Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-10T01:01:10.975Z Has data issue: false hasContentIssue false
  • English
  • Français

On the small-scale structure of turbulence and its impact on the pressure field

Published online by Cambridge University Press:  20 December 2018

Dimitar G. Vlaykov  and
Michael Wilczek Open the ORCID record for Michael Wilczek [Opens in a new window]
Dimitar G. Vlaykov
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany
Michael Wilczek*
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Understanding the small-scale structure of incompressible turbulence and its implications for the non-local pressure field is one of the fundamental challenges in fluid mechanics. Intense velocity gradient structures tend to cluster on a range of scales which affects the pressure through a Poisson equation. Here we present a quantitative investigation of the spatial distribution of these structures conditional on their intensity for Taylor-based Reynolds numbers in the range [160, 380]. We find that the correlation length of the second invariant of the velocity gradient is proportional to the Kolmogorov scale. It is also a good indicator for the spatial localization of intense enstrophy and strain-dominated regions, as well as the separation between them. We describe and quantify the differences in the two-point statistics of these regions and the impact they have on the non-locality of the pressure field as a function of the intensity of the regions. Specifically, across the examined range of Reynolds numbers, the pressure in strong rotation-dominated regions is governed by a dissipation-scale neighbourhood. In strong strain-dominated regions, on the other hand, it is determined primarily by a larger neighbourhood reaching inertial scales.

JFM classification

Turbulent Flows: Intermittency Turbulent Flows: Isotropic turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 861 , 25 February 2019 , pp. 422 - 446
Copyright
© 2018 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

Batchelor, G. K. 1951 Pressure fluctuations in isotropic turbulence. Math. Proc. Camb. Phil. Soc. 47 (2), 359–374.Google Scholar
Bershadskii, A., Kit, E. & Tsinober, A. 1993 On universality of geometrical invariants in turbulence experimental results. Phys. Fluids A: Fluid Dyn. 5 (7), 1523–1525.Google Scholar
Biferale, L. & Procaccia, I. 2005 Anisotropy in turbulent flows and in turbulent transport. Phys. Rep. 414 (2), 43–164.Google Scholar
Bodenschatz, E., Malinowski, S. P., Shaw, R. A. & Stratmann, F. 2010 Can we understand clouds without turbulence? Science 327 (5968), 970–971.Google Scholar
Brewer, C. A.2017 http://www.ColorBrewer.org. Accessed on 2017-10-17.Google Scholar
Cao, N., Chen, S. & Doolen, G. D. 1999 Statistics and structures of pressure in isotropic turbulence. Phys. Fluids 11 (8), 2235–2250.Google Scholar
Chun, J., Koch, D. L., Rani, S. L., Ahluwalia, A. & Collins, L. R. 2005 Clustering of aerosol particles in isotropic turbulence. J. Fluid Mech. 536, 219–251.Google Scholar
Clyne, J., Mininni, P., Norton, A. & Rast, M. 2007 Interactive desktop analysis of high resolution simulations: application to turbulent plume dynamics and current sheet formation. New J. Phys. 9 (8), 301.Google Scholar
Clyne, J. & Rast, M. 2005 A prototype discovery environment for analyzing and visualizing terascale turbulent fluid flow simulations. In Electronic Imaging 2005 (ed. Erbacher, R. F., Roberts, J. C., Gröhn, M. T. & Börner, K.), pp. 284–294. International Society for Optics and Photonics.Google Scholar
Constantin, P. 2014 Local formulae for the hydrodynamic pressure and applications. Russ. Math. Surv. 69, 395–418.Google Scholar
Davidson, P. A. 2004 Turbulence: An Introduction for Scientists and Engineers. Oxford University Press.Google Scholar
Davidson, P. A. 2011 Long-range interactions in turbulence and the energy decay problem. Phil. Trans. A Math. Phys. Eng. Sci. 369 (1937), 796–810.Google Scholar
Davidson, P. A., Ishida, T. & Kaneda, Y. 2008 Linear and angular momentum invariants in homogeneous turbulence. In Proceedings of the IUTAM Symposium on Computational Physics and New Perspectives in Turbulence, Nagoya University, Nagoya, Japan, September 11–14, 2006 (ed. Kaneda, Y.), pp. 19–26. Springer.Google Scholar
Donzis, D. A., Yeung, P. K. & Sreenivasan, K. R. 2008 Dissipation and enstrophy in isotropic turbulence: resolution effects and scaling in direct numerical simulations. Phys. Fluids 20 (4), 045108.Google Scholar
Douady, S., Couder, Y. & Brachet, M. E. 1991 Direct observation of the intermittency of intense vorticity filaments in turbulence. Phys. Rev. Lett. 67, 983–986.Google Scholar
Elsinga, G. E. & Marusic, I. 2010 Universal aspects of small-scale motions in turbulence. J. Fluid Mech. 662, 514–539.Google Scholar
Fauve, S., Laroche, C. & Castaing, B. 1993 Pressure fluctuations in swirling turbulent flows. J. Phys. II 3 (3), 271–278.Google Scholar
Fiscaletti, D., Westerweel, J. & Elsinga, G. E. 2014 Long-range 𝜇PIV to resolve the small scales in a jet at high Reynolds number. Exp. Fluids 55 (9), 1812.Google Scholar
Gotoh, T. & Rogallo, R. S. 1999 Intermittency and scaling of pressure at small scales in forced isotropic turbulence. J. Fluid Mech. 396, 257–285.Google Scholar
Hamlington, P. E., Schumacher, J. & Dahm, W. J. A. 2008 Local and nonlocal strain rate fields and vorticity alignment in turbulent flows. Phys. Rev. E 77 (2), 026303.Google Scholar
Holzer, M. & Siggia, E. 1993 Skewed, exponential pressure distributions from Gaussian velocities. Phys. Fluids A 5 (10), 2525–2532.Google Scholar
Hosokawa, I. 1991 Turbulence models and probability distributions of dissipation and relevant quantities in isotropic turbulence. Phys. Rev. Lett. 66, 1054–1057.Google Scholar
Hou, T. Y. & Li, R. 2007 Computing nearly singular solutions using pseudo-spectral methods. J. Comput. Phys. 226, 379–397.Google Scholar
Ishida, T., Davidson, P. A. & Kaneda, Y. 2006 On the decay of isotropic turbulence. J. Fluid Mech. 564, 455–475.Google Scholar
Jiménez, J., Wray, A. A., Saffman, P. G. & Rogallo, R. S. 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65–90.Google Scholar
La Porta, A., Voth, G. A., Moisy, F. & Bodenschatz, E. 2000 Using cavitation to measure statistics of low-pressure events in large-Reynolds-number turbulence. Phys. Fluids 12 (6), 1485–1496.Google Scholar
Lalescu, C. C. & Wilczek, M. 2018 How tracer particles sample the complexity of turbulence. New J. Phys. 20 (1), 013001.Google Scholar
Lawson, J. M. & Dawson, J. R. 2015 On velocity gradient dynamics and turbulent structure. J. Fluid Mech. 780, 60–98.Google Scholar
Lundgren, T. S. 2003 Linearly forced isotropic turbulence. In Annual Research Briefs, pp. 461–473. Center for Turbulence Research.Google Scholar
Meneveau, C. & Sreenivasan, K. R. 1991 The multifractal nature of turbulent energy dissipation. J. Fluid Mech. 224, 429–484.Google Scholar
Moisy, F. & Jiménez, J. 2004 Geometry and clustering of intense structures in isotropic turbulence. J. Fluid Mech. 513, 111–133.Google Scholar
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics: Mechanics of Turbulence, vol. II. MIT Press.Google Scholar
Nelkin, M. 1994 Universality and scaling in fully developed turbulence. Adv. Phys. 43 (2), 143–181.Google Scholar
Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A.2014 LMFIT: Non-linear least-square minimization and curve-fitting for Python. https://doi.org/10.5281/zenodo.11813.Google Scholar
Ohkitani, K. 1994 Kinematics of vorticity: vorticity-strain conjugation in incompressible fluid flows. Phys. Rev. E 50, 5107–5110.Google Scholar
Pope, S. B. 2000 Turbulent Flows, 1st edn. Cambridge University Press.Google Scholar
Pumir, A. 1994a A numerical study of pressure fluctuations in three-dimensional, incompressible, homogeneous, isotropic turbulence. Phys. Fluids 6 (6), 2071–2083.Google Scholar
Pumir, A. 1994b 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
Rosales, C. & Meneveau, C. 2005 Linear forcing in numerical simulations of isotropic turbulence: physical space implementations and convergence properties. Phys. Fluids. 17 (9), 095106.Google Scholar
Ruelle, D. 1990 Is there screening in turbulence? J. Stat. Phys. 61 (3–4), 865–868.Google Scholar
Schumacher, J. 2007 Sub-Kolmogorov-scale fluctuations in fluid turbulence. Europhys. Lett. 80 (5), 54001.Google Scholar
She, Z. S., Jackson, E. & Orszag, S. A. 1990 Intermittent vortex structures in homogeneous isotropic turbulence. Nature 344, 226–228.Google Scholar
Shu, C.-W. & Osher, S. 1988 Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77 (2), 439–471.Google Scholar
Sreenivasan, K. R. 2004 Possible effects of small-scale intermittency in turbulent reacting flows. Flow Turbul. Combust. 72 (2), 115–131.Google Scholar
Sreenivasan, K. R. & Antonia, R. A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29 (1), 435–472.Google Scholar
Vedula, P. & Yeung, P. K. 1999 Similarity scaling of acceleration and pressure statistics in numerical simulations of isotropic turbulence. Phys. Fluids 11 (5), 1208–1220.Google Scholar
Wallace, J. M. 2009 Twenty years of experimental and direct numerical simulation access to the velocity gradient tensor: What have we learned about turbulence? Phys. Fluids 21 (2), 021301.Google Scholar
Wilczek, M. & Friedrich, R. 2009 Dynamical origins for non-Gaussian vorticity distributions in turbulent flows. Phys. Rev. E 80, 016316.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
Worth, N. A. & Nickels, T. B. 2011 Time-resolved volumetric measurement of fine-scale coherent structures in turbulence. Phys. Rev. E 84, 025301.Google Scholar
Yeung, P. K., Donzis, D. A. & Sreenivasan, K. R. 2012 Dissipation, enstrophy and pressure statistics in turbulence simulations at high Reynolds numbers. J. Fluid Mech. 700, 5–15.Google Scholar