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The temperature spectrum generated by frictional heating in isotropic turbulence

Published online by Cambridge University Press:  28 March 2014

Wouter J. T. Bos
Wouter J. T. Bos*
Affiliation:
LMFA-CNRS, Université de Lyon, Ecole Centrale de Lyon, 69134 Ecully, France
*
†Email address for correspondence: [email protected]
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Abstract

In every turbulent flow with non-zero viscosity, heat is generated by viscous friction. This heat is then mixed by the velocity field. We consider how heat fluctuations generated in this way are injected and distributed over length scales in isotropic turbulence. A triadic closure is derived and numerically integrated. It is shown how the heat fluctuation spectrum depends on the Reynolds and Prandtl numbers.

JFM classification

Turbulent Flows: Isotropic turbulence Mixing: Mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 746 , 10 May 2014 , pp. 85 - 98
Copyright
© 2014 Cambridge University Press 

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References

Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113–133.CrossRefGoogle Scholar
Bos, W. J. T., Rubinstein, R. & Fang, L. 2012 Reduction of mean-square advection in turbulent passive scalar mixing. Phys. Fluids 24, 075104.CrossRefGoogle Scholar
Chen, H., Herring, J. R., Kerr, R. M. & Kraichnan, R. H. 1989 Non-Gaussian statistics in isotropic turbulence. Phys. Fluids A 1, 1844–1854.Google Scholar
De Marinis, D., Chibbaro, S., Meldi, M. & Sagaut, P. 2013 Temperature dynamics in decaying isotropic turbulence with Joule heat production. J. Fluid Mech. 724, 425–449.Google Scholar
Herring, J. R., Schertzer, D., Lesieur, M., Newman, G. R., Chollet, J. P. & Larcheveque, M. 1982 A comparative assessment of spectral closures as applied to passive scalar diffusion. J. Fluid Mech. 124, 411–437.CrossRefGoogle Scholar
Kraichnan, R. H. 1959 The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 5, 497–543.CrossRefGoogle Scholar
Landau, L. D. & Lifschitz, E. M. 1987 Fluid Mechanics. 2nd (Course of Theoretical Physics, vol. 6) ,. Pergamon Press.Google Scholar
Orszag, S. A. 1970 Analytical theories of turbulence. J. Fluid Mech. 41, 363–386.CrossRefGoogle Scholar
Roberts, P. H. 1961 Analytical theory of turbulent diffusion. J. Fluid Mech. 11, 257–283.CrossRefGoogle Scholar
Rubinstein, R. & Clark, T. T. 2013 Reassessment of the classical closures for scalar turbulence. J. Turbul. 14, 71–98.Google Scholar
Vignon, J.-M. & Cambon, C. 1980 Thermal spectral calculation using eddy-damped quasi-normal Markovian theory. Phys. Fluids 23, 1935–1937.Google Scholar