces on a cylinder undergoing vortex-induced vibration. J. Fluids Struct. 22 (6–7), 877884.CrossRefGoogle Scholar
Morse, T. L. & Williamson, C. H. K. 2009 Prediction of vortex-induced vibration response by employing controlled motion. J. Fluid Mech. 634, 539.CrossRefGoogle Scholar
Navrose, , Yogeswaran, V., Sen, S. & Mittal, S. 2014 Free vibrations of an elliptic cylinder at low Reynolds numbers. J. Fluids Struct. 51, 5567.CrossRefGoogle Scholar
Noca, F., Shiels, D. & Jeon, D. 1997 Measuring instantaneous fluid dynamic forces on bodies, using only velocity fields and their derivatives. J. Fluids Struct. 11 (3), 345350.CrossRefGoogle Scholar
Noca, F., Shiels, D. & Jeon, D. 1999 A comparison of methods for evaluating time-dependent fluid dynamic forces on bodies, using only velocity fields and their derivatives. J. Fluids Struct. 13 (5), 551578.CrossRefGoogle Scholar
Ongoren, A. & Rockwell, D. 1988 Flow structure from an oscillating cylinder. Part 2. Mode competition in the near wake. J. Fluid Mech. 191, 225245.CrossRefGoogle Scholar
Pan, L. S. & Chew, Y. T. 2002 A general formula for calculating forces on a 2-D arbitrary body in incompressible flow. J. Fluids Struct. 16 (1), 7182.CrossRefGoogle Scholar
Prasanth, T. K. & Mittal, S. 2008 Vortex-induced vibrations of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 594, 463491.CrossRefGoogle Scholar
Protas, B., Styczek, A. & Nowakowski, A. 2000 An effective approach to computation of forces in viscous incompressible flows. J. Comput. Phys. 159 (2), 231245.CrossRefGoogle Scholar
Quartappelle, L. & Napolitano, M. 1982 Force and moment in incompressible flows. AIAA J. 21 (6), 911913.CrossRefGoogle Scholar
Sarpkaya, T. 1978 Fluid forces on oscillating cylinders. J. Waterways Port Coast. Ocean Div. ASCE 104 (3), 275290.Google Scholar
Sarpkaya, T. 2001 On the force decompositions of Lighthill and Morison. J. Fluids Struct. 15 (2), 227233.CrossRefGoogle Scholar
Sarpkaya, T. 2004 A critical review of the intrinsic nature of vortex-induced vibrations. J. Fluids Struct. 19 (4), 389447.CrossRefGoogle Scholar
Seo, J. H. & Mittal, R. 2011 A sharp-interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations. J. Comput. Phys. 230 (19), 73477363.CrossRefGoogle ScholarPubMed
Singh, S. P. & Mittal, S. 2005 Vortex-induced oscillations at low Reynolds numbers: hysteresis and vortex-shedding modes. J. Fluids Struct. 20 (8), 10851104.CrossRefGoogle Scholar
Staubli, T. 1983 Calculation of the vibration of an elastically mounted cylinder using experimental data from forced oscillation. J. Fluids Engng 105 (2), 225.CrossRefGoogle Scholar
Triantafyllou, G. S., Triantafyllou, M. S. & Chryssostomidis, C. 1986 On the formation of vortex streets behind stationary cylinders. J. Fluid Mech. 170, 461477.CrossRefGoogle Scholar
Wang, H., Zhai, Q. & Chen, K. 2019 Vortex-induced vibrations of an elliptic cylinder with both transverse and rotational degrees of freedom. J. Fluids Struct. 84, 3655.CrossRefGoogle Scholar
Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36 (1), 413455.CrossRefGoogle Scholar
Williamson, C. H. K. & Roshko, A. 1988 Vortex formation in the wake of an oscillating cylinder. J. Fluids Struct. 2 (4), 355381.CrossRefGoogle Scholar
Wu, J. C. 1981 Theory for aerodynamic force and moment in viscous flows. AIAA J. 19 (4), 432441.CrossRefGoogle Scholar
Zdravkovich, M. M. 1981 Review and classification of various aerodynamic and hydrodynamic means for suppressing vortex shedding. J. Wind Engng Ind. Aerodyn. 7 (2), 145189.CrossRefGoogle Scholar
Zdravkovich, M. M. 1982 Modification of vortex shedding in the synchronization range. J. Fluid Engng 104 (4), 513517.CrossRefGoogle Scholar
Zhang, C. 2015 Mechanisms for aerodynamic force generation and flight stability in insects. PhD thesis, Johns Hopkins University.Google Scholar
Zhang, C., Hedrick, T. L. & Mittal, R. 2015 Centripetal acceleration reaction: an effective and robust mechanism for flapping flight in insects. PLoS ONE 10 (8), 116.Google ScholarPubMed
Zhu, Y., Su, Y. & Breuer, K. 2020 Nonlinear flow-induced instability of an elastically mounted pitching wing. J. Fluid Mech. 899, A35.CrossRefGoogle Scholar