Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-26T08:36:30.065Z Has data issue: false hasContentIssue false

Dipoles and streams in two-dimensional turbulence

Published online by Cambridge University Press:  14 October 2020

Javier Jiménez*
Affiliation:
School of Aeronautics, Universidad Politécnica Madrid, 28040Madrid, Spain
*
Email address for correspondence: jimenez@torroja.dmt.upm.es

Abstract

Following the suggestion from the Monte–Carlo experiments in Jiménez (J. Turbul., 2020, doi:10.1080/14685248.2020.1742918) that dipoles are as important to the dynamics of decaying two-dimensional turbulence as individual vortex cores, it is found that the kinetic energy of this flow is carried by elongated streams formed by the concatenation of dipoles. Vortices separate into a family of small fast-moving cores, and another family of larger slowly moving ones, which can be described as ‘frozen’ into a slowly evolving ‘crystal.’ The kinematics of both families are very different, and only the former is self-similar. The latter is responsible for most of the kinetic energy of the flow, and its vortices form the dipoles and the streams. Mechanisms are discussed for the growth of this slow component.

Type
JFM Papers
Copyright
© The Author(s), 2020. Published by 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

REFERENCES

Aref, H., Newton, P. K., Stremler, M. A., Tokieda, T. & Vainchtein, D. L. 2002 Vortex crystals. Adv. Appl. Mech. 39, 179.Google Scholar
Basdevant, C. & Sadourny, R. 1975 Ergodic properties of inviscid truncated models of two-dimensional incompressible flows. J. Fluid Mech. 69, 673688.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Batchelor, G. K. 1969 Computation of the energy spectrum in homogeneous two dimensional turbulence. Phys. Fluids 12, 233239.CrossRefGoogle Scholar
Benzi, R., Colella, M., Briscolini, M. & Santangelo, P. 1992 A simple point vortex model for two-dimensional decaying turbulence. Phys. Fluids A 4, 10361039.CrossRefGoogle Scholar
Benzi, R., Patarnello, S. & Santangelo, P. 1987 On the statistical properties of decaying two-dimensional turbulence. Europhys. Lett. 3, 811818.Google Scholar
Benzi, R., Patarnello, S. & Santangelo, P. 1988 Self-similar coherent structures in two-dimensional decaying turbulence. J. Phys. A: Math. Gen. 21, 12211237.CrossRefGoogle Scholar
Betchov, R. 1956 An inequality concerning the production of vorticity in isotropic turbulence. J. Fluid Mech. 1, 497504.CrossRefGoogle Scholar
Boffetta, G., Celani, A. & Vergassola, M. 2000 Inverse energy cascade in two-dimensional turbulence: deviations from Gaussian behavior. Phys. Rev. E 61, R29R32.CrossRefGoogle ScholarPubMed
Boffetta, G. & Ecke, R. E. 2012 Two-dimensional turbulence. Ann. Rev. Fluid Mech. 44, 427451.CrossRefGoogle Scholar
Brachet, M. E., Meneguzzi, M., Politano, H. & Sulem, P. L. 1988 The dynamics of freely decaying two-dimensional turbulence. J. Fluid Mech. 194, 333349.CrossRefGoogle Scholar
Brown, G. L. & Roshko, A. 1974 On the density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775816.CrossRefGoogle Scholar
Cardesa, J. I., Vela-Martín, A. & Jiménez, J. 2017 The turbulent cascade in five dimensions. Science 357, 782784.CrossRefGoogle ScholarPubMed
Carnevale, G. F., McWilliams, J. C., Pomeau, Y., Weiss, J. B. & Young, W. R. 1991 Evolution of vortex statistics in two-dimensional turbulence. Phys. Rev. Lett. 66, 27352737.CrossRefGoogle ScholarPubMed
Carnevale, G. F., McWilliams, J. C., Pomeau, Y., Weiss, J. B. & Young, W. R. 1992 Rates, pathways, and end states of nonlinear evolution in decaying two-dimensional turbulence: scaling theory versus selective decay. Phys. Fluids A 4, 13141316.CrossRefGoogle Scholar
Catrakis, H. J. & Dimotakis, P. E. 1996 Scale distributions and fractal dimensions in turbulence. Phys. Rev. Lett. 77, 37953798.CrossRefGoogle ScholarPubMed
Cross, M. & Greenside, H. 2009 Pattern Formation and Dynamics in Nonequilibrium Systems. Cambridge University Press.CrossRefGoogle Scholar
Dong, S., Lozano-Durán, A., Sekimoto, A. & Jiménez, J. 2017 Coherent structures in statistically stationary homogeneous shear turbulence. J. Fluid Mech. 816, 167208.Google Scholar
Dritschel, D. G. & McIntyre, M. E. 2008 Multiple jets as PV staircases: the Phillips effect and the resilience of eddy-transport barriers. J. Atmos. Sci. 65, 855874.CrossRefGoogle Scholar
Dritschel, D. G., Scott, R. K., Macaskill, C., Gottwald, G. A. & Tran, C. 2008 Unifying scaling theory for vortex dynamics in two-dimensional turbulence. Phys. Rev. Lett. 101, 094501.CrossRefGoogle ScholarPubMed
Eyink, G. L. 2006 Multiscale gradient expansion of the turbulent stress tensor. J. Fluid Mech. 549, 159190.CrossRefGoogle Scholar
Fine, K. S., Cass, A. C., Flynn, W. G. & Driscoll, C. F. 1995 Relaxation of 2D turbulence to vortex crystals. Phys. Rev. Lett. 75, 32773280.CrossRefGoogle ScholarPubMed
Flierl, G. R., Larichev, V. D., McWilliams, J. C. & Reznik, G. M. 1980 The dynamics of baroclinic and barotropic solitary eddies. Dyn. Atmos. Oceans 5, 141.CrossRefGoogle Scholar
Frisch, U., Sulem, P. L. & Nelkin, M. 1978 A simple dynamical model of intermittent fully developed turbulence. J. Fluid Mech. 87, 719736.CrossRefGoogle Scholar
Grossmann, S., Lohse, D. & Sun, C. 2016 High-Reynolds number Taylor–Couette turbulence. Ann. Rev. Fluid Mech. 48, 5380.CrossRefGoogle Scholar
Hernán, M. A. & Jiménez, J. 1982 Computer analysis of a high-speed film of the plane turbulent mixing layer. J. Fluid Mech. 119, 323345.CrossRefGoogle Scholar
Jiménez, J. 1988 Linear stability of a non-symmetric, inviscid, Kármán street of small uniform vortices. J. Fluid Mech. 189, 337348.CrossRefGoogle Scholar
Jiménez, J. 1994 Hyperviscous vortices. J. Fluid Mech. 279, 169176.CrossRefGoogle Scholar
Jiménez, J. 1996 Algebraic probability density functions in isotropic two-dimensional turbulence. J. Fluid Mech. 313, 223240.CrossRefGoogle Scholar
Jiménez, J. 2018 a Coherent structures in wall-bounded turbulence. J. Fluid Mech. 842, P1.CrossRefGoogle Scholar
Jiménez, J. 2018 b Machine-aided turbulence theory. J. Fluid Mech. 854, R1.CrossRefGoogle Scholar
Jiménez, J. 2020 a Computers and turbulence. Eur. J. Mech. B/Fluids 79, 111.CrossRefGoogle Scholar
Jiménez, J. 2020 b Monte Carlo science. J. Turbul. doi:10.1080/14685248.2020.1742918.CrossRefGoogle Scholar
Jiménez, J. & Guegan, A. 2007 Spontaneous generation of vortex crystals from forced two-dimensional homogeneous turbulence. Phys. Fluids 19, 085103.CrossRefGoogle Scholar
Jiménez, J. & Kawahara, G. 2013 Dynamics of wall-bounded turbulence. In Ten Chapters in Turbulence (ed. Davidson, P. A., Kaneda, Y. & Sreenivasan, K. R.), pp. 221268. Cambridge University Press.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, 6590.CrossRefGoogle Scholar
Jin, D. Z. & Dubin, D. H. E. 2000 Characteristics of two-dimensional turbulence that self-organizes into vortex crystals. Phys. Rev. Lett. 84, 14431446.CrossRefGoogle ScholarPubMed
Joyce, G. & Montgomery, D. 1973 Negative temperature states for the two-dimensional guiding-centre plasma. J. Plasma Phys. 10, 107121.CrossRefGoogle Scholar
Kraichnan, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 14171423.CrossRefGoogle Scholar
Lesieur, M. 2008 Turbulence in Fluids, 4th edn. Springer.CrossRefGoogle Scholar
Lozano-Durán, A., Flores, O. & Jiménez, J. 2012 The three-dimensional structure of momentum transfer in turbulent channels. J. Fluid Mech. 694, 100130.CrossRefGoogle Scholar
Maltrud, M. E. & Vallis, G. K. 1991 Energy spectra and coherent structures in forced two-dimensional and beta-plane turbulence. J. Fluid Mech. 228, 321342.Google Scholar
McWilliams, J. C. 1980 An application of equivalent modons to atmospheric blocking. Dyn. Atmos. Oceans 5, 4366.CrossRefGoogle Scholar
McWilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 2143.CrossRefGoogle Scholar
McWilliams, J. C. 1990 a A demonstration of the suppression of turbulent cascades by coherent vortices in two-dimensional turbulence. Phys. Fluids A 2, 547552.CrossRefGoogle Scholar
McWilliams, J. C. 1990 b The vortices of two-dimensional turbulence. J. Fluid Mech. 219, 361385.CrossRefGoogle Scholar
Meunier, P., Le Dizès, S. & Leweke, T. 2005 Physics of vortex merging. C. R. Phys. 6, 431450.Google Scholar
Moisy, F. & Jiménez, J. 2004 Geometry and clustering of intense structures in isotropic turbulence. J. Fluid Mech. 513, 111133.Google Scholar
Montgomery, D. & Joyce, G. 1974 Statistical mechanics of “negative temperature” states. Phys. Fluids 17, 11391145.Google Scholar
Montgomery, D., Matthaeus, W. H., Stribling, W. T., Martinez, D. & Oughton, S. 1992 Relaxation in two dimensions and the “sinh-Poisson” equation. Phys. Fluids A 4, 36.CrossRefGoogle Scholar
Montgomery, D., Shan, X. & Matthaeus, W. H. 1993 Navier–Stokes relaxation to sinh-Poisson states at finite Reynolds numbers. Phys. Fluids A 5, 22072216.CrossRefGoogle Scholar
Moore, D. W. & Saffman, P. G. 1975 The density of orgamized vortices in a turbulent mixing layer. J. Fluid Mech. 69, 465473.CrossRefGoogle Scholar
Onsager, L. 1949 Statistical hydrodynamics. Nuovo Cimento 6, 279286.CrossRefGoogle Scholar
Paret, J. & Tabeling, P. 1998 Intermittency in the two-dimensional inverse cascade of energy: experimental observations. Phys. Fluids 10, 31263136.Google Scholar
Poincaré, H. 1920 Science et Méthode. Flammarion. English translation in Dover books, 1952.Google Scholar
Richardson, L. F. 1920 The supply of energy from and to atmospheric eddies. Proc. R. Soc. Lond. A 97, 354373.Google Scholar
Sacco, F., Verzicco, R. & Ostilla-Mónico, R. 2019 Dynamics and evolution of turbulent Taylor rolls. J. Fluid Mech. 870, 970987.CrossRefGoogle Scholar
Saffman, P. G. 1971 On the spectrum and decay of random two-dimensional vorticity distributions at large Reynolds number. Stud. Appl. Maths 50, 377383.CrossRefGoogle Scholar
Smith, L. M. & Yakhot, V. 1993 Bose condensation and small-scale structure generation in a random-force driven 2D turbulence. Phys. Rev. Lett. 71, 352355.CrossRefGoogle Scholar
Smith, L. M. & Yakhot, V. 1994 Finite-size effects in forced two-dimensional turbulence. J. Fluid Mech. 274, 115138.CrossRefGoogle Scholar
Tabataba-Vakilia, F., Rogers, J. H., Eichstädt, G., Orton, G. S., Hansen, C. J., Momary, T. W., Sinclair, J. A., Giles, R. S., Caplinger, M. A., Ravine, M. A. et al. 2020 Long-term tracking of circumpolar cyclones on Jupiter from polar observations with JunoCam. Icarus 335, 113405.CrossRefGoogle Scholar
Tabeling, P. 2002 Two-dimensional turbulence: a physicist approach. Phys. Rep. 362, 162.CrossRefGoogle Scholar
Tsukahara, T., Kawamura, H. & Shingai, K. 2006 DNS of turbulent Couette flow with emphasis on the large-scale structure in the core region. J. Turbul. 7, 19.CrossRefGoogle Scholar
Vincent, A. & Meneguzzi, M. 1991 The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 120.CrossRefGoogle Scholar
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237255.CrossRefGoogle Scholar
Xiao, Z., Wan, M., Chen, S. & Eyink, G. L. 2009 Physical mechanism of the inverse energy cascade of two-dimensional turbulence: a numerical investigation. J. Fluid Mech. 619, 144.CrossRefGoogle Scholar