On self-preservation and log-similarity in a slightly heated axisymmetric mixing layer

Abstract

This paper reports an experimental investigation of self-preservation for one- and two-point statistics in a slightly heated axisymmetric mixing layer. Results indicate that the longitudinal velocity fluctuation u seems to approach self-preservation more rapidly than either the transverse velocity fluctuation v or the scalar fluctuation θ. The Reynolds number Reδ = U0δ/ν (U0 being the jet inlet velocity and δ the momentum thickness) that ought to be achieved for the one-point statistics to behave in a self-similar fashion is assessed. Second, the relevance of different sets of similarity variables for normalizing the energy spectra and structure functions is explored. In particular, a new set of shear similarity variables, emphasizing the range of scales influenced by the mean velocity and temperature gradient, is derived and tested. Since the Reynolds number based on the Taylor microscale increases with respect to the streamwise distance, complete self-preservation cannot be satisfied; instead, the range of scales over which spectra and structure functions comply with self-preservation depends on the particular choice of similarity variables. A similarity analysis of the two-point transport equation, which features the large scale production term, is performed and confirms this. Log-similarity, which implicitly accounts for the variation of the Reynolds number, is also proposed and appears to provide a reasonable approximation to self-preservation, at least for u and θ.