Skip to main content
SpringerLink
Log in

Splitting, merging and spanwise wavenumber selection of Dean vortex pairs

  • Originals
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

Splitting, merging and spanwise wavenumber selection are studied during the initial development of Dean vortex pairs in a channel with mild curvature, an aspect ratio of 40, and an inner to outer radius ratio of 0.979. Two types of splitting events, and four types of merging events are evident from flow visualizations at Dean numbers from 75 to 220. These events are described in detail along with observations that occurrances of these different events are tied to spatial and temporal variations of spanwise wavenumbers of vortex pair spacing. Also discussed are frequency spectra of different events, recurrent phenomena, and the part played by splitting and merging in laminar to turbulent transition in curved channels.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alfredsson PH; Persson H (1989) Instabilities in channel flow with system rotation. Fluid Mech 202: 543–557

    Google Scholar 

  • Avsec D; Luntz M (1937) Tourbillons thermoconvectifs et electroconvectifs. La Meteorologie 3: 180–194

    Google Scholar 

  • Baun LR (1988) The development and structural characteristics of Dean vortices in a curved rectangular channel. M. E. Thesis, Dept. of Mech. Eng., Naval Postgraduate School, Monterey, Ca.

    Google Scholar 

  • Bippes H (1972) Experimentelle Untersuchung des laminar-turbulenten Umschlags an einer parallel angeströmten konkaven Wand. Heidelberger Akademie der Wissenschaften. Mathematisch-naturwissenschaftliche Klasse, Sitzungsberichte. Klasse 3, 103–180. Also 1978: Experimental study of the laminar-turbulent transition of a concave wall in a parallel flow. NACA Technical Memorandum 75243. 1–69

    Google Scholar 

  • Bippes H; Görtler H (1972) Dreidimensionale Störungen in der Grenzschicht an einer konkaven Wand. Acta Mechanica 14: 251–267

    Google Scholar 

  • Bottaro A (1993) On longitudinal vortices in curved channel flow. J Fluid Mech 251: 627–660

    Google Scholar 

  • Bottaro A; Matsson OJE; Alfredsson PH (1991) Numerical and experimental results for developing curved channel flow. Physics of Fluids A. 3, 5: 1473–1476

    Google Scholar 

  • Brewster DB; Grosberg P; Nissan AH (1959) The stability of viscous flow between horizontal concentric cylinders. Proceedings of the Royal Society of London, Series A. 251: 76–91

    Google Scholar 

  • Dean WR (1928) Fluid motion in a curved channel. Proceedings of the Royal Society of London, Series A 121: 402–420

    Google Scholar 

  • Eckhaus W (1965) Studies in nonlinear stability theory. New York: Springer

    Google Scholar 

  • Fields WA (1990) Study of the effects of centrifugal instabilities on flow in a 40 to 1 aspect ratio rectangular curved channel for Dean numbers from 35 to fully turbulent conditions. M. E. Thesis, Dept. of Mech. Eng., Naval Postgraduate School, Monterey, Ca

    Google Scholar 

  • Finlay WH; Guo Y; Olsen D (1993) Inferring secondary flows from smoke or dye flow visualization: two case studies. Physics of Fluids A. 51, 11: 2689–2701

    CAS  PubMed  Google Scholar 

  • Finlay WH; Keller JB; Ferziger JH (1988) Instability and transition in curved channel flow. J Fluid Mech 194: 417–456

    Google Scholar 

  • Floryan JM; Saric WS (1984) Wavelength selection and growth of Görtler vortices. AIAA Journal 22, 11: 1529–1538

    Google Scholar 

  • Görtler H (1940) Über eine dreidimensionale Instabilität laminarer Grenzschichten an konkaven Wänden. Nach. Ges. d. Wiss. Göttingen, Mathematik-Physik Klasse. Neue Folge I, 2, 1–26. Also 1954: On the three-dimensional instability of laminar boundary layers on concave walls. NACA Technical Memorandum 1375. 1–32

    Google Scholar 

  • Görtler H (1959) Über eine Analogie zwischen den Instabilitäten laminarer Grenzschichtströmungen an konkaven Wänden und an erwärmten Wänden. Ingenieur-Archiv 28: 71–78

    Google Scholar 

  • Guo Y; Finlay WH (1991) Splitting, merging and wavelength selection of vortices in curved and/or rotating channel flow due to Eckhaus instability. J Fluid Mech 228: 661–691

    Google Scholar 

  • Guo Y; Finlay WH (1993) Spanwise secondary instability of spatially developing vortices. J Fluid Mech submitted

  • Hughes RE (1989) Development, qualification and measurements in two curved channels with 40 to 1 aspect ratio. M. S. Thesis, Dept. Mech. Eng., Naval Postgraduate School, Monterey, Ca

    Google Scholar 

  • Kelleher MD; Flentie DL; McKee RJ (1980) An experimental study of the secondary flow in a curved rectangular channel. ASME Transactions-Journal of Fluids Engineering 102: 92–96

    CAS  PubMed  Google Scholar 

  • Liepmann HW (1943) Investigation on laminar boundary layer stability and transition on curved boundaries. NACA Wartime Report No. W-107

  • Liepmann HW (1945) Investigation of boundary layer transition on concave walls. NACA Wartime Report No. W-87

  • Ligrani PM; Bradshaw P (1987) Subminiature hot-wire sensors: development and use. Physics E.-Scientific Instruments 20: 323–332

    Google Scholar 

  • Ligrani PM; Finlay WH; Fields WA; Fuqua SJ; Subramanian CS (1992) Features of wavy vortices in a curved channel from experimental and numerical studies. Physics of Fluids A. 4, 4: 695–709

    Google Scholar 

  • Ligrani PM; Niver RD (1988) Flow visualization of Dean vortices in a curved channel with 40 to 1 aspect ratio. Physics of Fluids 31: 3605–3617

    Google Scholar 

  • Ligrani PM; Singer BA; Baun LR (1989a) Miniature five-hole pressure probe for measurement of three mean velocity components in low-speed flows. Journal of Physics E.-Scientific Instruments 22: 868–876

    Google Scholar 

  • Ligrani PM; Singer BA; Baun LR (1989b) Spatial resolution and downwash velocity corrections for multiple-hole pressure probes in complex flows. Experiments Fluids 7: 424–426

    Google Scholar 

  • Longest JM (1989) Flow visualization studies in (1) a curved rectangular channel with 40 to 1 aspect ratio and (2) a straight channel with bulk flow unsteadiness. M. S. Thesis, Dept. of Mech. Eng., Naval Postgraduate School, Monterey, Ca

    Google Scholar 

  • Matsson OJ; Alfredsson PH (1990) Curvature- and rotation-induced instabilities in channel flow. J Fluid Mech 210: 537–563

    Google Scholar 

  • Musuda S; Matsubara M (1989) Visual study of boundary layer transition on rotating flat plate. IUTAM Symposium on Laminar-Turbulent Transition. New York: Springer

    Google Scholar 

  • Peerhossaini H; Wesfreid JE (eds.) (1990) Euromech 261: Colloquium on Görtler Vortex Flows. ISITEM, Nantes

    Google Scholar 

  • Rayleigh L (1916) On the dynamics of revolving fluids. Scientific Papers. Cambridge University Press. 6: 447–453

  • Saric WS (1994) Görtler vortices. Ann Rev Fluid Mech 26: 379–409

    Google Scholar 

  • Snyder HA (1969) Wave-number selection at finite amplitude in rotating Couette flow. J Fluid Mech 352: 273–298

    Google Scholar 

  • Subramanian CS; Ligrani PM; Tuzzolo MF (1992) Surface heat transfer and flow properties of vortex arrays artificially and from centrifugal instabilities. Int J Heat and Fluid Flow 13, 3: 210–223

    Google Scholar 

  • Taylor GI (1923) Stability of a viscous liquid contained between two rotating cylinders. Philosophical Transactions of the Royal Society, Series A. 223: 289–343

    Google Scholar 

  • Yang KS; Kim J (1991) Numerical investigation of instability and transition in rotating plane poiseuille flow. Physics of Fluids A 3, 4: 633–641

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Utah, UT 84112, Salt Lake City, USA

    P. M. Ligrani

  2. Department of Mechanical Engineering, Naval Postgraduate School, 93943, Monterey, CA, USA

    J. E. Longest, M. R. Kendall & W. A. Fields

Authors
  1. P. M. Ligrani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. E. Longest
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. R. Kendall
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. W. A. Fields
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This study was sponsored by the Propulsion Directorate, U.S. Army Aviation Research and Technology Activity-AVSCOM, NASA-Defense Purchase Request 030030-P. Professor C. S. Subramanian provided assistance in setting up the traversing system and data acquisition systems used for this study. Mr. R. E. Hughes assisted in obtaining some of the results presented.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ligrani, P.M., Longest, J.E., Kendall, M.R. et al. Splitting, merging and spanwise wavenumber selection of Dean vortex pairs. Experiments in Fluids 18, 41–58 (1994). https://doi.org/10.1007/BF00209360

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00209360

Keywords

Search

Navigation