Abstract
Turbulent mixing in a meandering non-buoyant chemical plume is far less understood than in a straight plume—partially due to difficulty separating the plume meander from the turbulent fluctuations. This study presents high-resolution measurements of the covariance of the turbulent fluctuations of velocity and concentration, i.e., the turbulent flux, in a phase-locked meandering plume, acquired by simultaneous particle tracking velocimetry and laser-induced fluorescence measurements. Analysis of the data reveals that the spatial distribution of the turbulent quantities is governed by the large-scale alternating-sign vortices that induce the plume meander. Further, the spatial variation of turbulent flux agrees well with the spatial variation of the phase-averaged concentration gradient. As a result, the eddy diffusivity framework effectively models the turbulent flux. As expected from turbulent mixing theory, the eddy diffusivity coefficient plateaus at a constant value once the plume width reaches the size of the largest eddies. However, when the plume width is less than the size of the largest eddies, the eddy diffusivity coefficient scales with the plume width to the \(n\) = 1 power. Analysis based on the measurements of the growth rate of the plume width yields a consistent prediction for the variation of the eddy diffusivity coefficient in the near field.
Graphical abstract
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arcoumanis C, McGuirk JJ, Palma JMLM (1990) On the use of fluorescent dyes for concentration measurements in water flows. Exp Fluids 10:177–180. https://doi.org/10.1007/BF00215028
Batchelor GK (1952) Diffusion in a field of homogeneous turbulence. II. The relative motion of particles. Proc Camb Philos Soc 48:345–362. https://doi.org/10.1017/S0305004100027687
Brooks NH (1960) Diffusion of sewage effluent in an ocean-current. In: Proceedings of 1st International conference on waste disposal in the marine environment, University of California, pp. 246–267.
Cowen EA, Chang K-A, Liao Q (2001) A single-camera coupled PTV-LIF technique. Exp Fluids 31:63–73. https://doi.org/10.1007/s003480000259
Cowen EA, Monismith SG (1997) A hybrid digital particle tracking velocimetry technique. Exp Fluids 22:199–211. https://doi.org/10.1007/s003480050038
Csanady GT (1973) Turbulent diffusion in the environment. D. Reidel Publishing Co., Boston
Fischer HB, List EJ, Koh RCY, Imberger J, Brooks NH (1979) Mixing in inland and coastal waters. Academic Press, New York
Fong DA, Stacey MT (2003) Horizontal dispersion of a near-bed coastal plume. J Fluid Mech 489:239–267. https://doi.org/10.1017/S002211200300510X
Foxworthy JE, Tibby RB, Barsom GM (1966) Dispersion of a surface waste field in the sea. J Water Pollut Control Feder 38:1170–1193
Gifford F (1959) Statistical properties of a fluctuating plume dispersion model. Adv Geophys 6:117–136. https://doi.org/10.1016/S0065-2687(08)60099-0
Hanna SR (1986) Spectra of concentration fluctuations: the two time scales of a meandering plume. Atmos Environ 20:1131–1137. https://doi.org/10.1016/0004-6981(86)90145-9
Huang Z, Kawall JG, Keffer JF, Ferre JA (1995) On the entrainment process in plane turbulent wakes. Phys Fluids 7:1130–1141. https://doi.org/10.1063/1.868554
Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 285:69–94. https://doi.org/10.1017/S0022112095000462
Jones NL, Lowe RJ, Pawlak G, Fong DA, Monismith SG (2008) Plume dispersion on a fringing coral reef system. Limnol Oceanogr 53:2273–2286. https://doi.org/10.4319/lo.2008.53.5_part_2.2273
Kim W, Yoo JY, Sung J (2006) Dynamics of vortex lock-on in a perturbed cylinder wake. Phys Fluids 18:074103. https://doi.org/10.1063/1.2221350
Kolmogorov AN (1941) The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Doklady Akademiia Nauk SSSR 30:301–305
Kundu PK, Cohen IM, Dowling DR (2015) Fluid mechanics, 6th edn. Elsevier Academic Press, Cambridge MA
Liao Q, Cowen EA (2010) Relative dispersion of a scalar plume in a turbulent boundary layer. J Fluid Mech 661:412–445. https://doi.org/10.1017/S0022112010003058
Lyn DA, Einav S, Rodi W, Park JH (1995) A laser-Doppler velocimetry study of the ensemble-averaged characteristics of the turbulent near wake of a square cylinder. J Fluid Mech 304:285–319. https://doi.org/10.1017/S0022112095004435
Maas HG, Gruen A, Papantoniou D (1993) Particle tracking velocimetry in three-dimensional flows. Part 1. Photogrammetric determination of particle coordinates. Exp Fluids 15:133–146. https://doi.org/10.1007/BF00190953
Malik NA, Dracos T, Papantoniou DA (1993) Particle tracking velocimetry in three-dimensional flows. Part 2. Particle tracking. Exp Fluids 15:279–294. https://doi.org/10.1007/BF00223406
Nakagawa S, Nitta K, Senda M (1999) An experimental study on unsteady turbulent near wake of a rectangular cylinder in channel flow. Exp Fluids 27:284–294. https://doi.org/10.1007/s003480050353
Okubo A (1968) Some remarks on the importance of the “shear effect” on horizontal diffusion. J Oceanogr Soc Jpn 24:60–69
Okubo A (1971) Oceanic diffusion diagrams. Deep-Sea Res 18:789–802. https://doi.org/10.1016/0011-7471(71)90046-5
Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge
Rahman S, Webster DR (2005) The effect of bed roughness on scalar fluctuations in turbulent boundary layers. Exp Fluids 38:372–384. https://doi.org/10.1007/s00348-004-0919-7
Richardson LF (1926) Atmospheric diffusion shown on a distance-neighbour graph. Proc Royal Soc London A 110:709–737. https://doi.org/10.1098/rspa.1926.0043
Roberts PJ, Webster DR (2002) Turbulent diffusion. In Shen HH, Cheng AHD, Wang K, Teng MH, Liu CCK (eds) Environmental fluid mechanics: theories and applications. American Society of Civil Engineers, Reston, VA, pp 7–47 DOI:https://doi.org/10.1002/9780470057339.vat029
Saha AK, Muralidhar K, Biswas G (2000) Vortex structures and kinetic energy budget in two-dimensional flow past a square cylinder. Comput Fluids 29:669–694. https://doi.org/10.1016/S0045-7930(99)00021-3
Sawford BL, Stapountzis H (1986) Concentration fluctuations according to fluctuating plume models in one and two dimensions. Bound-Layer Meteorol 37:89–105. https://doi.org/10.1007/BF00122758
Stacey MT, Cowen EA, Powell TM, Dobbins E, Monismith SG, Koseff JR (2000) Plume dispersion in a stratified near-coastal flow: measurements and modeling. Cont Shelf Res 20:637–663. https://doi.org/10.1016/S0278-4343(99)00061-8
Stommel H (1949) Horizontal diffusion due to oceanic turbulence. J Mar Res 8:199–225
Talluru KM, Philip J, Chauhan KA (2018) Local transport of passive scalar released from a point source in a turbulent boundary layer. J Fluid Mech 846:292–317. https://doi.org/10.1017/jfm.2018.280
Tracy HJ, Lester CM (1961) Resistance coefficients and velocity distribution smooth rectangular channel. US Geological Survey Water Supply Paper 1592-A DOI: https://doi.org/10.3133/wsp1592A
Vanderwel C, Tavoularis S (2014) Measurements of turbulent diffusion in uniformly sheared flow. J Fluid Mech 754:488–514. https://doi.org/10.1017/jfm.2014.406
Webel G, Schatzmann M (1984) Transverse mixing in open channel flow. J Hydraul Eng 110:423–435. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:4(423)
Webster DR, Rahman S, Dasi LP (2003) Laser-induced fluorescence measurements of a turbulent plume. J Eng Mech 129:1130–1137. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:10(1130)
Webster DR, Roberts PJW, Ra’ad L (2001) Simultaneous DPTV/PLIF measurements of a turbulent jet. Exp Fluids 30:65–72. https://doi.org/10.1007/s003480000137
Young DL, Larsson AI, Webster DR (2021) Structure and mixing of a meandering turbulent chemical plume: concentration and velocity fields. Exp Fluids 62:240. https://doi.org/10.1007/s00348-021-03337-x
Acknowledgments
The authors thank Dr. Phil Roberts (Georgia Institute of Technology) for helpful discussions.
Funding
The authors gratefully acknowledge financial support provided by the University of Gothenburg, the Swedish Research Council FORMAS (Dnr: 2012–1134), and the US National Science Foundation via grant OCE-1234449.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Young, D.L., Webster, D.R. & Larsson, A.I. Structure and mixing of a meandering turbulent chemical plume: turbulent mixing and eddy diffusivity. Exp Fluids 63, 3 (2022). https://doi.org/10.1007/s00348-021-03354-w
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00348-021-03354-w