Skip to main content

The horseshoe vortex and vortex shedding around a vertical wall-mounted cylinder exposed to waves

  • B. M. Sumer (a1), N. Christiansen (a1) and J. Fredsøe (a1)

This study concerns the flow around the base of a vertical, wall-mounted cylinder - a pile - exposed to waves. The study comprises (i) flow visualization of horseshoe-vortex flow in front of and the lee-wake-vortex flow behind the pile and (ii) bed shear stress measurements around the pile conducted in a wave flume, plus supplementary bed shear stress measurements carried out in an oscillatory-flow water tunnel. The Reynolds number range of the flume experiments is ReD = (2-9) x 103 and that of the tunnel experiments is ReD = 103—5 x 104, in which ReD is based on the pile size. Steadycurrent tests were also carried out for reference. The horseshoe-vortex flow (like leewake-vortex flow) is governed primarily by the Keulegan-Carpenter number, KC. The range of KC was from 0 to about 25 in the flume experiments, and from 4 to 120 in the tunnel experiments. The experiments were conducted mainly with circular piles. The results indicate that no horseshoe vortex exists for KC < 6. The size and lifespan of the horseshoe vortex increase with KC. The influence of the cross-sectional shape of the pile on the horseshoe vortex was investigated. The results show that a square pile with 90° orientation produces the largest horseshoe vortex while that with 45° orientation produces the smallest one, the circular-pile result being between the two. The influence of a superimposed current on the horseshoe vortex was also investigated. The range of the current-to-wave-induced-velocity ratio, Uc/Um, was from 0 to about 0.8. The overall effect of the superimposed current is to increase the size and lifespan of the horseshoe vortex. This effect increases with increasing Uc/Um. Regarding the near-bed lee-wake flow, the flow regimes observed for the two-dimensional free-cylinder case exist for the present case, too, but with one exception: in the present case, no transverse vortex street was observed in the so-called single-pair regime. The results show that the bed shear stress beneath the horseshoe vortex and in the lee-wake area is heavily influenced by KC. The amplification of the bed shear stress with respect to its undisturbed value is maximum (O(4)) at the side edges of the pile, in contrast to what occurs in steady currents where the maximum occurs at an angle of about 45° from the upstream edge of the pile with an amplification of O(10).

Hide All
Baker, C. J. 1979 The laminar horseshoe vortex. J. Fluid Mech. 95, 347367.
Baker, C. J. 1985 The position of points of maximum and minimum shear stress upstream of cylinders mounted normal to flat plates. J. Wind Engng Indust. Aerodyn. 18, 263274.
Baker, C. J. 1991 The oscillation of horseshoe vortex systems. Trans. ASMEI: J. Fluids Engng 113, 489495.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Bearman, P. W., Graham, J. M. R., Naylor, P. & Obasaju, E. D. 1981 The role of vortices in oscillatory flow about bluff cylinders. In Proc. Intl Symp. on Hydrodyn. in Ocean Engng, Trondheim, Norway (ed. Gisvold, K. M. et al.). Norwegian Hydrodynamic Laboratories, Norwegian Institute of Technology.
Belik, L. 1973 The secondary flow about circular cylinders mounted normal to a flat plate. Aero. Q. February, 4754.
Briley, W. R. & McDonald, H. 1981 Computation of three dimensional horseshoe vortex flow using the Navier-Stokes equations. Proc. 7th ICNMFD, Stanford, CA (ed. Reynolds, W. C. & MacCormack, R. W.). Lecture Notes in Physics, vol. 141 Springer.
Dargahi, B. 1989 The turbulent flow field around a circular cylinder. Exps. Fluids 8, 112.
Ding, G. B. & Piquet, J. 1992 Navier-Stokes computations of horseshoe vortex flows. Intl J. Numer. Meth. Fluids 15, 99124.
Driest, E. R. Van 1956 On turbulent flow near a wall. J. Aero. Sci. 23, 10071011.
Hjorth, P. 1975 Studies on the nature of local scour. Dept. of Water Resources Engng, Lund Inst. of Technology, Univ. of Lund, Sweden, Bull Series A 46.
Jensen, B. L., Sumer, B. M. & Fredsoe, J. 1989 Turbulent oscillatory boundary layers at high Reynolds numbers. J. Fluid Mech. 206, 265297.
Kobayashi, T. 1992 Three-dimensional analysis of the flow around a vertical cylinder on a scoured seabed. Intl Conf. on Coastal Engineering, 4-9 October 1992, Venice, Italy (ed. Edge, B. L.). ASCE.
Kwak, D., Rogers, S. E., Kaul, U. K. & Chang, J. L. C. 1986 A numerical study of incompressible juncture flows. NASA Tech. Mem. 88319. Ames Research Center, Moffet Field, CA 94035.
Longuet-Higgins, M. S. 1957 The mechanics of the boundary-layer near the bottom in a progressive wave. Appendix to ‘An experimental investigation of drift profiles in a closed channel’ by R. C. H. Russell & J. D. C. Osorio. Proc. 6th Intl Conf. Coast. Eng., Miami, FL., pp. 184193.
Niedoroda, A. W. & Dalton, C. 1982 A review of the fluid mechanics of ocean scour. Ocean Engng 9, 159170.
Sarpkaya, T. 1986 Force on a circular cylinder in viscous oscillatory flow at low Keulegen- Carpenter numbers. J. Fluid Mech. 165, 6171.
Sarpkaya, T. & Isaacson, M. 1981 Mechanics of Wave Forces on Offshore Structures. Van Nostrand Reinhold.
Schwind, R. 1962 The Three-dimensional boundary layer near a strut. Gas turbine Lab., Rep. 67. MIT.
Sleath, J. F. A. 1984 Sea Bed Mechanics. John Wiley and Sons.
Sumer, B. M., Arnskov, M. M., Christiansen, N. & Jorgensen, F. E. 1993 Two-Component hotfilm probe for measurements of wall shear stress. Exps. Fluids 15, 380384.
Williamson, C. H. K. 1985 Sinusoidal flow relative to circular cylinders. J. Fluid Mech. 155, 141174.
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: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed