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Connecting the time evolution of the turbulence interface to coherent structures

  • Marius M. Neamtu-Halic (a1) (a2), Dominik Krug (a3), Jean-Paul Mollicone (a4), Maarten van Reeuwijk (a4), George Haller (a5) and Markus Holzner (a2) (a6)...
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The surface area of turbulent/non-turbulent interfaces (TNTIs) is continuously produced and destroyed via stretching and curvature/propagation effects. Here, the mechanisms responsible for TNTI area growth and destruction are investigated in a turbulent flow with and without stable stratification through the time evolution equation of the TNTI area. We show that both terms have broad distributions and may locally contribute to either production or destruction. On average, however, the area growth is driven by stretching, which is approximately balanced by destruction by the curvature/propagation term. To investigate the contribution of different length scales to these processes, we apply spatial filtering to the data. In doing so, we find that the averages of the stretching and the curvature/propagation terms balance out across spatial scales of TNTI wrinkles and this scale-by-scale balance is consistent with an observed scale invariance of the nearby coherent vortices. Through a conditional analysis, we demonstrate that the TNTI area production (destruction) is localized at the front (lee) edge of the vortical structures in the interface proximity. Finally, we show that while basic mechanisms remain the same, increasing stratification reduces the rates at which TNTI surface area is produced as well as destroyed. We provide evidence that this reduction is largely connected to a change in the multiscale geometry of the interface, which tends to flatten in the wall-normal direction at all active length scales of the TNTI.


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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.
Candel, S. M. & Poinsot, T. J. 1990 Flame stretch and the balance equation for the flame area. Combust. Sci. Technol. 70 (1–3), 115.
Corrsin, S. & Kistler, A. L.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.
Davidson, P. A. 2015 Turbulence: An Introduction for Scientists and Engineers. Oxford University Press.
Dimotakis, P. E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 6998.
Dopazo, C., Martín, J. & Hierro, J. 2006 Iso-scalar surfaces, mixing and reaction in turbulent flows. C. R. Méc. 334 (8–9), 483492.
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6 (3), 423448.
Haller, G. 2015 Lagrangian coherent structures. Annu. Rev. Fluid Mech. 47, 137162.
Haller, G. 2016 Dynamic rotation and stretch tensors from a dynamic polar decomposition. J. Mech. Phys. Solids 86, 7093.
Haller, G., Hadjighasem, A., Farazmand, M. & Huhn, F. 2016 Defining coherent vortices objectively from the vorticity. J. Fluid Mech. 795, 136173.
Holzner, M., Liberzon, A., Guala, M., Tsinober, A. & Kinzelbach, W. 2006 Generalized detection of a turbulent front generated by an oscillating grid. Exp. Fluids 41 (5), 711719.
Holzner, M., Liberzon, A., Nikitin, N., Kinzelbach, W. & Tsinober, A. 2007 Small-scale aspects of flows in proximity of the turbulent/nonturbulent interface. Phys. Fluids 19 (7), 071702.
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.
Krug, D., Chung, D., Philip, J. & Marusic, I. 2017a Global and local aspects of entrainment in temporal plumes. J. Fluid Mech. 812, 222250.
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.
Krug, D., Holzner, M., Marusic, I. & van Reeuwijk, M. 2017b Fractal scaling of the turbulence interface in gravity currents. J. Fluid Mech. 820, R3.
Lee, J., Sung, H. J. & Zaki, T. A. 2017 Signature of large-scale motions on turbulent/non-turbulent interface in boundary layers. J. Fluid Mech. 819, 165187.
Legg, S., Briegleb, B., Chang, Y., Chassignet, E. P., Danabasoglu, G., Ezer, T., Gordon, A. L., Griffies, S., Hallberg, R., Jackson, L. et al. 2009 Improving oceanic overflow representation in climate models: the gravity current entrainment climate process team. Bull. Am. Meteorol. Soc. 90 (5), 657670.
MacDonald, D. G., Carlson, J. & Goodman, L. 2013 On the heterogeneity of stratified-shear turbulence: observations from a near-field river plume. J. Geophys. Res. 118 (11), 62236237.
Mater, B. 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.
Mellado, J. P. 2010 The evaporatively driven cloud-top mixing layer. J. Fluid Mech. 660, 536.
Meneveau, C. & Sreenivasan, K. R. 1990 Interface dimension in intermittent turbulence. Phys. Rev. A 41 (4), 22462248.
Mistry, D., Philip, J. & Dawson, J. R. 2019 Kinematics of local entrainment and detrainment in a turbulent jet. J. Fluid Mech. 871, 896924.
Mistry, D., Philip, J., Dawson, J. R. & Marusic, I. 2016 Entrainment at multi-scales across the turbulent/non-turbulent interface in an axisymmetric jet. J. Fluid Mech. 802, 690725.
Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234 (1196), 123.
Murthy, S. 2013 Turbulent Mixing in Nonreactive and Reactive Flows. Springer.
Neamtu-Halic, M. M., Krug, D., Haller, G. & Holzner, M. 2019 Lagrangian coherent structures and entrainment near the turbulent/non-turbulent interface of a gravity current. J. Fluid Mech. 877, 824843.
Phillips, O. M. 1972 The entrainment interface. J. Fluid Mech. 51 (1), 97118.
van Reeuwijk, M., Holzner, M. & Caulfield, C. P. 2019 Mixing and entrainment are suppressed in inclined gravity currents. J. Fluid Mech. 873, 786815.
van Reeuwijk, M., Krug, D. & Holzner, M. 2018 Small-scale entrainment in inclined gravity currents. Environ. Fluid Mech. 18 (1), 225239.
Serra, M. & Haller, G. 2016 Objective Eulerian coherent structures. Chaos 26 (5), 053110.
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. & dos Reis, R. J. N. 2011 The role of coherent vortices near the turbulent/non-turbulent interface in a planar jet. Phil. Trans. R. Soc. Lond. A 369 (1937), 738753.
de Silva, C. M., Philip, J., Chauhan, K. l, Meneveau, C. & Marusic, I. 2013 Multiscale geometry and scaling of the turbulent-nonturbulent interface in high Reynolds number boundary layers. Phys. Rev. Lett. 111 (4), 044501.
Silva, T. S., Zecchetto, M. & da Silva, C. B. 2018 The scaling of the turbulent/non-turbulent interface at high Reynolds numbers. J. Fluid Mech. 843, 156179.
Simpson, J. E. 1999 Gravity Currents: In the Environment and the Laboratory. Cambridge University Press.
Sinibaldi, J. O., Driscoll, J. F., Mueller, C. J., Donbar, J. M. & Carter, C. D. 2003 Propagation speeds and stretch rates measured along wrinkled flames to assess the theory of flame stretch. Combust. Flame 133 (3), 323334.
Sreenivasan, K. R., Ramshankar, R. & Meneveau, C. H. 1989 Mixing, entrainment and fractal dimensions of surfaces in turbulent flows. Proc. R. Soc. Lond. A 421 (1860), 79108.
Townsend, A. A. 1966 The mechanism of entrainment in free turbulent flows. J. Fluid Mech. 26 (4), 689715.
Tritton, D. J. 1988 Physical Fluid Dynamics. Clarendon.
Tsinober, A. 2009 An Informal Conceptual Introduction to Turbulence, vol. 483. Springer.
Wang, H., Hawkes, E. R., Chen, J. H., Zhou, B., Li, Z. & Aldén, M. 2017 Direct numerical simulations of a high Karlovitz number laboratory premixed jet flame – an analysis of flame stretch and flame thickening. J. Fluid Mech. 815, 511536.
Watanabe, T., Jaulino, R., Taveira, R. R., da Silva, C. B., Nagata, K. & Sakai, Y. 2017 Role of an isolated eddy near the turbulent/non-turbulent interface layer. Phy. Rev. Fluid 2 (9), 094607.
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. 2005 Mechanics of the turbulent-nonturbulent interface of a jet. Phys. Rev. Lett. 95 (17), 174501.
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.
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Connecting the time evolution of the turbulence interface to coherent structures

  • Marius M. Neamtu-Halic (a1) (a2), Dominik Krug (a3), Jean-Paul Mollicone (a4), Maarten van Reeuwijk (a4), George Haller (a5) and Markus Holzner (a2) (a6)...
  • Please note a correction has been issued for this article.


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