Skip to main content
    • Aa
    • Aa

Self-similar vortex-induced vibrations of a hanging string

  • C. Grouthier (a1), S. Michelin (a1), Y. Modarres-Sadeghi (a2) and E. de Langre (a1)

An experimental analysis of the vortex-induced vibrations of a hanging string with variable tension along its length is presented in this paper. It is shown that standing waves develop along the hanging string. First, the evolution of the Strouhal number $\mathit{St}$ with the Reynolds number $\mathit{Re}$ follows a trend similar to what is observed for a circular cylinder in a flow for relatively low Reynolds numbers ( $32\lt \mathit{Re}\lt 700$ ). Second, the extracted mode shapes are self-similar: a rescaling of the spanwise coordinate by a self-similarity coefficient allows all of them to collapse onto a unique function. The self-similar behaviour of the spatial distribution of the vibrations along the hanging string is then explained theoretically by performing a linear stability analysis of an adapted wake-oscillator model. This linear stability analysis finally provides an accurate description of the mode shapes and of the evolution of the self-similarity coefficient with the flow speed.

Corresponding author
Email address for correspondence:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

G. S. Baarholm , C. M. Larsen & H. Lie 2006 On fatigue damage accumulation from in-line and cross-flow vortex-induced vibrations on risers. J. Fluids Struct. 22, 109127.

R. Bourguet , G. E. Karniadakis & M. S. Triantafyllou 2011a Vortex-induced vibrations of a long flexible cylinder in shear flow. J. Fluid Mech. 677, 342382.

R. Bourguet , Y. Modarres-Sadeghi , G. E. Karniadakis & M. S. Triantafyllou 2011b Wake–body resonance of long flexible structures is dominated by counterclockwise orbits. Phys. Rev. Lett. 107, 134502.

J. R. Chaplin , P. W. Bearman , F. J. Huera-Huarte & R. J. Pattenden 2005 Laboratory measurements of vortex-induced vibrations of a vertical tension riser in a stepped current. J. Fluids Struct. 21, 324.

C. Evangelinos & G. E. Karniadakis 1999 Dynamics and flow structures in the turbulent wake of rigid and flexible cylinders subject to vortex-induced vibrations. J. Fluid Mech. 400, 91124.

M. L. Facchinetti , E. de Langre & F. Biolley 2004 Coupling of structure and wake oscillators in vortex-induced vibrations. J. Fluids Struct. 19, 123140.

U. Fey , M. König & H. Eckelmann 1998 A new Strouhal–Reynolds-number relationship for the circular cylinder in the range $47\lt Re\lt 2\times 1{0}^{5} $. Phys. Fluids 10 (7), 15471549.

F. J. Huera-Huarte & P. W. Bearman 2009 Wake structures and vortex-induced vibrations of a long flexible cylinder – Part 1: Dynamic response. J. Fluids Struct. 25, 979990.

L. Mathelin & E. de Langre 2005 Vortex-induced vibrations and waves unders shear flow with a wake oscillator model. Eur. J. Mech. (B/Fluids) 24, 478490.

Y. Modarres-Sadeghi , F. Chasparis , M. S. Triantafyllou , M. Tognarelli & P. Beynet 2011 Chaotic response is a generic feature of vortex-induced vibrations of flexible risers. J. Sound Vib. 330, 25652579.

Y. Modarres-Sadeghi , H. Mukundan , J. M. Dahl , F. S. Hover & M. S. Triantafyllou 2010 The effect of higher harmonic forces on fatigue life of marine risers. J. Sound Vib. 329, 4355.

D. J. Newman & G. E. Karniadakis 1997 A direct numerical simulation study of flow past a freely vibrating cable. J. Fluid Mech. 344, 95136.

C. Norberg 2003 Fluctuating lift on a circular cylinder: review and new measurements. J. Fluids Struct. 17, 5796.

N. Srinil 2010 Multi-mode interactions in vortex-induced vibrations of flexible curved/straight structures with geometric nonlinearities. J. Fluids Struct. 26, 10981122.

N. Srinil 2011 Analysis and prediction of vortex-induced vibrations of variable-tension vertical risers in linearly sheared currents. Appl. Ocean Res. 33, 4153.

M. S. Triantafyllou & G. S. Triantafyllou 1991 The paradox of the hanging string: an explanation using singular perturbations. J. Sound Vib. 148 (2), 343351.

A. D. Trim , H. Braaten , H. Lie & M. A. Tognarelli 2005 Experimental investigation of vortex-induced vibration of long marine risers. J. Fluids Struct. 21, 335361.

J. K. Vandiver , V. Jaiswal & V. Jhingran 2009 Insights on vortex-induced, traveling waves on long risers. J. Fluids Struct. 25, 641653.

R. Violette , E. de Langre & J. Szydlowski 2007 Computations of vortex-induced vibrations of long structures using a wake oscilator model: comparison with DNS and experiments. Comput. Struct. 85, 11341141.

R. Violette , E. de Langre & J. Szydlowski 2010 A linear stability approach to vortex-induced vibrations and waves. J. Fluids Struct. 26 (3), 442466.

C. H. K. Williamson & G. L. Brown 1998 A series in $1/ \sqrt{Re} $ to represent the Strouhal–Reynolds number relationship of the cylinder wake. J. Fluids Struct. 12, 10731085.

C. H. K. Williamson & R. Govardhan 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36, 413455.

X. Wu , F. Ge & Y. Hong 2012 A review of recent studies on vortex-induced vibrations of long slender cylinders. J. Fluids Struct. 28, 292308.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 25 *
Loading metrics...

Abstract views

Total abstract views: 111 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 26th September 2017. This data will be updated every 24 hours.