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Global and local aspects of entrainment in temporal plumes

  • Dominik Krug (a1), Daniel Chung (a1), Jimmy Philip (a1) and Ivan Marusic (a1)

Abstract

To date, the understanding of the role buoyancy plays in the entrainment process in unstable configurations such as turbulent plumes remains incomplete. Towards addressing this question, we set up a flow in which a plume evolves in time instead of space. We demonstrate that the temporal problem is equivalent to a spatial plume in a strong coflow and address in detail how the temporal plume can be realized via direct numerical simulation. Using numerical data of plume simulations up to $Re_{\unicode[STIX]{x1D706}}\approx 100$ , we show that the entrainment coefficient can be determined consistently using a global entrainment analysis in an integral framework as well as via a local approach. The latter is based on a study of the local propagation of the turbulent/non-turbulent interface relative to the fluid. Locally, this process is dominated by small-scale diffusion which is amplified by interface convolutions such that the total entrained flux is independent of viscosity. Further, we identify a direct buoyancy contribution to entrainment by baroclinic torque, which accounts for 8 %–12 % of the entrained flux locally, comparable to the 15 % buoyancy contribution at the integral level. It appears that the baroclinic torque is a mechanism that might explain higher values of the entrainment coefficient in spatial plumes compared with jets.

Copyright

Corresponding author

Email address for correspondence: dominik.krug@unimelb.edu.au

References

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Bisset, D. K., Hunt, J. C. R. & Rogers, M. M. 2002 The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech. 451, 383410.
van den Bremer, T. S. & Hunt, G. R. 2014 Two-dimensional planar plumes and fountains. J. Fluid Mech. 750, 210244.
Carazzo, G., Kaminski, E. & Tait, S. 2006 The route to self-similarity in turbulent jets and plumes. J. Fluid Mech. 547, 137148.
Chung, D. & Matheou, G. 2012 Direct numerical simulation of stationary homogeneous stratified sheared turbulence. J. Fluid Mech. 696, 434467.
Chung, D. & Pullin, D. I. 2009 Large-eddy simulation and wall modelling of turbulent channel flow. J. Fluid Mech. 631, 281309.
Corrsin, S. & Kistler, A.1954 The free-stream boundaries of turbulent flows. NACA TN-3133, TR-1244, 1033–1064.
Craske, J. & van Reeuwijk, M. 2015 Energy dispersion in turbulent jets. Part 1. Direct simulation of steady and unsteady jets. J. Fluid Mech. 763, 500537.
Craske, J. & van Reeuwijk, M. 2016 Generalised unsteady plume theory. J. Fluid Mech. 792, 10131052.
Fox, D. G. 1970 Forced plume in a stratified fluid. J. Geophys. Res. 75 (33), 68186835.
Holzner, M., Liberzon, A., Nikitin, N., Lüthi, B., Kinzelbach, W. & Tsinober, A. 2008 A Lagrangian investigation of the small-scale features of turbulent entrainment through particle tracking and direct numerical simulation. J. Fluid Mech. 598, 465475.
Holzner, M. & Lüthi, B. 2011 Laminar superlayer at the turbulence boundary. Phys. Rev. Lett. 106 (13), 134503.
Holzner, M., Song, B., Avila, M. & Hof, B. 2013 Lagrangian approach to laminar–turbulent interfaces in transitional pipe flow. J. Fluid Mech. 723, 140162.
Hou, T. Y. & Li, R. 2007 Computing nearly singular solutions using pseudo-spectral methods. J. Comput. Phys. 226 (1), 379397.
Hunt, G. R. & Van den Bremer, T. S. 2011 Classical plume theory: 1937–2010 and beyond. IMA J. Appl. Maths 76 (3), 424448.
Kaminski, E., Tait, S. & Carazzo, G. 2005 Turbulent entrainment in jets with arbitrary buoyancy. J. Fluid Mech. 526, 361376.
Krug, D., Holzner, M., Lüthi, B., Wolf, M., Kinzelbach, W. & Tsinober, A. 2015 The turbulent/non-turbulent interface in an inclined dense gravity current. J. Fluid Mech. 765, 303324.
List, E. J. 1982 Turbulent jets and plumes. Annu. Rev. Fluid Mech. 14 (1), 189212.
Mater, P. D. & Venayagamoorthy, S. K. 2014 A unifying framework for parameterizing stably stratified shear-flow turbulence. Phys. Fluids 26 (3), 036601.
Mathew, J. & Basu, A. J. 2002 Some characteristics of entrainment at a cylindrical turbulence boundary. Phys. Fluids 14 (7), 20652072.
Morton, B. R. 1959 Forced plumes. J. Fluid Mech. 5 (01), 151163.
Morton, B. R., Taylor, G. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234, 123.
Paillat, S. & Kaminski, E. 2014 Entrainment in plane turbulent pure plumes. J. Fluid Mech. 755, R2.
Philip, J., Bermejo-Moreno, I., Chung, D. & Marusic, I.2015 Characteristics of the entrainment velocity in a developing wake. In International Symposium on Turbulence and Shear Flow Phenomena, TSFP-9, Melbourne, Australia. Available at: http://www.tsfp-conference.org/proceedings/proceedings-of-tsfp-9-2015-melbourne.html.
Philip, J., Meneveau, C., de Silva, C. M. & Marusic, I. 2014 Multiscale analysis of fluxes at the turbulent/non-turbulent interface in high Reynolds number boundary layers. Phys. Fluids 26 (1), 015105.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Priestley, C. H. B. & Ball, F. K. 1955 Continuous convection from an isolated source of heat. Q. J. R. Meteorol. Soc. 81 (348), 144157.
Ramaprian, B. R. & Chandrasekhara, M. S. 1989 Measurements in vertical plane turbulent plumes. Trans. ASME J. Fluids Engng 111 (1), 6977.
Redford, J. A., Castro, I. P. & Coleman, G. N. 2012 On the universality of turbulent axisymmetric wakes. J. Fluid Mech. 710, 419452.
van Reeuwijk, M. & Craske, J. 2015 Energy-consistent entrainment relations for jets and plumes. J. Fluid Mech. 782, 333355.
van Reeuwijk, M. & Holzner, M. 2014 The turbulence boundary of a temporal jet. J. Fluid Mech. 739, 254275.
van Reeuwijk, M., Salizzoni, P., Hunt, G. R & Craske, J. 2016 Turbulent transport and entrainment in jets and plumes: a DNS study. Phys. Rev. Fluids 1, 074301.
de Rooy, W. C., Bechtold, P., Fröhlich, K., Hohenegger, C., Jonker, H., Mironov, D., Siebesma, P., Teixeira, J. & Yano, J.-I. 2013 Entrainment and detrainment in cumulus convection: an overview. Q. J. R. Meteorol. Soc. 139 (670), 119.
da Silva, C. B., Hunt, J. C. R., Eames, I. & Westerweel, J. 2014 Interfacial layers between regions of different turbulence intensity. Annu. Rev. Fluid Mech. 46, 567590.
da Silva, C. B. & Pereira, J. C. F. 2008 Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets. Phys. Fluids 20 (5), 55101.
Sreenivasan, K. R., Ramshankar, R. & Meneveau, C. 1989 Mixing, entrainment and fractal dimensions of surfaces in turbulent flows. Proc. R. Soc. Lond. A 421 (1860), 79108.
Taveira, R. R. & da Silva, C. B. 2013 Kinetic energy budgets near the turbulent/nonturbulent interface in jets. Phys. Fluids 25 (1), 015114.
Tennekes, H. & Lumley, J. L. 1994 A First Course in Turbulence. MIT.
Townsend, A. A. R. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Tsinober, A. 2009 An Informal Conceptual Introduction to Turbulence: Second Edition of An Informal Introduction to Turbulence. Springer.
Turner, J. S. 1986 Turbulent entrainment – the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech. 173, 431471.
Watanabe, T., Sakai, Y., Nagata, K., Ito, Y. & Hayase, T. 2014 Enstrophy and passive scalar transport near the turbulent/non-turbulent interface in a turbulent planar jet flow. Phys. Fluids 26 (10), 105103.
Westerweel, J., Fukushima, C., Pedersen, J. M. & Hunt, J. C. R. 2009 Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech. 631, 199230.
Wolf, M., Holzner, M., Lüthi, B., Krug, D., Kinzelbach, W. & Tsinober, A. 2013 Effects of mean shear on the local turbulent entrainment process. J. Fluid Mech. 731, 95116.
Wolf, M., Lüthi, B., Holzner, M., Krug, D., Kinzelbach, W. & Tsinober, A. 2012 Investigations on the local entrainment velocity in a turbulent jet. Phys. Fluids 24 (10), 105110.
Woods, A. W. 2010 Turbulent plumes in nature. Annu. Rev. Fluid Mech. 42, 391412.
Zeldovich, Y. B. 1937 The asymptotic laws of freely-ascending convective flows. Zh. Eksp. Teor. Fiz. 7, 14631465.
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Global and local aspects of entrainment in temporal plumes

  • Dominik Krug (a1), Daniel Chung (a1), Jimmy Philip (a1) and Ivan Marusic (a1)

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