Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-26T18:07:14.845Z Has data issue: false hasContentIssue false
  • English
  • Français

Meandering due to large eddies and the statistically self-similar dynamics of quasi-two-dimensional jets

Published online by Cambridge University Press:  06 January 2012

Julien R. Landel ,
C. P. Caulfield  and
Andrew W. Woods
Julien R. Landel*
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
C. P. Caulfield
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
Andrew W. Woods
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
*
†Email address for correspondence: jl501@cam.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate experimentally the structure of quasi-two-dimensional plane turbulent jets discharged vertically from a slot of width into a fluid confined between two relatively close rigid boundaries with gap . At large vertical distances the jet structure consists of a meandering core with large counter-rotating eddies, which develop on alternate sides of the core. Using particle image velocimetry, we observe an inverse cascade typical of quasi-two-dimensional turbulence where both the core and the eddies grow linearly with and travel at an average speed proportional to . However, although the present study concerns quasi-two-dimensional confined jets, the jets are self-similar and the mean properties are consistent with both experimental results and theoretical models of the time-averaged properties of fully unconfined planar two-dimensional jets. We believe that the dynamics of the interacting core and large eddies accounts for the Gaussian profile of the mean vertical velocity as shown by the spatial statistical distribution of the core and eddy structure. The lateral excursions (caused by the propagating eddies) of this high-speed central core produce a Gaussian distribution for the time-averaged vertical velocity. In addition, we find that approximately 75 % of the total momentum flux of the jet is contained within the core. The eddies travel substantially slower (at approximately 25 % of the maximum speed of the core) at each height and their growth is primarily attributed to entrainment of ambient fluid. The frequency of occurrence of the eddies decreases in a stepwise manner due to merging, with a well-defined minimum value of the corresponding Strouhal number .

JFM classification

Wakes/Jets: Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 692 , 10 February 2012 , pp. 347 - 368
Copyright
Copyright © Cambridge University Press 2012

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

1.Albertson, M. L., Dai, Y. B., Jensen, R. A. & Rouse, H. 1950 Diffusion of submerged jets. Trans. ASCE 115, 639–664.Google Scholar
2.Antonia, R. A., Satyaprakash, B. R. & Hussain, A. K. M. F. 1980 Measurements of dissipation rate and some other characteristics of turbulent plane and circular jets. Phys. Fluids 23, 695–700.CrossRefGoogle Scholar
3.Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 2007 Transport Phenomena, 2nd edn. John Wiley & Sons.Google Scholar
4.Cervantes de Gortari, J. & Goldschmidt, V. W. 1981 The apparent flapping motion of a turbulent plane jet – further experimental results. Trans. ASME: J. Fluids Engng 103, 119–126.Google Scholar
5.Chen, D. & Jirka, G. H. 1998 Linear stability analysis of turbulent mixing layers and jets in shallow water layers. J. Hydraul. Res. 36, 815–830.Google Scholar
6.De Young, D. S. 1997 Growth of large scale structures in two-dimensional mixing layers. Phys. Fluids 9, 2168–2170.CrossRefGoogle Scholar
7.Dimotakis, P. E., Miake-Lye, R. C. & Papantoniou, D. A. 1983 Structure and dynamics of round turbulent jets. Phys. Fluids 26, 3185–3192.CrossRefGoogle Scholar
8.Dracos, T., Giger, M. & Jirka, G. H. 1992 Plane turbulent jets in a bounded fluid layer. J. Fluid Mech. 241, 587–614.CrossRefGoogle Scholar
9.Drayton, M. J. 1993 Eulerian and Lagrangian studies of inhomogeneous turbulence generated by an oscillating grid. PhD thesis, University of Cambridge, Cambridge, UK.Google Scholar
10.Foss, J. F. & Jones, J. B. 1968 Secondary flow effects in a bounded rectangular jet. Trans. ASME: J. Basic Engng 90, 241–248.CrossRefGoogle Scholar
11.Fung, J. C. H. 1990 Kinematic simulation of turbulent flow and particle motion. PhD thesis, University of Cambridge, Cambridge, UK.Google Scholar
12.Giger, M., Dracos, T. & Jirka, G. H. 1991 Entrainment and mixing in plane turbulent jets in shallow water. J. Hydraul. Res. 29, 615–642.CrossRefGoogle Scholar
13.Holdeman, J. D. & Foss, J. F. 1975 Initiation, development, and decay of secondary flow in a bounded jet. Trans. ASME: J. Fluids Engng 97, 342–352.Google Scholar
14.Hussein, H. J., Capp, S. P. & George, W. K. 1994 Velocity measurements in a high-Reynolds number, momentum-conserving, axisymmetric, turbulent jet. J. Fluid Mech. 258, 31–75.CrossRefGoogle Scholar
15.Jirka, G. H. 2001 Large scale flow structures and mixing processes in shallow flows. J. Hydraul. Res. 39, 567–573.CrossRefGoogle Scholar
16.Jirka, G. H. 2006 Integral model for turbulent buoyant jets in unbounded stratified flows. Part 2. Plane jet dynamics resulting from multiport diffuser jets. Environ. Fluid Mech. 6, 43–100.CrossRefGoogle Scholar
17.Jirka, G. H. & Harleman, D. R. F. 1979 Stability and mixing of a vertical plane buoyant jet in confined depth. J. Fluid Mech. 94, 275–304.CrossRefGoogle Scholar
18.Kotsovinos, N. E. 1975 A study of the entrainment and turbulence in a plane buoyant jet. PhD thesis, California Institute of Technology, Pasadena, USA.Google Scholar
19.Kotsovinos, N. E. 1976 A note on the spreading rate and virtual origin of a plane turbulent jet. J. Fluid Mech. 77, 305–311.CrossRefGoogle Scholar
20.Kotsovinos, N. E. & List, E. J. 1977 Plane turbulent buoyant jets. Part 1. Integral properties. J. Fluid Mech. 81, 25–44.CrossRefGoogle Scholar
21.Kuang, J., Hsu, C.-T. & Qiu, H. 2001 Experiments on vertical turbulent plane jets in water of finite depth. J. Engng Mech. ASCE 127, 18–26.CrossRefGoogle Scholar
22.List, E. J. 1982 Turbulent jets and plumes. Annu. Rev. Fluid Mech. 14, 189–212.CrossRefGoogle Scholar
23.Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234, 1–23.Google Scholar
24.Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
25.Ramaprian, B. R. & Chandrasekhara, M. S. 1985 LDA measurements in plane turbulent jets. Trans. ASME: J. Fluids Engng 107, 264–271.Google Scholar
26.Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.CrossRefGoogle Scholar
27.Rowland, J. C., Stacey, M. T. & Dietrich, W. E. 2009 Turbulent characteristics of a shallow wall-bounded plane jet: experimental implications for river mouth hydrodynamics. J. Fluid Mech. 627, 423–449.CrossRefGoogle Scholar
28.Shinneeb, A.-M., Bugg, J. D. & Balachandar, R. 2011 Coherent structures in shallow water jets. Trans. ASME: J. Fluids Engng 133, 011203.Google Scholar
29.Sveen, J. K. & Dalziel, S. B. 2005 A dynamic masking technique for combined measurements of PIV and synthetic schlieren applied to internal gravity waves. Meas. Sci. Technol. 16, 1954–1960.CrossRefGoogle Scholar
30.Thomas, F. O. & Brehob, E. G. 1986 An investigation of large-scale structure in the similarity region of a two-dimensional turbulent jet. Phys. Fluids 29, 1788–1795.CrossRefGoogle Scholar
31.Wang, H. W. & Law, A. W.-K. 2002 Second-order integral model for a round turbulent buoyant jet. J. Fluid Mech. 459, 397–428.CrossRefGoogle Scholar
32.Xu, H. & Bodenschatz, E. 2008 Motion of inertial particles with size larger than Kolmogorov scale in turbulent flows. Physica D 237, 2095–2100.CrossRefGoogle Scholar