Stochastic estimation of large structures in an incompressible mixing layer

High-vector density planar velocity fields were obtained for an incompressible mixing layer using particle image velocimetry (PIV) for the purpose of determining spatial correlations of velocity fluctuations and linear stochastic estimates of the large-scale structures. The linear stochastic estimates were calculated based on the deformation tensor. The velocity ratio of the mixing layer was 0.575, and the density ratio was unity. At the location where the PIV images were obtained, Re_x = 1.8 × 10⁵, Re_δω = 1.1 × 10⁴, and the pairing parameter was Rx/λ = 8. Preliminary hot-film measurements showed the mixing-layer mean velocity and turbulence profiles to be self-similar at this location. The mixing layer was found to be largely two-dimensional with well-organized Brown-Roshko roller structures and braids (Brown, G.L., and Roshko, A., "On Density Effects and Large Structures in Turbulent Mixing Layers," Journal of Fluid Mechanics, Vol. 64, 1974, pp. 775-814). Measured velocity fluctuations and Reynolds shear stress data agree well with previous experimental results. The R_u′u′ correlation is a horizontally oriented ellipse, with a slight inclination from horizontal. The R_v′v′ correlation is a vertically oriented ellipse. The linear stochastic estimate of a roller suggests that these structures are very slightly elliptical, with a horizontal major axis. The linear stochastic estimate of a braid suggests that the braids are obliquely oriented with stagnation occurring at a point.