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Lagrangian coherent structures and entrainment near the turbulent/non-turbulent interface of a gravity current

Published online by Cambridge University Press:  27 August 2019

Marius M. Neamtu-Halic
Affiliation:
Institute of Environmental Engineering, ETH Zürich, CH-8039 Zürich, Switzerland
Dominik Krug
Affiliation:
Physics of Fluids Group and Twente Max Planck Center, Department of Science and Technology, Mesa+ Institute, and J. M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
George Haller
Affiliation:
Institute of Mechanical Systems, ETH Zürich, CH-8092 Zürich, Switzerland
Markus Holzner
Affiliation:
Institute of Environmental Engineering, ETH Zürich, CH-8039 Zürich, Switzerland
Corresponding
E-mail address:

Abstract

In this paper, we employ the theory of Lagrangian coherent structures for three-dimensional vortex eduction and investigate the effect of large-scale vortical structures on the turbulent/non-turbulent interface (TNTI) and entrainment of a gravity current. The gravity current is realized experimentally and different levels of stratification are examined. For flow measurements, we use a multivolume three-dimensional particle tracking velocimetry technique. To identify vortical Lagrangian coherent structures (VLCSs), a fully automated three-dimensional extraction algorithm for multiple flow structures based on the so-called Lagrangian-averaged vorticity deviation method is implemented. The size, the orientation and the shape of the VLCSs are analysed and the results show that these characteristics depend only weakly on the strength of the stratification. Through conditional analysis, we provide evidence that VLCSs modulate the average TNTI height, consequently affecting the entrainment process. Furthermore, VLCSs influence the local entrainment velocity and organize the flow field on both the turbulent and non-turbulent sides of the gravity current boundary.

Type
JFM Papers
Copyright
© 2019 Cambridge University Press 

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References

Bisset, D. K., Hunt, J. C. R. & Rogers, M. M. 2002 The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech. 451, 383410.10.1017/S0022112001006759CrossRefGoogle Scholar
Cantwell, B. J. 1993 On the behavior of velocity gradient tensor invariants in direct numerical simulations of turbulence. Phys. Fluids A 5 (8), 20082013.10.1063/1.858828CrossRefGoogle Scholar
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2 (5), 765777.10.1063/1.857730CrossRefGoogle Scholar
Corrsin, S. & Kistler, A. L. 1954 The free-stream boundaries of turbulent flows. NACA TN-3133, TR-1244, pp. 10331064.Google Scholar
Dimotakis, P. E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 6998.10.1017/S0022112099007946CrossRefGoogle Scholar
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6 (3), 423448.10.1017/S0022112059000738CrossRefGoogle Scholar
Hadjighasem, A. & Haller, G. 2016 Geodesic transport barriers in Jupiter’s atmosphere: a video-based analysis. SIAM Rev. 58 (1), 6989.Google Scholar
Haller, G. 2015 Lagrangian coherent structures. Annu. Rev. Fluid Mech. 47, 137162.10.1146/annurev-fluid-010313-141322CrossRefGoogle Scholar
Haller, G. 2016 Dynamic rotation and stretch tensors from a dynamic polar decomposition. J. Mech. Phys. Solids 86, 7093.10.1016/j.jmps.2015.10.002CrossRefGoogle Scholar
Haller, G. & Beron-Vera, F. J. 2013 Coherent Lagrangian vortices: The black holes of turbulence. J. Fluid Mech. 731, R4.10.1017/jfm.2013.391CrossRefGoogle Scholar
Haller, G., Hadjighasem, A., Farazmand, M. & Huhn, F. 2016 Defining coherent vortices objectively from the vorticity. J. Fluid Mech. 795, 136173.10.1017/jfm.2016.151CrossRefGoogle Scholar
Haller, G. & Yuan, G. 2000 Lagrangian coherent structures and mixing in two-dimensional turbulence. Physica D 147 (3-4), 352370.Google Scholar
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, 465475.10.1017/S0022112008000141CrossRefGoogle Scholar
Holzner, M. & Lüthi, B. 2011 Laminar superlayer at the turbulence boundary. Phys. Rev. Lett. 106 (13), 134503.10.1103/PhysRevLett.106.134503CrossRefGoogle ScholarPubMed
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent gas flows. NASA Tech. Rep. 89-24555.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.10.1017/S0022112095000462CrossRefGoogle Scholar
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417422.10.1063/1.869889CrossRefGoogle Scholar
Krug, D., Chung, D., Philip, J. & Marusic, I. 2017a Global and local aspects of entrainment in temporal plumes. J. Fluid Mech. 812, 222250.10.1017/jfm.2016.786CrossRefGoogle Scholar
Krug, D., Holzner, M., Lüthi, B., Wolf, M., Kinzelbach, W. & Tsinober, A. 2013 Experimental study of entrainment and interface dynamics in a gravity current. Exp. Fluids 54 (5), 1530.10.1007/s00348-013-1530-6CrossRefGoogle Scholar
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, 303324.10.1017/jfm.2014.738CrossRefGoogle Scholar
Krug, D., Holzner, M., Lüthi, B., Wolf, M., Tsinober, A. & Kinzelbach, W. 2014 A combined scanning PTV/LIF technique to simultaneously measure the full velocity gradient tensor and the 3D density field. Meas. Sci. Technol. 25 (6), 065301.10.1088/0957-0233/25/6/065301CrossRefGoogle Scholar
Krug, D., Holzner, M., Marusic, I. & van Reeuwijk, M. 2017b Fractal scaling of the turbulence interface in gravity currents. J. Fluid Mech. 820, R3.10.1017/jfm.2017.245CrossRefGoogle Scholar
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, 165187.10.1017/jfm.2017.170CrossRefGoogle Scholar
Lüthi, B., Tsinober, A. & Kinzelbach, W. 2005 Lagrangian measurement of vorticity dynamics in turbulent flow. J. Fluid Mech. 528, 87118.10.1017/S0022112004003283CrossRefGoogle Scholar
Mathew, J. & Basu, A. J. 2002 Some characteristics of entrainment at a cylindrical turbulence boundary. Phys. Fluids 14 (7), 20652072.10.1063/1.1480831CrossRefGoogle Scholar
Mathur, M., Haller, G., Peacock, T., Ruppert-Felsot, J. E. & Swinney, H. L. 2007 Uncovering the Lagrangian skeleton of turbulence. Phys. Rev. Lett. 98 (14), 144502.10.1103/PhysRevLett.98.144502CrossRefGoogle ScholarPubMed
Meneveau, C. 2011 Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 43, 219245.10.1146/annurev-fluid-122109-160708CrossRefGoogle Scholar
Mistry, D., Philip, J. & Dawson, J. R. 2019 Kinematics of local entrainment and detrainment in a turbulent jet. J. Fluid Mech. 871, 896924.10.1017/jfm.2019.327CrossRefGoogle Scholar
Negretti, M. E., Flòr, J. B. & Hopfinger, E. J. 2017 Development of gravity currents on rapidly changing slopes. J. Fluid Mech. 833, 7097.10.1017/jfm.2017.696CrossRefGoogle Scholar
Odier, P., Chen, J. & Ecke, R. E. 2014 Entrainment and mixing in a laboratory model of oceanic overflow. J. Fluid Mech. 746, 498535.10.1017/jfm.2014.104CrossRefGoogle Scholar
Ouellette, N. T. 2012 On the dynamical role of coherent structures in turbulence. C. R. Phys. 13, 866877.10.1016/j.crhy.2012.09.006CrossRefGoogle Scholar
van Reeuwijk, M., Holzner, M. & Caulfield, C. P. 2019 Mixing and entrainment are suppressed in inclined gravity currents. J. Fluid Mech. 873, 786815.10.1017/jfm.2019.430CrossRefGoogle Scholar
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, 567590.10.1146/annurev-fluid-010313-141357CrossRefGoogle Scholar
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), 738753.10.1098/rsta.2010.0300CrossRefGoogle Scholar
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, 156179.10.1017/jfm.2018.143CrossRefGoogle Scholar
Soria, J., Ooi, A. & Chong, M. S. 1997 Volume integrals of the QA-RA invariants of the velocity gradient tensor in incompressible flows. Fluid Dyn. Res. 19 (4), 219233.10.1016/S0169-5983(97)00034-8CrossRefGoogle Scholar
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), 79108.10.1098/rspa.1989.0004CrossRefGoogle Scholar
Townsend, A. A. R. 1980 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Tritton, D. J. 1988 Physical Fluid Dynamics. Clarendon.Google Scholar
Tsinober, A. 2000 Vortex stretching versus production of strain/dissipation. In Turbulence Structure and Vortex Dynamics (ed. Hunt, J. C. R. & Vassilicos, J.), pp. 164191. Cambridge University Press.Google Scholar
Tsinober, A. 2009 An Informal Conceptual Introduction to Turbulence, vol. 483. Springer.10.1007/978-90-481-3174-7CrossRefGoogle Scholar
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.Google Scholar
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.Google ScholarPubMed
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, 199230.10.1017/S0022112009006600CrossRefGoogle Scholar
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), 105110.10.1063/1.4761837CrossRefGoogle Scholar
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