Transition arising from a separated region of flow is quite common and plays an important role in engineering. It is difficult to predict using conventional models and the transition mechanism is still not fully understood. We report the results of a numerical simulation to study the physics of separated boundary-layer transition induced by a change of curvature of the surface. The geometry is a flat plate with a semicircular leading edge. The Reynolds number based on the uniform inlet velocity and the leading-edge diameter is 3450. The simulated mean and turbulence quantities compare well with the available experimental data.The numerical data have been comprehensively analysed to elucidate the entire transition process leading to breakdown to turbulence. It is evident from the simulation that the primary two-dimensional instability originates from the free shear in the bubble as the free shear layer is inviscidly unstable via the Kelvin–Helmholtz mechanism. These initial two-dimensional instability waves grow downstream with a amplification rate usually larger than that of Tollmien–Schlichting waves. Three-dimensional motions start to develop slowly under any small spanwise disturbance via a secondary instability mechanism associated with distortion of two-dimensional spanwise vortices and the formation of a spanwise peak–valley wave structure. Further downstream the distorted spanwise two-dimensional vortices roll up, leading to streamwise vorticity formation. Significant growth of three-dimensional motions occurs at about half the mean bubble length with hairpin vortices appearing at this stage, leading eventually to full breakdown to turbulence around the mean reattachment point. Vortex shedding from the separated shear layer is also observed and the ‘instantaneous reattachment’ position moves over a distance up to 50% of the mean reattachment length. Following reattachment, a turbulent boundary layer is established very quickly, but it is different from an equilibrium boundary layer.

A large-eddy simulation has been performed of a flat-plate boundary layer undergoing transition to turbulence under free-stream turbulence at a level of 6%. The properties of the simulated transition match those found experimentally: not only is the position and length of transition in agreement with available data, but the mechanism of transition also appears to correspond closely, since disturbances seen in the laminar layer prior to transition are found in the simulation. Statistical data have been gathered that allow the computation of all terms in the derived equations for the Reynolds stresses at four x stations. Aspects of these balances are presented that allow new insights into the physical mechanisms at work. The importance of the wall-normal component of free-stream turbulence and the timing of the redistribution of energy into this component through the fluctuating pressure field are revealed. 0 1995 American Institute of Physics.

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Large-eddy simulation (LES) is used to calculate the concentration fluctuations of passive plumes from an elevated source (ES) and a ground-level source (GLS) in a turbulent boundary layer over a rough wall. The mean concentration, relative fluctuations and spectra are found to be in good agreement with the wind-tunnel measurements for both ES and GLS. In particular, the calculated relative fluctuation level for GLS is quite satisfactory, suggesting that the LES is reliable and the calculated instantaneous data can be used for further post-processing. Animations are shown of the meandering of the plumes, which is one of the main features to the numerical simulations. Extreme value theory (EVT), in the form of the Generalised Pareto distribution (GPD), is applied to model the upper tail of the probability density function of the concentration time series collected at many typical locations for GLS and ES from both LES and experiments. The relative maxima (defined as maximum concentration normalized by the local mean concentration) and return levels estimated from the numerical data are in good agreement with those from the experimental data. The relative maxima can be larger than 50. The success of the comparisons suggests that we can achieve significant insight into the physics of dispersion in turbulent flows by combining LES and EVT.

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