# Corrsin Equation - plays the role of the [[Karman-Howarth equation]] for the temperature field $\frac{\partial B_{\theta\theta}(r, t)}{\partial t} = 2\left(\frac{\partial}{\partial r} + \frac{2}{r}\right)\left[B_{L\theta, \theta}(r, t) + \chi\frac{\partial B_{\theta\theta}(r, t)}{\partial r}\right]$ - Spectral form: $\frac{\partial F_{\theta\theta}(k, t)}{\partial t} = \Gamma_{\theta\theta}(k, t) - 2\chi k^2 F_{\theta\theta}(k, t);\quad\quad\Gamma_{\theta\theta}(k, t) = -2kF_{L\theta,\theta}(k, t)$ or $\frac{\partial E_{\theta\theta}(k, t)}{\partial t} = T_{\theta\theta}(k, t) - 2\chi k^2 E_{\theta\theta}(k, t);\quad\quad T_{\theta\theta}(k, t) = -8\pi k^3 F_{L\theta,\theta}(k, t)$ ## References 1. Monin, Yaglom - Statistical Fluid Mechanics