Alternate method for estimating the scalar dissipation rate from large-scale quantities

The most fundamental parameter characterizing the scalar field in a turbulent flow is the scalar dissipation rate, $\epsilon_{\theta}$, which i) is the scalar field analogue of the dissipation rate of turbulent kinetic energy, $\epsilon$, and ii) characterizes the rate at which scalar fluctuations are smeared by the scalar's (molecular) diffusivity. Although $\epsilon$ is a quantity characterizing the small-scale nature of the flow, it is well-known that it may be approximated by measuring only large-scale quantities of the flow (Taylor, 1935, \textit{Proc. Roy. Soc. London}). A similar approach can also be used to estimate $\epsilon_{\theta}$. However, the canonical versions of these estimates have been shown to depend on the flow configuration, thus limiting their accuracy. Inspired by a novel approach for estimating $\epsilon$ that has been shown to give more flow-independent estimates (Mouri et al, 2012, \textit{Phys. Rev. E.}), a new method for estimating $\epsilon_{\theta}$ from large-scale quantities is tested. Using data acquired by way of hot-wire anemometry and cold-wire thermometry in multiple turbulent flows, the results suggest this method minimizes the flow-dependence of the estimates of $\epsilon_{\theta}$, reducing their variation by approximately 60\%.