Introduction to Turbulent Transport of Particles, Temperature and Magnetic Fields

In this Chapter we consider a turbulent transport of temperature field in an isotropic homogeneous and incompressible turbulence. We discuss the Kolmogorov theory of the hydrodynamic turbulence and obtain spectrumof velocity fluctuations for fully developed turbulence using the dimensional analysis. We study isotropic and anisotropic spectra of temperature fluctuations in different subranges of turbulent scales and different Prandtl numbers applying the dimensional analysis.We derivemean-field equationsfor the temperature field and obtain expressions for turbulent heat flux, turbulent diffusion and level of temperature fluctuations for small and large P'eclet numbers by means of various analytical methods, namely the dimensional analysis, the quasi-linear approach and the spectral tau approach (the relaxation approach). Keywords: hydrodynamic turbulence; spectra of velocity and temperature fluctuations; turbulent heat flux and turbulent diffusion--