Similarity solution of temperature structure functions in decaying homogeneous isotropic turbulence

An equilibrium similarity analysis is applied to the transport equation for <(deltatheta)(2)>, the second-order temperature structure function, for decaying homogeneous isotropic turbulence. A possible solution is that the temperature variance decays as x(n), and that the characteristic length scale, identifiable with the Taylor microscale lambda, or equivalently the Corrsin microscale lambda(theta), varies as x(1/2). The turbulent Reynolds and Péclet numbers decay as x((m+1)/2) when m<-1, where m is the exponent which characterizes the decay of the turbulent energy , viz., approximately x(m). Measurements downstream of a grid-heated mandoline combination show that, like <(deltaq)(2)>, <(deltatheta)(2)> satisfies similarity approximately over a significant range of scales r, when lambda, lambda(theta), , and are used as the normalizing scales. This approximate similarity is exploited to calculate the third-order structure functions. Satisfactory agreement is found between measured and calculated distributions of and , where deltau is the longitudinal velocity increment.