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Effect of instantaneous stirring process on mixing between initially distant scalars in turbulent obstacle wakes

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Abstract

A two-channel planar laser-induced fluorescence technique is used to study mixing and reactions between two initially distant scalars in the turbulent wake of a cylindrical obstacle. The scalars are released continuously and isokinetically upstream of the cylinder, with a lateral separation that initially impedes mixing between them. The effect of the turbulent wake on mixing and reaction enhancement is determined by measuring the segregation parameter for cases with and without the cylinder obstruction. Results indicate that scalar mixing and reaction rates (in the low-Damkohler limit) increase significantly in the presence of the cylinder wake. The study also shows that the dominant contribution of total reaction derives from the scalar covariance associated with instantaneous flow processes, and depends strongly on streamwise location within the wake. The results have broad implications for mixing processes in engineering and ecology.

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References

  • Adrian R, Christensen K, Liu ZC (2000) Analysis and interpretation of instantaneous turbulent velocity fields. Exp Fluids 29(3):275–290

    Article  Google Scholar 

  • Adrian RJ (2007) Hairpin vortex organization in wall turbulence a. Phys Fluids (1994-present) 19(4):041301

    Article  MATH  Google Scholar 

  • Batchelor G (1959) Small-scale variation of convected quantities like temperature in turbulent fluid part 1. General discussion and the case of small conductivity. J Fluid Mech 5(01):113–133

    Article  MathSciNet  MATH  Google Scholar 

  • Breidenthal R (1981) Structure in turbulent mixing layers and wakes using a chemical reaction. J Fluid Mech 109:1–24

    Article  Google Scholar 

  • Cantwell BJ (1981) Organized motion in turbulent flow. Annu Rev Fluid Mech 13(1):457–515

    Article  Google Scholar 

  • Celik B, Beskok A (2009) Mixing induced by a transversely oscillating circular cylinder in a straight channel. Phys Fluids (1994-present) 21(7):073601

    Article  MATH  Google Scholar 

  • Crimaldi JP (2008) Planar laser induced fluorescence in aqueous flows. Exp Fluids 44(6):851–863. doi:10.1007/s00348-008-0496-2

    Article  Google Scholar 

  • Crimaldi JP, Browning HS (2004) A proposed mechanism for turbulent enhancement of broadcast spawning efficiency. J Mar Syst 49(1–4):3–18. doi:10.1016/j.jmarsys.2003.06.005

    Article  Google Scholar 

  • Crimaldi JP, Kawakami TR (2013) Reaction of initially distant scalars in a cylinder wake. Phys Fluids (1994-present) 25(5):053604

    Article  Google Scholar 

  • Crimaldi JP, Zimmer RK (2014) The physics of broadcast spawning in benthic invertebrates. Ann Rev Mar Sci 6:141–165

    Article  Google Scholar 

  • Crimaldi JP, Hartford JR, Weiss JB (2006) Reaction enhancement of point sources due to vortex stirring. Phys Rev E 74(1):016307

    Article  Google Scholar 

  • Crimaldi JP, Cadwell JR, Weiss JB (2008) Reaction enhancement of isolated scalars by vortex stirring. Phys Fluids 20(073):605

    MATH  Google Scholar 

  • Deshmukh SR, Vlachos DG (2005) Novel micromixers driven by flow instabilities: application to post-reactors. AIChE J 51(12):3193–3204

    Article  Google Scholar 

  • Dong C, McWilliams JC (2007) A numerical study of island wakes in the Southern California Bight. Cont Shelf Res 27(9):1233–1248

    Article  Google Scholar 

  • Dong C, McWilliams JC, Shchepetkin AF (2007) Island wakes in deep water. J Phys Oceanogr 37(4):962–981

    Article  Google Scholar 

  • Ferrier G, Davies P, Anderson J (1996) Cover remote sensing observations of a vortex street downstream of an obstacle in an estuarine flow. Int J Remote Sens 17(1):1–8

    Article  Google Scholar 

  • Froncioni AM, Muzzio FJ, Peskin RL, Swanson PD (1997) Chaotic motion of fluid and solid particles in plane wakes. Chaos Solitons Fractals 8(1):109–130

    Article  MATH  Google Scholar 

  • Garrett C (1983) On the initial streakness of a dispersing tracer in two-and three-dimensional turbulence. Dyn Atmos Oceans 7(4):265–277

    Article  Google Scholar 

  • Guichard F, Bourget E (1998) Topographic heterogeneity, hydrodynamics, and benthic community structure: a scale-dependent cascade. Mar Ecol Prog Ser 171:59–70

    Article  Google Scholar 

  • Hasegawa D, Yamazaki H, Lueck RG, Seuront L (2004) How islands stir and fertilize the upper ocean. Geophys Res Lett 31(16). doi:10.1029/2004GL020143

  • Heywood KJ, Barton ED, Simpson JH (1990) The effects of flow disturbance by an oceanic island. J Mar Res 48(1):55–73

    Article  Google Scholar 

  • Hinch E (1999) Mixing: turbulence and chaos—an introduction. In: Mixing, Springer, pp 37–56

  • Jackson J (1986) Modes of dispersal of clonal benthic invertebrates: consequences for species’ distributions and genetic structure of local populations. Bull Mar Sci 39(2):588–606

    Google Scholar 

  • Jung C, Tél T, Ziemniak E (1993) Application of scattering chaos to particle transport in a hydrodynamical flow. Chaos Interdiscip J Nonlinear Sci 3(4):555–568

    Article  Google Scholar 

  • Károlyi G, Péntek Á, Toroczkai Z, Tél T, Grebogi C (1999) Chemical or biological activity in open chaotic flows. Phys Rev E 59(5):5468

    Article  Google Scholar 

  • Károlyi G, Péntek A, Scheuring I, Tél T, Toroczkai Z (2000) Chaotic flow: the physics of species coexistence. Proceedings of the National Academy of Sciences, vol 97, No. 25, pp 13661–13665

  • Kastrinakis E, Nychas S (1998) Mixing at high Schmidt numbers in the near wake of a circular cylinder. Chem Eng Sci 53(23):3977–3989

    Article  Google Scholar 

  • Mao KW, Toor HL (1971) Second-order chemical reactions with turbulent mixing. Ind Eng Chem Fundam 10(2):192–197. doi:10.1021/i160038a002

    Article  Google Scholar 

  • Mi J, Zhou Y, Nathan GJ (2004) The effect of reynolds number on the passive scalar field in the turbulent wake of a circular cylinder. Flow Turbul Combust 72(2–4):311–331

    Article  Google Scholar 

  • Miller K, Mundy C (2003) Rapid settlement in broadcast spawning corals: implications for larval dispersal. Coral Reefs 22(2):99–106

    Article  Google Scholar 

  • Pratt KR, Meiss JD, Crimaldi JP (2015) Reaction enhancement of initially distant scalars by Lagrangian coherent structures. Phys Fluids (1994-present) 27(3):035106

    Article  Google Scholar 

  • Richards K (1990) Physical processes in the benthic boundary layer. Philos Trans R Soc Lond Ser A Math Phys Sci 331(1616):3–13

    Article  Google Scholar 

  • Richards KJ, Brentnall SJ (2006) The impact of diffusion and stirring on the dynamics of interacting populations. J Theor Biol 238(2):340–347

    Article  MathSciNet  Google Scholar 

  • Sandulescu M, López C, Hernández-García E, Feudel U (2008) Plankton blooms in vortices: the role of biological and hydrodynamic time scales. arXiv:08023973 (preprint)

  • Scheuring I, KÁrolyi G, PÉntek A, TÉl T, Toroczkai Z (2000) A model for resolving the plankton paradox: coexistence in open flows. Freshw Biol 45(2):123–132

  • Scheuring I, Károlyi G, Toroczkai Z, Tél T, Péntek A (2003) Competing populations in flows with chaotic mixing. Theor Popul Biol 63(2):77–90

    Article  MATH  Google Scholar 

  • Soltys MA, Crimaldi JP (2015) Joint probabilities and mixing of isolated scalars emitted from parallel jets. J Fluid Mech 769:130–153

    Article  Google Scholar 

  • Soltys MA, Crimaldi JP (2011) Scalar interactions between parallel jets measured using a two-channel PLIF technique. Exp Fluids. doi:10.1007/s00348-010-1019-5

    Google Scholar 

  • Tel T, Károlyi G, Péntek A, Scheuring I, Toroczkai Z, Grebogi C, Kadtke J (2000) Chaotic advection, diffusion, and reactions in open flows. Chaos Interdiscip J Nonlinear Sci 10(1):89–98

    Article  MathSciNet  MATH  Google Scholar 

  • Toroczkai Z, Károlyi G, Péntek Á, Tél T, Grebogi C (1998) Advection of active particles in open chaotic flows. Phys Rev Lett 80(3):500

    Article  Google Scholar 

  • Wang CT, Hu YC (2010) Mixing of liquids using obstacles in y-type microchannels. Tamkang J Sci Eng 13:385–394

    Google Scholar 

  • Ziemniak EM, Jung C, Tél T (1994) Tracer dynamics in open hydrodynamical flows as chaotic scattering. Phys D Nonlinear Phenom 76(1):123–146

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Science Foundation under Grants No. 0849695 and 1205816.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Colorado, Boulder, CO, 80309-0428, USA

    F. Shoaei & J. P. Crimaldi

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  1. F. Shoaei
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  2. J. P. Crimaldi
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Correspondence to J. P. Crimaldi.

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Shoaei, F., Crimaldi, J.P. Effect of instantaneous stirring process on mixing between initially distant scalars in turbulent obstacle wakes. Exp Fluids 58, 26 (2017). https://doi.org/10.1007/s00348-017-2303-4

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