Similarity solution of temperature structure functions in decaying homogeneous isotropic turbulence
Abstract
An equilibrium similarity analysis is applied to the transport equation for <(δθ)^{2}>, the secondorder temperature structure function, for decaying homogeneous isotropic turbulence. A possible solution is that the temperature variance <θ^{2}> decays as x^{n}, and that the characteristic length scale, identifiable with the Taylor microscale λ, or equivalently the Corrsin microscale λ_{θ}, 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 <q^{2}>, viz., <q^{2}>∼x^{m}. Measurements downstream of a gridheated mandoline combination show that, like <(δq)^{2}>, <(δθ)^{2}> satisfies similarity approximately over a significant range of scales r, when λ, λ_{θ}, <q^{2}>, and <θ^{2}> are used as the normalizing scales. This approximate similarity is exploited to calculate the thirdorder structure functions. Satisfactory agreement is found between measured and calculated distributions of <δu(δq)^{2}> and <δu(δθ)^{2}>, where δu is the longitudinal velocity increment.
 Publication:

Physical Review E
 Pub Date:
 January 2004
 DOI:
 10.1103/PhysRevE.69.016305
 Bibcode:
 2004PhRvE..69a6305A
 Keywords:

 47.27.Te