Hostname: page-component-5c6d5d7d68-7tdvq Total loading time: 0 Render date: 2024-08-07T06:14:16.308Z Has data issue: false hasContentIssue false
  • English
  • Français

Lagrangian investigations of velocity gradients in compressible turbulence: lifetime of flow-field topologies

Published online by Cambridge University Press:  10 June 2019

Nishant Parashar Open the ORCID record for Nishant Parashar [Opens in a new window] ,
Sawan Suman Sinha Open the ORCID record for Sawan Suman Sinha [Opens in a new window]  and
Balaji Srinivasan
Nishant Parashar*
Affiliation:
Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi 110016, India
Sawan Suman Sinha
Affiliation:
Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi 110016, India
Balaji Srinivasan
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India
*
†Email address for correspondence: nishantparashar14@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

We perform Lagrangian investigations of the dynamics of velocity gradients in compressible decaying turbulence. Specifically, we examine the evolution of the invariants of the velocity-gradient tensor. We employ well-resolved direct numerical simulations over a range of Mach number along with a Lagrangian particle tracker to examine trajectories of fluid particles in the space of the invariants of the velocity gradient tensor. This allows us to accurately measure the lifetimes of major topologies of compressible turbulence and provide an explanation of why some selective topologies tend to exist longer than the others. Further, the influence of dilatation on the lifetime of various topologies is examined. Finally, we explain why the so-called conditional mean trajectories (CMT) used previously by several researchers fail to predict the lifetime of topologies accurately.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Homogeneous turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 872 , 10 August 2019 , pp. 492 - 514
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Armitage, P. J. 2010 Astrophysics of Planet Formation. Cambridge University Press.Google Scholar
Ashurst, W. T., Chen, J. Y. & Rogers, M. M. 1987a Pressure gradient alignment with strain rate and scalar gradient in simulated Navier–Stokes turbulence. Phys. Fluids 30 (10), 3293–3294.Google Scholar
Ashurst, W. T., Kerstein, A. R., Kerr, R. M. & Gibson, C. H. 1987b Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence. Phys. Fluids 30 (8), 2343–2353.Google Scholar
Atkinson, C., Chumakov, S., Bermejo, M. I. & Soria, J. 2012 Lagrangian evolution of the invariants of the velocity gradient tensor in a turbulent boundary layer. Phys. Fluids 24 (10), 105104.Google Scholar
Bechlars, P. & Sandberg, R. D. 2017a Evolution of the velocity gradient tensor invariant dynamics in a turbulent boundary layer. J. Fluid Mech. 815, 223–242.Google Scholar
Bechlars, P. & Sandberg, R. D. 2017b Variation of enstrophy production and strain rotation relation in a turbulent boundary layer. J. Fluid Mech. 812, 321–348.Google Scholar
Bhatnagar, A., Gupta, A., Mitra, D., Pandit, R. & Perlekar, P. 2016 How long do particles spend in vortical regions in turbulent flows? Phys. Rev. E 94 (5), 1–8.Google Scholar
Biferale, L. & Toschi, F. 2005 Joint statistics of acceleration and vorticity in fully developed turbulence. J. Turbul. 6, N40.Google Scholar
Buxton, O. R. H. & Ganapathisubramani, B. 2010 Amplification of enstrophy in the far field of an axisymmetric turbulent jet. J. Fluid Mech. 651, 483502.Google Scholar
Cantwell, B. J. 1992 Exact solution of a restricted Euler equation for the velocity gradient tensor. Phys. Fluids A 4 (4), 782–793.Google Scholar
Cantwell, B. J. 1993 On the behavior of velocity gradient tensor invariants in direct numerical simulations of turbulence. Phys. Fluids A 5 (8), 2008–2013.Google Scholar
Cantwell, B. J. & Coles, D. 1983 An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder. J. Fluid Mech. 136, 321–374.Google Scholar
Chevillard, L. & Meneveau, C. 2006 Lagrangian dynamics and statistical geometric structure of turbulence. Phys. Rev. Lett. 97 (17), 174501.Google Scholar
Chevillard, L. & Meneveau, C. 2011 Lagrangian time correlations of vorticity alignments in isotropic turbulence: observations and model predictions. Phys. Fluids 23 (10), 101704.Google Scholar
Chevillard, L., Meneveau, C., Biferale, L. & Toschi, F. 2008 Modeling the pressure Hessian and viscous Laplacian in turbulence: comparisons with direct numerical simulation and implications on velocity gradient dynamics. Phys. Fluids 20 (10), 101504.Google Scholar
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2 (5), 765–777.Google Scholar
Chu, Y. B. & Lu, X. Y. 2013 Topological evolution in compressible turbulent boundary layers. J. Fluid Mech. 733, 414–438.Google Scholar
Danish, M., Sinha, S. S. & Srinivasan, B. 2016a Influence of compressibility on the lagrangian statistics of vorticity–strain-rate interactions. Phys. Rev. E 94 (1), 013101.Google Scholar
Danish, M., Suman, S. & Girimaji, S. S. 2016b Influence of flow topology and dilatation on scalar mixing in compressible turbulence. J. Fluid Mech. 793, 633–655.Google Scholar
Elghobashi, S. & Truesdell, G. C. 1992 Direct simulation of particle dispersion in a decaying isotropic turbulence. J. Fluid Mech. 242, 655–700.Google Scholar
Elsinga, G. E. & Marusic, I. 2010 Evolution and lifetimes of flow topology in a turbulent boundary layer. Phys. Fluids 22 (1), 015102.Google Scholar
Falkovich, G., Fouxon, A. & Stepanov, M. G. 2002 Acceleration of rain initiation by cloud turbulence. Nature 419 (6903), 151.Google Scholar
Girimaji, S. S. & Pope, S. B. 1990a A diffusion model for velocity gradients in turbulence. Phys. Fluids A 2 (2), 242–256.Google Scholar
Girimaji, S. S. & Pope, S. B. 1990b Material-element deformation in isotropic turbulence. J. Fluid Mech. 220, 427–458.Google Scholar
Girimaji, S. S. & Speziale, C. G. 1995 A modified restricted Euler equation for turbulent flows with mean velocity gradients. Phys. Fluids 7 (6), 1438–1446.Google Scholar
Kerimo, J. & Girimaji, S. S. 2007 Boltzmann–BGK approach to simulating weakly compressible 3D turbulence: comparison between lattice Boltzmann and gas kinetic methods. J. Turbul. 8 (46), 1–16.Google Scholar
Kumar, G., Girimaji, S. S. & Kerimo, J. 2013 WENO-enhanced gas-kinetic scheme for direct simulations of compressible transition and turbulence. J. Comput. Phys. 234, 499–523.Google Scholar
Liao, W., Peng, Y. & Luo, L. S. 2009 Gas-kinetic schemes for direct numerical simulations of compressible homogeneous turbulence. Phys. Rev. E 80 (4), 046702.Google Scholar
Lüthi, B., Tsinober, A. & Kinzelbach, W. 2005 Lagrangian measurement of vorticity dynamics in turbulent flow. J. Fluid Mech. 528, 87–118.Google Scholar
Martín, J., Ooi, A., Chong, M. S. & Soria, J. 1998 Dynamics of the velocity gradient tensor invariants in isotropic turbulence. Phys. Fluids 10, 2336–2346.Google Scholar
Martín, M. P., Taylor, E. M., Wu, M. & Weirs, V. G. 2006 A bandwidth-optimized WENO scheme for the effective direct numerical simulation of compressible turbulence. J. Comput. Phys. 220 (1), 270–289.Google Scholar
Meneveau, C. 2011 Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 43, 219–245.Google Scholar
Ohkitani, K. 1993 Eigenvalue problems in three-dimensional Euler flows. Phys. Fluids A 5 (10), 2570–2572.Google Scholar
O’Neill, P. & Soria, J. 2005 The relationship between the topological structures in turbulent flow and the distribution of a passive scalar with an imposed mean gradient. Fluid Dyn. Res. 36 (3), 107–120.Google Scholar
Ooi, A., Martin, J., Soria, J. & Chong, M. S. 1999 A study of the evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence. J. Fluid Mech. 381, 141–174.Google Scholar
Parashar, N., Sinha, S. S., Danish, M. & Srinivasan, B. 2017a Lagrangian investigations of vorticity dynamics in compressible turbulence. Phys. Fluids 29 (10), 105110.Google Scholar
Parashar, N., Sinha, S. S., Srinivasan, B. & Manish, A. 2017b GPU-accelerated direct numerical simulations of decaying compressible turbulence employing a GKM–based solver. Intl J. Numer. Meth. Fluids 83 (10), 737–754.Google Scholar
Pater, I. D. & Lissauer, J. J. 2015 Planetary Sciences. Cambridge University Press.Google Scholar
Pinsky, M. B. & Khain, A. P. 1997 Turbulence effects on droplet growth and size distribution in clouds-A review. J. Aerosol Sci. 28 (7), 1177–1214.Google Scholar
Pirozzoli, S. & Grasso, F. 2004 Direct numerical simulations of isotropic compressible turbulence: influence of compressibility on dynamics and structures. Phys. Fluids 16 (12), 4386–4407.Google Scholar
Pope, S. B. 2000 Turbulent Flows, pp. 483–489. Cambridge University Press.Google Scholar
Pope, S. B. 2002 Stochastic Lagrangian models of velocity in homogeneous turbulent shear flow. Phys. Fluids 14 (5), 1696–1702.Google Scholar
Pumir, A. 1994 A numerical study of the mixing of a passive scalar in three dimensions in the presence of a mean gradient. Phys. Fluids 6 (6), 2118–2132.Google Scholar
Samtaney, R., Pullin, D. I. & Kosovic, B. 2001 Direct numerical simulation of decaying compressible turbulence and shocklet statistics. Phys. Fluids 13 (5), 1415–1430.Google Scholar
Sarkar, S., Erlebacher, G. & Hussaini, M. Y. 1991 Direct simulation of compressible turbulence in a shear flow. Theor. Comp. Fluid Dyn. 2 (5-6), 291–305.Google Scholar
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.Google Scholar
Soria, J., Sondergaard, R., Cantwell, B. J., Chong, M. S. & Perry, A. E. 1994 A study of the fine-scale motions of incompressible time-developing mixing layers. Phys. Fluids 6 (2), 871–884.Google Scholar
Suman, S. & Girimaji, S. S. 2009 Homogenized Euler equation: a model for compressible velocity gradient dynamics. J. Fluid Mech. 620, 177–194.Google Scholar
Suman, S. & Girimaji, S. S. 2010 Velocity gradient invariants and local flow-field topology in compressible turbulence. J. Turbul. 11 (2), 1–24.Google Scholar
Suman, S. & Girimaji, S. S. 2012 Velocity-gradient dynamics in compressible turbulence: influence of Mach number and dilatation rate. J. Turbul. 13 (8), 1–23.Google Scholar
Toschi, F., Biferale, L., Boffetta, G., Celani, A., Devenish, B. J. & Lanotte, A. 2005 Acceleration and vortex filaments in turbulence. J. Turbul. 6, N15.Google Scholar
Vaghefi, N. S. & Madnia, C. K. 2015 Local flow topology and velocity gradient invariants in compressible turbulent mixing layer. J. Fluid Mech. 774, 67–94.Google Scholar
Vieillefosse, P. 1982 Local interaction between vorticity and shear in a perfect incompressible fluid. J. Phys. 43 (6), 837–842.Google Scholar
Wang, L. & Lu, X. Y. 2012 Flow topology in compressible turbulent boundary layer. J. Fluid Mech. 703, 255–278.Google Scholar
Wilczek, M. & Meneveau, C. 2014 Pressure Hessian and viscous contributions to velocity gradient statistics based on Gaussian random fields. J. Fluid Mech. 756, 191–225.Google Scholar
Xu, H., Pumir, A. & Bodenschatz, E. 2011 The pirouette effect in turbulent flows. Nature Phys. 7 (9), 709–712.Google Scholar
Xu, K. 2001 A gas-kinetic BGK scheme for the Navier–Stokes equations and its connection with artificial dissipation and Godunov method. J. Comput. Phys. 171 (1), 289–335.Google Scholar
Yeung, P. K. & Pope, S. B. 1988 An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulence. J. Comput. Phys. 79 (2), 373–416.Google Scholar
Yeung, P. K. & Pope, S. B. 1989 Lagrangian statistics from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 207, 531–586.Google Scholar
Zhou, Y., Nagata, K., Sakai, Y., Ito, Y. & Hayase, T. 2015 On the evolution of the invariants of the velocity gradient tensor in single-square-grid-generated turbulence. Phys. Fluids 27 (7), 075107.Google Scholar