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Three-dimensional large-eddy simulations of two-stream mixing layers developing spatially from laminar boundary layers are presented, replicating wind-tunnel experiments carried out in Part 1 of this study. These simulations have been continued through the mixing transition and into the fully turbulent self-similar flow beyond. In agreement with the experiments, the simulations show that the familiar mechanism of growth by vortex amalgamation is replaced at the mixing transition by a previously unrecognised mechanism in which the spanwise-coherent large structures individually undergo continuous linear growth. In the post-transition flow it is this continuous linear growth of the individual structures that produces the self-similar growth of the mixing-layer thickness, the large-structure interactions occurring as a consequence of the growth, not its cause. New information is also presented on the topography of the organised post-transition flow and on its cyclical evolution through the lifetimes of the individual large structures. The dynamic and kinematic implications of these findings are discussed and shown to define quantitatively the growth rate of the homogeneous post-transition mixing layer in its organised state. _______________________________________________________________

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In this paper Large Eddy Simulations are performed on the spatially developing plane turbulent mixing layer. The simulated mixing layers originate from initially laminar conditions. The focus of this research is on the e↵ect of the nature of the imposed fluctuations on the large-scale spanwise and streamwise structures in the flow. Two simulations are performed; one with low-level three-dimensional inflow fluctuations obtained from pseudo-random numbers, the other with physically-correlated fluctuations of the same magnitude obtained from an inflow generation technique. Where white-noise fluctuations provide the inflow disturbances, no spatially stationary streamwise vortex structure is observed, and the large-scale spanwise turbulent vortical structures grow continuously and linearly. These structures are observed to have a three-dimensional internal geometry with branches and dislocations. Where physically-correlated provide the inflow disturbances a 'streaky' streamwise structure that is spatially stationary is observed, with the large-scale turbulent vortical structures growing with the square-root of time. These large-scale structures are quasi-two-dimensional, on top of which the secondary structure rides. The simulation results are discussed in the context of the varying interpretations of mixing layer growth that have been postulated. Recommendations are made concerning the data required from experiments in order to produce accurate numerical simulation recreations of real flows.

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SUMMARYA series of spatially developing mixing layers are simulated using the large eddy simulation (LES) technique. A hyperbolic tangent function and data derived from boundary layer simulations are used to generate the inflow condition, and their effects on the flow are compared. The simulations are performed in both two and three dimensions. In two-dimensional simulations, both types of inflow conditions produce a layer that grows through successive pairings of Kelvin-Helmholtz (K-H) vortices, but the composition ratio is lower for the hyperbolic tangent inflow simulations. The two-dimensional simulations do not undergo a transition to turbulence. The three-dimensional simulations produce a transition to turbulence, and coherent structures are found in the post-transition region of the flow. The composition ratio of the three-dimensional layers is reduced in comparison to the counterpart two-dimensional runs. The mechanisms of growth are investigated in each type of simulation, and amalgamative pairing interactions are found in the pre-transition region of the three-dimensional simulations, and throughout the entire computational domain of those carried out in two-dimensions. The structures beyond the post-transition region of the three-dimensional simulations appear to behave in a much different manner to their pre-transition cousins, with no pairingtype interactions observed in the turbulent flow. In order to accurately simulate spatially developing mixing layers, it is postulated that the inflow conditions must closely correspond to the conditions present in the reference experiment.

Large Eddy Simulation is used to simulate a series of plane mixing layers. The influence of the spanwise domain on the development of the mixing layer, and the evolution of the coherent structures are considered. The mixing layers originate from laminar conditions, and an idealised inflow condition is found to produce accurate flow predictions when the spanwise computational domain extent is sufficient to avoid confinement effects. Spanwise domain confinement of the flow occurs when the ratio of spanwise domain extent to local momentum thickness reaches a value of ten. Flow confinement results in changes to both the growth mechanism of the turbulent coherent structures, and the nature of the interactions that occur between them. The results demonstrate that simulations of the two-dimensional mixing layer flow requires a three-dimensional computational domain in order that the flow will evolve in a manner that is free from restraints imposed by the spanwise domain.

Large Eddy Simulations (LES) of spatially developing turbulent mixing layers have been performed for flows of uniform density and Reynolds numbers of up to 50,000 based on the visual thickness of the layer and the velocity difference across it. On a fine LES grid, a validation simulation performed with a hyperbolic tangent inflow profile produces flow statistics that compare extremely well with reference Direct Numerical Simulation (DNS) data. An inflow profile derived from laminar Blasius profiles produces a flow that is significantly different to the reference DNS, particularly with respect to the initial development of the flow. When compared with experimental data, however, it is the boundary layer-type inflow simulation produces the better prediction of the flow statistics, including the mean transition location. It is found that the boundary layer inflow condition is more unstable than the hyperbolic tangent inlet profile. A suitably designed coarse LES grid produces good predictions of the mean transition location with boundary layer inflow conditions at a low computational cost. The results suggest that hyperbolic tangent functions may produce unreliable DNS data when used as the initial condition for studies of the transition in the mixing layer flow.