Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T20:47:05.590Z Has data issue: false hasContentIssue false
  • English
  • Français

Self-sustained oscillations of shallow flow past sequential cavities

Published online by Cambridge University Press:  10 October 2014

B. A. Tuna  and
D. Rockwell
B. A. Tuna
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
D. Rockwell*
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
*
†Email address for correspondence: dor0@lehigh.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Shallow flow past successive cavities is characterized by means of high-image-density particle image velocimetry (PIV). Highly coherent, self-sustained oscillations arise due to coupling between the inherent instability of the separated shear layer along the opening of each sequential cavity; and a gravity standing wave mode within each cavity. The globally coupled nature of the flow structure is evident through dominance of the same spectral component in the undulating vorticity layers along each of the successive cavities and the wall pressure fluctuations within the cavities. Unlike coupled phenomena associated with flow past a single cavity, optimal coupling for successive cavities requires a defined phase shift between the gravity standing wave patterns in adjacent cavities and, furthermore, an overall phase shift of the undulating shear layer along the cavity openings. The magnitudes of these phase shifts depend on the mode of the gravity standing wave in each cavity, i.e. longitudinal or transverse mode, which is respectively aligned with or normal to the main stream. Such phase shifts result in corresponding displacements of patterns of phase-referenced vorticity concentrations along the cavity openings and changes in the timing of impingement of these concentrations upon the downstream corners of successive cavities. All of the foregoing aspects are related to the unsteady recirculation flow within the cavity, the time-dependent streamline topology, and concentrations of Reynolds stress along the cavity opening.

JFM classification

Geophysical and Geological Flows: Shallow water flows Waves/Free-surface Flows: Surface gravity waves Vortex Flows: Vortex interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 758 , 10 November 2014 , pp. 655 - 685
Copyright
© 2014 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.)

References

Adrian, R. J. & Westerweel, J. 2010 Particle Image Velocimetry. Cambridge University Press.Google Scholar
Alavian, V. & Chu, V. H.1985 Turbulent exchange flow in shallow compound channel. In Proceedings of the 21st International Congress of IAHR, pp. 446–451.Google Scholar
Babarutsi, S. & Chu, V. H. 1991 Dye-concentration distribution in shallow recirculating flows. J. Hydraul. Engng 117, 643–659.Google Scholar
Babarutsi, S. & Chu, V. H. 1993 Reynolds-stress model for quasi-two-dimensional turbulent shear flow, Engineering Turbulence Modelling and Experiments, vol. 2, pp. 93–102. Elsevier.Google Scholar
Babarutsi, S. & Chu, V. H. 1998 Modeling transverse mixing layer in shallow open-channel flows. J. Hydraul. Engng 124, 718–727.Google Scholar
Babarutsi, S., Ganoulis, J. & Chu, V. H. 1989 Experimental investigation of shallow recirculating flows. J. Hydraul. Engng 115, 906–924.CrossRefGoogle Scholar
Basley, J., Pastur, L. R., Lusseyran, F., Faure, T. M. & Delprat, N. 2011 Experimental investigation of global structures in an incompressible cavity flow using time-resolved PIV. Exp. Fluids 50 (4), 905–918.Google Scholar
Bian, S., Driscoll, J. F., Elbing, B. R. & Geccio, S. L. 2011 Time resolved flow-field measurements of a turbulent mixing layer over a rectangular cavity. Exp. Fluids 51, 51–63.Google Scholar
Biron, P. M., Ramamurthy, A. S. & Han, S. 2004 Three-dimensional numerical modeling of mixing at river confluences. J. Hydraul. Engng 130, 243–253.Google Scholar
Booij, R. & Tukker, J. 2001 Integral model of shallow mixing layers. J. Hydraul Res. 39, 169–179.Google Scholar
Chu, V. H. & Babarutsi, S. 1988 Confinement and bed-friction effects in shallow turbulent mixing layers. J. Hydraul. Engng 114, 1257–1274.Google Scholar
Chu, V. H., Wu, J. H. & Khayat, R. E. 1991 Stability of transverse shear flows in shallow open channels. J. Hydraul. Engng 117, 1370–1388.Google Scholar
Constantinescu, G., 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, 587–615.Google Scholar
Ekmekci, A. & Rockwell, D. 2007 Oscillation of shallow flow past a cavity: resonant coupling with a gravity wave. J. Fluids Struct. 23 (6), 809–838.Google Scholar
Ekmekci, A. & Rockwell, D. 2010 Effects of a geometrical surface disturbance on flow past a circular cylinder: a large-scale spanwise wire. J. Fluid Mech. 665, 120–157.Google Scholar
Engelhardt, C., Kruger, A., Sukhodolov, A. & Nicklisch, A. 2004 A study of phytoplankton spatial distributions, flow structure and characteristics of mixing in a river reach with groynes. J. Plankton Res. 26, 1351–1366.CrossRefGoogle Scholar
Ercan, A. & Younis, B. A. 2009 Prediction of bank erosion in a reach of the sacramento river and its mitigation with groynes. Water Resour. Manage. 23, 3121–3147.Google Scholar
Fiedler, H. E. & Mensing, P. 1985 The plane turbulent shear layer with periodic excitation. J. Fluid Mech. 150 (1), 281–309.Google Scholar
Fujihara, M., Sakurai, Y. & Okamoto, T. 2011 Hydraulic structure and material transport in an irrigation channel with a side-cavity for aquatic habitat. Trans. Japan. Soc. Irrig. Drain. Rural Engng 78, 17–22.Google Scholar
Ghidaoui, M. S. & Kolyshkin, A. A. 1999 Linear stability analysis of lateral motions in compound open channels. J. Hydraul. Engng 125, 871–880.Google Scholar
Ikeda, S., Yoshike, T. & Sugimoto, T. 1999 Experimental study on the structure of open channel flow with impermeable spur dikes. Annu. J. Hydraul. Engng-JSCE 43, 281–286.Google Scholar
Jirka, G. H. 2001 Large scale flow structures and mixing processes in shallow flows. J. Hydraul. Res. 39, 567–573.Google Scholar
Jirka, G. H. & Uijttewaal, W. S. J. 2004 Shallow Flows: a Definition. Taylor and Francis.Google Scholar
Kadotani, K., Fujita, I., Matsubara, T. & Tsubaki, R.2008 Analysis of water surface oscillation at open channel side cavity by image analysis and large eddy simulation. In ICHE Conference.Google Scholar
Kang, J., Yeo, H. & Kim, C. 2012 An experimental study on a characteristics of flow around groyne area by install conditions. Engineering 4, 636–645.Google Scholar
Kimura, I. & Hosoda, T. 1997 Fundamental properties of flows in open channels with dead zone. J. Hydraul. Engng 123, 98–107.CrossRefGoogle Scholar
Knisely, C. & Rockwell, D. 1982 Self-sustained low-frequency components in an impinging shear layer. J. Fluid Mech. 116, 157–186.Google Scholar
Kolyshkin, A. A. & Ghidaoui, M. S. 2002 Gravitational and shear instabilities in compound and composite channels. J. Hydraul. Engng 128, 1076–1086.Google Scholar
Kolyshkin, A. A. & Ghidaoui, M. S. 2003 Stability analysis of shallow wake flows. J. Fluid Mech. 494, 355–377.Google Scholar
Kurzke, M., Weitbrecht, V. & Jirka, G. H.2002 Laboratory concentration measurements for determination of mass exchange between groin fields and main stream. In Proceedings of the IAHR Congress.Google Scholar
Liu, X. & Katz, J.2011 Time resolved PIV measurements elucidate the feedback mechanism that causes low-frequency undulation in an open cavity shear layer. In 9th International Symposium on Particle Image Velocimetry-PIV11, pp. 21–23.Google Scholar
McCoy, A., Constantinescu, G. & Weber, L. 2007 A numerical investigation of coherent structures and mass exchange processes in channel flow with two lateral submerged groynes. Water Resour. Res. 43, W05445.CrossRefGoogle Scholar
McCoy, A., Constantinescu, G. & Weber, L. 2008 Numerical investigation of flow hydrodynamics in a channel with a series of groynes. J. Hydraul. Engng 134, 157–172.Google Scholar
Michalke, A. 1964 On the inviscid instability of the hyperbolictangent velocity profile. J. Fluid Mech. 19 (04), 543–556.Google Scholar
Michalke, A. 1965 On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23 (3), 521–544.Google Scholar
Mizumura, K. & Yamasaka, M. 2002 Flow in open-channel embayments. J. Hydraul. Engng 128, 1098–1101.Google Scholar
Muto, Y., Imamoto, H. & Ishigaki, T. 2000 Turbulence characteristics of a shear flow in an embayment attached to a straight open channel. In Proceedings of the 4th International Conference on HydroScience and Engineering, p. 232. IAHR.Google Scholar
Naudascher, E. & Rockwell, D. 1994 Flow-Induced Vibrations: an Engineering Guide. Dover Publications, Inc.Google Scholar
Nazarovs, S.2005 Stability analysis of shallow wake flows with free surface. In Proceedings of the International Conference on Theory and Application of Mathematics and Informatics, pp. 345–354.Google Scholar
Nezu, I. & Onitsuka, K. 2002 PIV measurements of side-cavity open-channel flows-wando model in rivers. J. Vis. 5, 77–84.Google Scholar
Ohmoto, T., Hirakawa, R. & Watanabe, K.2005 Flow patterns and exchange processes in dead zones of rivers. In 31st IAHR Congress, pp. 347–348.Google Scholar
Ohmoto, T., Hirakawa, R. & Watanabe, K. 2009 Effects of spur dike directions on river bed forms and flow structures. In Advances in Water Resources and Hydraulic Engineering, pp. 957–962. Springer.Google Scholar
Ribi, J. M., Boillat, J. L. & Schleiss, A. J. 2010 Flow exchange between a channel and a rectangular embayment equipped with a diverting structure. In Proceedings International Conference on Fluvial Hydraulics, pp. 665–671. IAHR.Google Scholar
Riviere, N., Garcia, M., Mignot, E. & Travin, G. 2010 Characteristics of the recirculation cell pattern in a lateral cavity. In Proceedings International Conference on Fluvial Hydraulics, pp. 673–679. IAHR.Google Scholar
Rockwell, D. 1983 Oscillations of impinging shear layers. AIAA J. 21, 645–664.Google Scholar
Rockwell, D. & Naudascher, E. 1978 Review: self-sustaining oscillations of flow past cavities. Trans. ASME J. Fluids Engng 100 (2), 152–165.Google Scholar
Rockwell, D. & Naudascher, E. 1979 Self-sustained oscillations of impinging free shear layers. Annu. Rev. Fluid Mech. 11, 67–94.Google Scholar
Sanjou, M. & Nezu, I. 2013 Hydrodynamic characteristics and related mass-transfer properties in open-channel flows with rectangular embayment zone. Environ. Fluid Mech. 13, 527–555.Google Scholar
Shankar, P. N. & Deshpande, M. D. 2000 Fluid mechanics in the driven cavity. Annu. Rev. Fluid Mech. 32 (1), 93–136.CrossRefGoogle Scholar
Socolofsky, S. A. & Jirka, G. H. 2004 Large-scale flow structures and stability in shallow flows. J. Environ. Engng Sci. 3, 451–462.CrossRefGoogle Scholar
Stansby, P. K. 2003 A mixing-length model for shallow turbulent wakes. J. Fluid Mech. 495, 369–384.CrossRefGoogle Scholar
Sukhodolov, A., Engelhardt, C., Kruger, A. & Bungartz, H. 2004 Case study: turbulent flow and sediment distributions in a groyne field. J. Hydraul. Engng 130, 1–9.Google Scholar
Sukhodolov, A., Uijttewaal, W. S. J. & Engelhardt, C. 2002 On the correspondence between morphological and hydrodynamical patterns of groyne fields. Earth Surf. Process. Landf. 27, 289–305.Google Scholar
Tang, Y. P. & Rockwell, D. 1983 Instantaneous pressure fields at a corner associated with vortex impingement. J. Fluid Mech. 126, 187–204.Google Scholar
Tukker, J. & Booij, R. 1996 The influence of shallowness on large-scale coherent structures. In Advances in Turbulence VI, pp. 141–144. Springer.Google Scholar
Tuna, B. A., Tinar, E. & Rockwell, D. 2013 Shallow flow past a cavity: globally coupled oscillations as a function of depth. Exp. Fluids 54, 1–20.CrossRefGoogle Scholar
Uijttewaal, W. S. J. 2005 Effects of groyne layout on the flow in groyne fields: laboratory experiments. J. Hydraul. Engng 131, 782–791.CrossRefGoogle Scholar
Uijttewaal, W. S. J.2011 Horizontal mixing in shallow flows. In 34th IAHR World Congress, pp. 3808–3814.Google Scholar
Uijttewaal, W. S. J. & Booij, R. 2000 Effects of shallowness on the development of free-surface mixing layers. Phys. Fluids 12, 392–402.Google Scholar
Uijttewaal, W. S. J., Lehmann, D. & Mazijk, A. V. 2001 Exchange processes between a river and its groyne fields: model experiments. J. Hydraul. Engng 127, 928–936.Google Scholar
Uijttewaal, W. S. J. & Tukker, J. 1998 Development of quasi two-dimensional structures in a shallow free-surface mixing layer. Exp. Fluids 24, 192–200.Google Scholar
van Prooijen, B. C. & Uijttewaal, W. S. J. 2002 A linear approach for the evolution of coherent structures in shallow mixing layers. Phys. Fluids 14, 4105–4114.Google Scholar
Wallast, I., Uijttewaal, W. S. J. & van Mazijk, A.1999 Exchange processes between groyne field and main stream. In Proceedings from the 28th IAHR Congress.Google Scholar
Weitbrecht, V. & Jirka, G. H.2001 Flow patterns and exchange processes in dead zones of rivers. In Proceedings of the IAHR Congress, pp. 439–445.Google Scholar
Wolfinger, M., Ozen, C. A. & Rockwell, D. 2012 Shallow flow past a cavity: coupling with a standing gravity wave. Phys. Fluids 24, 104103.Google Scholar
Yaeger, M. & Duan, J.2010 Mean flow and turbulence around two series of experimental dikes. In World Environmental and Water Resources Congress, pp. 1692–1701.Google Scholar
Yossef, M. F. & de Vriend, H. J. 2011 Flow details near river groynes: experimental investigation. J. Hydraul. Engng 137, 504–516.CrossRefGoogle Scholar