Environmental Fluid Mechanics

, Volume 15, Issue 1, pp 179–206 | Cite as

Shallow flow past a cavity: attenuation of oscillations via a bed perturbation

  • B. A. Tuna
  • D. RockwellEmail author
Original Article


Fully turbulent shallow flow past a cavity can give rise to highly coherent oscillations, which arise from coupling between the inherent instability of the separated shear layer along the cavity opening and a gravity standing wave within the cavity. The objective of the present investigation is to attenuate these oscillations by a single geometric perturbation (cylinder) on the bed (bottom surface), which is located near the leading corner of the cavity. The patterns of the flow structure are characterized as a function of height of the cylinder above the bed by using particle image velocimetry. Reduced amplitude of the coupled oscillation can be attained for values of cylinder diameter and height nearly an order of magnitude smaller than the water depth. The reduction of oscillation amplitude is associated with an increased width of the separated shear layer along the opening of the cavity, even at elevations above the bed much larger than the height of the cylinder. Near the bed, a vorticity defect in the separated shear layer and deflection of the layer away from the cavity opening are evident. The attenuation of the oscillation amplitude is associated with: a major decrease in the peak values of the normal and shear Reynolds stresses in the separated shear layer; degradation of coherent, phase-averaged patterns of vortex formation; and decreased scale of the coherent vortical structures that propagate downstream along the cavity opening. These changes in the stresses and the flow structure are, in turn, directly correlated with lower values of exchange velocity along the opening of the cavity, which is due to the decreased entrainment demand of the separated shear layer. This decrease in magnitude of the exchange velocity in the presence of the cylinder results in a 50 % reduction of the value of mass exchange coefficient between the cavity and the mainstream.


Shallow flow Instabilities Resonant coupling  Passive control 



The support of the National Science Foundation, Grant CBET-0965293, is gratefully acknowledged.


  1. 1.
    Jirka GH, Uijttewaal WSJ (2004) Shallow flows: a definition. In: Jirka GH, Uijttewaal WSJ (eds) Proceedings of the international symposium on shallow flows. Balkema, RotterdamGoogle Scholar
  2. 2.
    Rockwell D, Naudascher E (1978) Review-self-sustaining oscillations of flow past cavities. ASME Trans J Fluids Eng 100:152–165CrossRefGoogle Scholar
  3. 3.
    Chu VH, Babarutsi S (1988) Confinement and bed-friction effects in shallow turbulent mixing layers. J Hydraul Eng 114:1257CrossRefGoogle Scholar
  4. 4.
    Uijttewaal WSJ, Booij R (2000) Effects of shallowness on the development of free-surface mixing layers. Phys Fluids 12:392CrossRefGoogle Scholar
  5. 5.
    van Prooijen BC, Uijttewaal WSJ (2002) A linear approach for the evolution of coherent structures in shallow mixing layers. Phys Fluids 14:4105CrossRefGoogle Scholar
  6. 6.
    Uijttewaal WS (2011) Horizontal mixing in shallow flows. 34th IAHR World Congress, Balance and Uncertainty, Brisbane, 26 June–1 July 2011Google Scholar
  7. 7.
    Constantinescu G (2013) LE of shallow mixing interfaces: a review. Environ Fluid Mech. doi: 10.1007/s10652-013-9303-6
  8. 8.
    Chu VH, Wu JH, Khayat RE (1991) Stability of transverse shear flows in shallow open channels. J Hydraul Eng 117(10):1370–1388CrossRefGoogle Scholar
  9. 9.
    Chen D, Jirka GH (1998) Linear stability analysis of turbulent mixing layers and jets in shallow water layers. J Hydraul Res 36:815CrossRefGoogle Scholar
  10. 10.
    Socolofsky SA, Jirka GH (2004) Large-scale flow structures and stability in shallow flows. J Environ Eng Sci 3:451–462CrossRefGoogle Scholar
  11. 11.
    Ghidaoui MS, Kolyshkin AA (1999) Linear stability analysis of lateral motions in compound open channels. J Hydraul Eng 125:871CrossRefGoogle Scholar
  12. 12.
    Kolyshkin AA, Ghidaoui MS (2003) Stability analysis of shallow wake flows. J Fluid Mech 494:355–377CrossRefGoogle Scholar
  13. 13.
    Nazarovs S (2005) Stability analysis of shallow wake flows with free surface. Proceedings of the int. conference on theory and app. of mathematics and informatics ICTAMI 2005, Alba IuliaGoogle Scholar
  14. 14.
    Kolyshkin AA, Ghidaoui MS (2002) Gravitational and shear instabilities in compound and composite channels. J Hydraul Eng 128:1076–1085CrossRefGoogle Scholar
  15. 15.
    McCoy A, Constantinescu G, Weber L (2006) Exchange processes in a channel with two vertical emerged obstructions. Flow Turbul Combust 77(1–4):97–126CrossRefGoogle Scholar
  16. 16.
    Chang K, Constantinescu G, Park SO (2007) Assessment of predictive capabilities of detached eddy simulation to simulate flow and mass transport past open cavities. J Fluids Eng 129(11):1372–1383CrossRefGoogle Scholar
  17. 17.
    Constantinescu SG, Sukhodolov A, McCoy A (2009) Mass exchange in a shallow channel flow with a series of groynes: LES study and comparison with laboratory and field experiments. Environ Fluid Mech 9(6):587–615. doi: 10.1007/s10652-009-9155-2 CrossRefGoogle Scholar
  18. 18.
    Uijttewaal WSJ, Lehmann D, van Mazijk A (2001) Exchange processes between a river and its groyne fields: model experiments. J Hydraul Eng ASCE 127(11):928–936CrossRefGoogle Scholar
  19. 19.
    Sanjou M, Nezu I (2013) Hydrodynamic characteristics and related mass-transfer properties in open-channel flows with rectangular embayment zone. Environ Fluid Mech 13(6):527–555CrossRefGoogle Scholar
  20. 20.
    Brevis W, García-Villalba M, Niño Y (2014) Experimental and large eddy simulation study of the flow developed by a sequence of lateral obstacles. Environ Fluid Mech. doi: 10.1007/s10652-013-9328-x
  21. 21.
    Wallast I, Uijttewaal W, Mazijk A van (1999) Exchange processes between groyne field and main stream. Proceedings of the XXVIII IAHR CongressGoogle Scholar
  22. 22.
    Weitbrecht V, Jirka GH (2001) Flow patterns and exchange processes in dead zones of rivers. In: Li G, Wang Z, Pettitjean A, Fisher RK (eds) IAHR World Congress Proceedings. Tsinghua University Press, Beijing, p 439Google Scholar
  23. 23.
    Kurzke M, Weitbrecht V, Jirka GH (2002) Laboratory concentration measurements for determination of mass exchange between groin fields and main stream. Proceedings of 1st international conference on Fluvial Hydraulics River Flow, vol 1, pp 369–376Google Scholar
  24. 24.
    Uijttewaal WS (2005) Effects of groyne layout on the flow in groyne fields: laboratory experiments. J Hydraul Eng 131(9):782–791CrossRefGoogle Scholar
  25. 25.
    Meile T, Boillat JL, Schleiss AJ (2011) Water-surface oscillations in channels with axi-symmetric cavities. J Hydraul Res 49(1):73–81CrossRefGoogle Scholar
  26. 26.
    Kimura I, Hosoda T (1997) Fundamental properties of flows in open channels with dead zone. J Hydraul Eng 123:98CrossRefGoogle Scholar
  27. 27.
    Ikeda S, Yoshike T, Sugimoto T (1999) Experimental study on the structure of open channel flow with impermeable spur dikes. Annu J Hydraul Eng JSCE 43:281–286CrossRefGoogle Scholar
  28. 28.
    Nezu I, Onitsuka K (2002) PIV measurements of side-cavity open-channel flows: Wando model in rivers. J Vis 5(1):77–84CrossRefGoogle Scholar
  29. 29.
    Wolfinger M, Ozen CA, Rockwell D (2012) Shallow flow past a cavity: coupling with a standing gravity wave. Phys Fluids 24:104103CrossRefGoogle Scholar
  30. 30.
    Tuna BA, Tinar E, Rockwell D (2013) Shallow flow past a cavity: globally coupled oscillations as a function of depth. Exp Fluids 54(8):1–20CrossRefGoogle Scholar
  31. 31.
    Cattafesta LN III, Song Q, Williams DR, Rowley CW, Alvi FS (2008) Active control of flow-induced cavity oscillations. Prog Aerosp Sci 44(7):479–502CrossRefGoogle Scholar
  32. 32.
    Ukeiley LS, Ponton MK, Seiner JM, Jansen B (2004) Suppression of pressure loads in cavity flows. AIAAJ 42(1):70–79CrossRefGoogle Scholar
  33. 33.
    Mongeau L, Franchek MA, Kook H (1999) Control of interior pressure fluctuations due to flow over vehicle openings. In: Proceedings of the 1999 noise and vibration conference, vol 2, pp 1257–66Google Scholar
  34. 34.
    Zhang X, Chen XX, Rona A (1999) Attenuation of cavity flow oscillation through leading edge flow control. J Sound Vib 221(1):23–47CrossRefGoogle Scholar
  35. 35.
    Arunajatesan S, Shipman JD, Sinha N (2002) Hybrid RANS-LES simulation of cavity flow fields with control. AIAA Paper, 1130, 2002Google Scholar
  36. 36.
    Panickar P, Raman G (2008) Understanding the mechanisms of cavity resonance suppression using a cylindrical rod in crossflow. 46th AIAA Aerospace Sciences Meeting and Exhibit AIAA 2008-54.Google Scholar
  37. 37.
    Sarpotdar S, Panickar P, Raman G (2009) Cavity tone suppression using a rod in cross flow-Investigation of shear layer stability mechanism. American Institute of Aeronautics and Astronautics Paper, 700, 2009Google Scholar
  38. 38.
    Martinez MA, Onorato M (2009) Cavity flow control by a rod in crossflow. Acc Sc Torino Atti Sc Fis 143:55–65Google Scholar
  39. 39.
    Dudley J, Ukeiley L (2011) Detached eddy simulation of a supersonic cavity llow with and without passive flow control. AIAA Paper 2011-3844, AIAA computational fluid dynamics conferenceGoogle Scholar
  40. 40.
    Martinez MA, Di Cicca GM, Iovieno M, Onorato M (2012) Control of cavity flow oscillations by high frequency forcing. J Fluids Eng 134:051201CrossRefGoogle Scholar
  41. 41.
    Adrian RJ, Westerweel J (2011) Particle image velocimetry, vol 30. Cambridge University Press, CambridgeGoogle Scholar
  42. 42.
    Adrian RJ, Christensen KT, Liu ZC (2000) Analysis and interpretation of instantaneous turbulent velocity fields. Exp Fluids 29(3):275–290CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and MechanicsLehigh UniversityBethlehemUSA

Personalised recommendations