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Reynolds and Prandtl number scaling of viscous heating in isotropic turbulence
Phys. Rev. Fluids 2, 084606 – Published 21 August, 2017
DOI: https://doi.org/10.1103/PhysRevFluids.2.084606
Abstract
Viscous heating is investigated using high-resolution direct numerical simulations. Scaling relations are derived and verified for different values of the Reynolds and Prandtl numbers. The scaling of the heat fluctuations is shown to depend on Lagrangian correlation times and on the scaling of dissipation-rate fluctuations. The convergence of the temperature spectrum to asymptotic scaling is observed to be slow, due to the broadband character of the temperature production spectrum and the slow convergence of the dissipation-rate spectrum to its asymptotic form.
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References (21)
- D. De Marinis, S. Chibbaro, M. Meldi, and P. Sagaut, Temperature dynamics in decaying isotropic turbulence with Joule heat production, J. Fluid Mech. 724, 425 (2013).
- W. J. T. Bos, The temperature spectrum generated by frictional heating in isotropic turbulence, J. Fluid Mech. 746, 85 (2014).
- A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics II (MIT Press, Cambridge, 1975).
- W. J. T. Bos, R. Chahine, and A. V. Pushkarev, On the scaling of temperature fluctuations induced by frictional heating, Phys. Fluids 27, 095105 (2015).
- A. S. Gurvich and S. L. Zubkovskii, On experimental estimate of the fluctuations of turbulent energy dissipation, Izv. Akad. Nauk SSSR, Ser. Geofiz. 12, 1856 (1963).
- S. Pond and R. W. Stewart, Measurements of the statistical characteristics of small-scale turbulent motions, Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 1, 914 (1965).
- C. W. Van Atta and W. Y. Chen, Structure functions of turbulence in the atmospheric boundary layer over the ocean, J. Fluid Mech. 44, 145 (1970).
- T. Gotoh and R. S. Rogallo, Intermittency and scaling of pressure at small scales in forced isotropic turbulence, J. Fluid Mech. 396, 257 (1999).
- Z.-S. She and E. Lévêque, Universal Scaling Laws in Fully Developed Turbulence, Phys. Rev. Lett. 72, 336 (1994).
- H. Chen, J. R. Herring, R. M. Kerr, and R. H. Kraichnan, Non-Gaussian statistics in isotropic turbulence, Phys. Fluids A 1, 1844 (1989).
- W. J. T. Bos and R. Rubinstein, On the strength of the nonlinearity in isotropic turbulence, J. Fluid Mech. 733, 158 (2013).
- T. Ishihara, Y. Kaneda, M. Yokokawa, K. Itakura, and A. Uno, Spectra of energy dissipation, enstrophy and pressure by high-resolution direct numerical simulations of turbulence in a periodic box, J. Phys. Soc. Jpn. 72, 983 (2003).
- R. H. Kraichnan, Lagrangian-history closure approximation for turbulence, Phys. Fluids 8, 575 (1965).
- S. Corrsin, On the spectrum of isotropic temperature fluctuations in an isotropic turbulence, J. Appl. Phys. 22, 469 (1951).
- A. M. Obukhov, The structure of the temperature field in a turbulent flow, Dokl. Akad. Nauk SSSR 39, 391 (1949).
- G. K. Batchelor, I. D. Howells, and A. A. Townsend, Small-scale variation of convected quantities like temperature in turbulent fluid. Part 2, J. Fluid Mech 5, 134 (1959).
- K. Alvelius, Random forcing of three-dimensional homogeneous turbulence, Phys. Fluids 11, 1880 (1999).
- J.-B. Lagaert, G. Balarac, and G.-H. Cottet, Hybrid spectral-particle method for the turbulent transport of a passive scalar, J. Comput. Phys. 260, 127 (2014).
- Y. Kaneda, T. Ishihara, M. Yokokawa, K. Itakura, and A. Uno, Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box, Phys. Fluids 15, L21 (2003).
- Y. Kaneda and T. Ishihara, High-resolution direct numerical simulation of turbulence, J. Turbul. 7, N20 (2006).
- T. Watanabe and T. Gotoh, Intermittency in passive scalar turbulence under the uniform mean scalar gradient, Phys. Fluids 18, 058105 (2006).