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Entrainment dynamics of buoyant jets in a stably stratified environment

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Abstract

Entrainment characteristics of a pure jet and buoyant jets in a stably-stratified ambient are compared with the help of laboratory experiments employing simultaneous particle image velocimetry and planar laser induced fluorescence techniques. For the buoyant jet, two cases of background stratification are considered, N = 0.4 s\(^{-1}\) and 0.6 s\(^{-1}\), where N is the buoyancy frequency. Evolution of volume flux, Q, momentum flux, M, buoyancy flux, F, characteristic velocity, \(w_m\), width, \(d_m\), and buoyancy, \(b_m\) with axial distance is quantified that helps in understanding the mean flow characteristics. Subsequently, two different methods are used for computing the entrainment coefficient, \(\alpha\); namely the standard entrainment hypothesis based on the mass conservation equation and energy-consistent entrainment relation proposed by van Reeuwijk and Craske (J Fluid Mech 782:333–355, 2015). It is observed that entrainment coefficient is constant for the pure jet (\(\alpha _{pj}\approx\) 0.1) up until the point where the upper horizontal boundary starts to influence the flow. The entrainment coefficient for buoyant jets, \(\alpha _{bj}\), is not constant and varies with axial location before starting to detrain near the neutral layer. Near the source, \(\alpha _{bj}\approx\) 0.12 for both the values of N, while away from the source, N = 0.6 s\(^{-1}\) exhibits a higher value of \(\alpha _{bj}\approx\) 0.15 in comparison to \(\alpha _{bj}\approx\) 0.13 for N = 0.4 s\(^{-1}\). During detrainment near the neutral layer, \(\alpha _{bj}\approx\) – 0.2 for N = 0.4 \({\mathrm{s}}^{-1}\) and \(\alpha _{bj}\approx\) – 0.3 for N = 0.6 \({\mathrm{s}}^{-1}\). Importantly, close to the source, \(\alpha\) from standard entrainment hypothesis and energy-consistent relation are in reasonable match for pure jet and buoyant jets. However, far away from the source, the energy-consistent relation is ineffective in quantifying the entrainment coefficient in the pure jet and detrainment in buoyant jets. We propose ways in which the energy-consistent relation could be reconciled with standard entrainment hypothesis in the far-field region.

Article Highlights

  • Entrainment coefficient stays invariant for jets till the finite size of the domain in the axial direction disrupts this feature.

  • Entrainment coefficient for buoyant jets evolving in a stratified ambient varies with axial distance followed by detrainment beyond the neutral layer.

  • The existing entrainment relation performs reasonably well in the momentum dominated region but performs poorly when the finite size of the domain affects the flow for pure jet and when the flow is buoyancy dominated for the case of buoyant jets.

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References

  1. van Reeuwijk M, Craske J (2015) Energy-consistent entrainment relations for jets and plumes. J Fluid Mech 782:333–355

    Article  Google Scholar 

  2. Corrsin S (1943) Investigation of flow in an axially symmetrical heated jet of air. Wash, Wartime report

  3. Davies POAL, Fisher MJ, Barratt MJ (1963) The characteristics of the turbulence in the mixing region of a round jet. J Fluid Mech 15(3):337–367

    Article  Google Scholar 

  4. Crow SC, Champagne FH (1971) Orderly structure in jet turbulence. J Fluid Mech 48(3):547–591

    Article  Google Scholar 

  5. Priestley CHB, Ball FK (1955) Continuous convection from an isolated source of heat. Q J R Meteorol Soc 81(348):144–157

    Article  Google Scholar 

  6. Morton BR, Taylor GI, Turner JS (1956) Turbulent gravitational convection from maintained and instantaneous sources. Proc R Soc Lond Ser A Math Phys Sci 234(1196):1–23. https://doi.org/10.1098/rspa.1956.0011

    Google Scholar 

  7. Morton BR (1959) Forced plumes. J Fluid Mech 5(1):151–163

    Article  Google Scholar 

  8. Wong DR, Wright SJ (1988) Submerged turbulent jets in stagnant linearly stratified fluids. J Hydraul Res 26(2):199–223

    Article  Google Scholar 

  9. Turner JS (1986) Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J Fluid Mech 173:431–471

    Article  Google Scholar 

  10. Ellison TH, Turner JS (1959) Turbulent entrainment in stratified flows. J Fluid Mech 6(3):423–448

    Article  Google Scholar 

  11. Princevac M, Fernando HJS, Whiteman CD (2005) Turbulent entrainment into natural gravity-driven flows. J Fluid Mech 533:259–268

    Article  Google Scholar 

  12. Fischer HB, List EJ, Koh RCY, Imberger J, Brooks NH (1979) Chapter 9—turbulent jets and plumes. In: Mixing in inland and coastal waters. Academic Press, San Diego, pp 315–389. ISBN:978-0-08-051177-1

  13. Bloomfield LJ, Kerr RC (2000) A theoretical model of a turbulent fountain. J Fluid Mech 424:197–216

    Article  Google Scholar 

  14. Narasimha R, Diwan SS, Duvvuri S, Sreenivas KR, Bhat GS (2011) Laboratory simulations show diabatic heating drives cumulus-cloud evolution and entrainment. Proc Natl Acad Sci 108(39):16164–16169

    Article  Google Scholar 

  15. Telford JW (1966) The Convective Mechanism in Clear Air. J Atmosp Sci 23(6):652–666

    Article  Google Scholar 

  16. Papanicolaou PN, List EJ (1988) Investigations of round vertical turbulent buoyant jets. J Fluid Mech 195:341–391

    Article  Google Scholar 

  17. Panchapakesan NR, Lumley JL (1993) Turbulence measurements in axisymmetric jets of air and helium. Part 1. Air jet. J Fluid Mech 246:197–223

    Article  Google Scholar 

  18. Panchapakesan NR, Lumley JL (1993) Turbulence measurements in axisymmetric jets of air and helium. part 2. Helium jet. J Fluid Mech 246:225–247

    Article  Google Scholar 

  19. Shabbir A, George WK (1994) Experiments on a round turbulent buoyant plume. J Fluid Mech 275:1–32

    Article  Google Scholar 

  20. Duo X, Chen J (2012) Experimental study of stratified jet by simultaneous measurements of velocity and density fields. Exp Fluids 53(1):145–162

    Article  Google Scholar 

  21. Mirajkar HN, Mukherjee P, Balasubramanian S (2020) Piv study of the dynamics of a forced plume in a stratified ambient. J Flow Visualiz Image Process 27:1

    Article  Google Scholar 

  22. Talluru KM, Armfield S, Williamson N, Kirkpatrick MP, Milton-McGurk L (2021) Turbulence structure of neutral and negatively buoyant jets. J Fluid Mech 909:A14

    Article  Google Scholar 

  23. Breda M, Buxton ORH (2018) Influence of coherent structures on the evolution of an axisymmetric turbulent jet. Phys Fluids 30(3):035109

    Article  Google Scholar 

  24. Krug D, Chung D, Philip J, Marusic I (2017) Global and local aspects of entrainment in temporal plumes. J Fluid Mech 812:222–250

    Article  Google Scholar 

  25. Pant CS, Bhattacharya A (2018) Evaluation of an energy consistent entrainment model for volumetrically forced jets using large eddy simulations. Phy Fluids 30(10):105107

    Article  Google Scholar 

  26. Kaminski E, Tait S, Carazzo G (2005) Turbulent entrainment in jets with arbitrary buoyancy. J Fluid Mech 526:361–376

    Article  Google Scholar 

  27. Oster G, Yamamoto M (1963) Density gradient techniques. Chem Rev 63(3):257–268

    Article  Google Scholar 

  28. Mehta RD, Bradshaw P (1979) Design rules for small low speed wind tunnels. Aeronaut J (1968) 83(827):443–453

    Article  Google Scholar 

  29. Adrian RJ (1991) Particle-imaging techniques for experimental fluid mechanics. Annu Rev Fluid Mech 23(1):261–304

    Article  Google Scholar 

  30. Mirajkar HN, Balasubramanian S (2017) Effects of varying ambient stratification strengths on the dynamics of a turbulent buoyant plume. J Hydraul Eng 143(7):04017013

    Article  Google Scholar 

  31. Matulka A, López P, Redondo JM, Tarquis A (2014) On the entrainment coefficient in a forced plume: quantitative effects of source parameters. Nonlinear Process Geophys 21(1):269–278

    Article  Google Scholar 

  32. Peltier WR, Caulfield CP (2003) Mixing efficiency in stratified shear flows. Annu Rev Fluid Mech 35(1):135–167

    Article  Google Scholar 

  33. Morton BR (1971) The choice of conservation equations for plume models. J Geophys Res (1896–1977) 76(30):7409–7416

    Article  Google Scholar 

Download references

Acknowledgements

Sridhar Balasubramanian is grateful for the funding support from Ministry of Earth Sciences (MoES) and Department of Science and Technology (DST). Partho Mukherjee and Harish Mirajkar acknowledge research scholarship from Ministry of Education, India.

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Authors and Affiliations

  1. Geophysical and Multiphase Flows Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra, 400076, India

    Partho Mukherjee & Sridhar Balasubramanian

  2. Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bengaluru, Karnataka, 560064, India

    Harish N. Mirajkar

  3. Interdisciplinary Program in Climate Studies, Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra, 400076, India

    Sridhar Balasubramanian

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  1. Partho Mukherjee
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Correspondence to Sridhar Balasubramanian.

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Mukherjee, P., Mirajkar, H.N. & Balasubramanian, S. Entrainment dynamics of buoyant jets in a stably stratified environment. Environ Fluid Mech 23, 1051–1073 (2023). https://doi.org/10.1007/s10652-022-09893-y

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