Concurrent scale interactions in the far-field of a turbulent mixing layer

Abstract

13.04.15 Kb. Ok to add accepted version to spira

Modulation of the velocity gradient tensor by concurrent large-scale velocity fluctuations in a turbulent mixing layer

“…The data are identical to that used by Buxton et al (2011) in the developed, far field region of a turbulent planar mixing layer that closely matches the experimental dataset of Buxton & Ganapathisubramani (2014). The mixing layer is produced by means of a DNS of two flows of different free stream velocities, U 1 and U 2 in the ratio U 1 /U 2 = 2, either side of a splitter plate of thickness h to which a wedge of angle 4…”

“…This is a measure that quantifies the loss of information in modelling a statistical distribution of small-scale quantities conditioned on concurrent positive large-scale fluctuations by that conditioned on negative large-scale fluctuations. It is observed that the small-scale turbulence is appreciably "rougher" when the concurrent large-scale fluctuation is positive in the low-speed side of a fully developed turbulent mixing layer which lends further evidence to the convective scale modulation argument of Buxton & Ganapathisubramani (2014). The definition of the small scales is varied and regardless of whether the small-scale fluctuations are dominated by dissipation or have the characteristic features of inertial range turbulence they are shown to be modulated by the concurrent large-scale fluctuations.…”

“…Within this region of the flow the centreline Reynolds number based on the Taylor micro-scale is Re λ ≈ 220 which approximates the experimental mixing layer data of Buxton & Ganapathisubramani (2014) (Re λ ≈ 260 at the centre-line).…”

“…This is explained by a smaller contribution from the viscous diffusion term in the dynamics of the velocity gradient tensor. Buxton & Ganapathisubramani (2014) proposed a convective mechanism for the modulation of the "roughness" of the small-scale turbulence by the large-scale velocity fluctuations. For a developed turbulent free shear flow the peak ensemble averaged Reynolds stresses are observed on the centreline and thus a positive cross-stream (v) fluctuation will on average convect a fluid element of "rougher" turbulence towards the high speed side of the mixing layer.…”

“…This was extended by O'Neil & Meneveau (1997) who showed that large-scale organised structures within a turbulent free shear flow are shown to impact the statistical distribution of small-scale (SGS) velocity gradient quantities, such as the dissipation rate. The study of Buxton & Ganapathisubramani (2014) presented evidence for the concurrent interaction between large-scale velocity fluctuations in a fully developed turbulent mixing layer and the "roughness" of the fine-scale turbulence. Due to intrinsic experimental uncertainties analogues to dissipation, namely ǫ ∼ ν u S λ 2 and ǫ ∼ σ uS , in which λ is the Taylor microscale and σ uS is the variance of the small-scale fluctuations, were used to identify the modulation of small-scale dissipation by large-scale fluctuations.…”