Small-scale variation of convected quantities like temperature in turbulent fluid Part 2. The case of large conductivity

The analysis reported in Part 1 is extended here to the case in which the conductivity κ is large compared with the viscosity ν, the conduction ‘cut-off’ to the θ-spectrum then being at wave-number (ε/κ 3) ¼. It is shown, with a plausible and consistent hypothesis, that the convective supply of ² -stuff to Fourier components of θ with wave-numbers n in the range (ε/κ 3) ¼ Lt n Gt (ε/ν 3) ¼ is due primarily to motion on a length scale of order n -1 acting on a uniform gradient of θ of magnitude () ²^ {12}. The consequent form of the theta;-spectrum within this same wave-number range is (n) = 13C ^ {23} k^-3n^ - {17 3}. The way in which conduction influences (and restricts) the effect of convection on the distribution of θ at these wave-numbers beyond the conduction cut-off is discussed.