Access by Xinjiang University

Anisotropy freezing of passive scalar fields in anisotropy growing homogeneous turbulence

Katsunori Yoshimatsu ^*

Yukio Kaneda^†

Institute of Materials and Systems for Sustainability, Nagoya University, Nagoya, 464-8601, Japan

Aichi Institute of Technology, 1247, Yachikusa, Yakusacho, Toyota, 470-0392, Japan

^*yoshimatsu@nagoya-u.jp
^†Present address: Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan.

PDF

Phys. Rev. Fluids 5, 014604 – Published 29 January, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.014604

Abstract

We study the mixing of a passive scalar in homogeneous turbulent flow with and without anisotropic external force. It is assumed that no scalar source exists and the scalar spectrum at an initial time instant $t_{0}$ is given by the form $C k^{2} + o (k^{2})$ at the wave number $k \to 0$ , where $C$ is independent of $k$ . We have performed direct numerical simulations (DNSs) of the mixing, in which the initial integral length scales of the scalar field are comparable to those of the velocity field and the Schmidt number is unity. The DNSs show that even though the large-scale anisotropy of the velocity field grows with time owing to the external force, its scalar field counterpart remains almost unchanged, i.e., frozen with respect to time, in a state where the scalar field evolves in a self-similar manner. The degree of the anisotropy of each of the velocity and scalar fields is measured by the ratios of the integral length scales in different Cartesian directions. The DNSs also suggest that the scalar spectrum keeps the form $C k^{2} + o (k^{2})$ at small $k$ for time $t (\geq t_{0})$ , and that $C$ is time independent.

Physics Subject Headings (PhySH)

Article Text

References (23)

Z. Warhaft, Passive scalars in turbulent flows, Annu. Rev. Fluid Mech. 32, 203 (2000).
B. I. Shraiman and E. D. Sigga, Scalar turbulence, Nature (London) 405, 639 (2000).
T. Gotoh and P. K. Yeung, Passive scalar transport in turbulence: a computational perspective, in Ten Chapters in Turbulence, edited by P. A. Davidson, Y. Kaneda, and K. R. Sreenivasan (Cambridge University Press, New York, 2013), pp. 87–131.
S. Corrsin, The decay of isotropic temperature fluctuations in an isotropic turbulence, J. Aeronaut. Sci. 18, 417 (1951).
M. Larcheveque, J. P. Chollet, J. R. Herring, M. Lesieur, G. R. Newman, and D. Schertzer, Two-point closure applied to a passive scalar in decaying isotropic turbulence, in Turbulent Shear Flows 2, edited by L. J. S. Bradbury, F. Durst, B. E. Launder, F. W. Schmidt, and J. H. Whitelaw (Springer, Berlin, 1980), pp. 50–66.
J. R. Chasnov, Similarity states of passive scalar transport in isotropic turbulence, Phys. Fluids 6, 1036 (1994).
P. A. Davidson, Turbulence: An Introduction for Scientists and Engineers, 2nd ed. (Oxford University Press, New York, 2015).
A. Briard, T. Gomez, P. Sagaut, and S. Memari, Passive scalar decay laws in isotropic turbulence: Prandtl number effects, J. Fluid Mech. 784, 274 (2015).
A. Briard, T. Gomez, and C. Cambon, Spectral modelling for passive scalar dynamics in homogeneous anisotropic turbulence, J. Fluid Mech. 799, 159 (2016).
K. Yoshimatsu and Y. Kaneda, Large-scale structure of velocity and passive scalar fields in freely decaying homogeneous anisotropic turbulence, Phys. Rev. Fluids 3, 104601 (2018).
P. A. Davidson, Turbulence in Rotating, Stratified and Electrically Conducting Fluids (Cambridge University Press, New York, 2013).
P. Sagaut and C. Cambon, Homogeneous Turbulence Dynamics, 2nd ed. (Springer International, Cham, 2018).
B. Knaepen, S. Kassinos, and D. Carati, Magnetohydrodynamic turbulence at moderate magnetic Reynolds number, J. Fluid Mech. 513, 199 (2004).
G. K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge University Press, Cambridge, 1953).
K. Yoshimatsu and Y. Kaneda, No return to reflection symmetry in freely decaying homogeneous turbulence, Phys. Rev. Fluids 4, 024611 (2019).
P. A. Davidson, N. Okamoto, and Y. Kaneda, On freely decaying, anisotropic, axisymmetric Saffman turbulence, J. Fluid Mech. 706, 150 (2012).
B. Favier, F. S. Godeferd, C. Cambon, A. Delache, and W. T. J. Bos, Quasi-static magnetohydrodynamic turbulence at high Reynolds number, J. Fluid Mech. 681, 434 (2011).
X. M. Zhai and P. K. Yeung, Evolution of anisotropy in direct numerical simulations of MHD turbulence in a strong magnetic field on elongated periodic domains, Phys. Rev. Fluids 3, 084602 (2018).
P. G. Saffman, Note on decay of homogeneous turbulence, Phys. Fluids 10, 1349 (1967).
M. Sinhuber, E. Bodenschatz, and G. P. Bewley, Decay of Turbulence at High Reynolds Numbers, Phys. Rev. Lett. 114, 034501 (2015).
K. R. Sreenivasan, Decay of scalar variance in isotropic turbulence, Phys. Fluids 24, 1909 (1981).
A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence Volume II (Dover, New York, 2007).
M. Kinet, P. Burattini, D. Carati, and B. Knaepen, Decay of passive scalar fluctuations in homogeneous magnetohydrodynamic turbulence, Phys. Fluids 20, 075105 (2008).

Physical Review Fluids

Export citation

Export citation

Anisotropy freezing of passive scalar fields in anisotropy growing homogeneous turbulence

Abstract

Physics Subject Headings (PhySH)

Article Text

References (23)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation