No abstract

The absolute or convective character of inviscid instabilities in parallel shear flows can be determined by examining the branch-point singularities of the dispersion relation for complex frequencies and wavenumbers. According to a criterion developed in the study of plasma instabilities, a flow is convectively unstable when the branch-point singularities are in the lower half complex-frequency plane. These concepts are applied to a family of free shear layers with varying velocity ratio $R = \Delta U/2\overline{U}$, where ΔU is the velocity difference between the two streams and $\overline{U}$ their average velocity. It is demonstrated that spatially growing waves can only be observed if the mixing layer is convectively unstable, i.e. when the velocity ratio is smaller than Rt = 1.315. When the velocity ratio is larger than Rt, the instability develops temporally. Finally, the implications of these concepts are discussed also for wakes and hot jets.

Wall-bounded turbulent flows at high Reynolds numbers have become an increasingly active area of research in recent years. Many challenges remain in theory, scaling, physical understanding, experimental techniques, and numerical simulations. In this paper we distill the salient advances of recent origin, particularly those that challenge textbook orthodoxy. Some of the outstanding questions, such as the extent of the logarithmic overlap layer, the universality or otherwise of the principal model parameters such as the von Kármán "constant," the parametrization of roughness effects, and the scaling of mean flow and Reynolds stresses, are highlighted. Research avenues that may provide answers to these questions, notably the improvement of measuring techniques and the construction of new facilities, are identified. We also highlight aspects where differences of opinion persist, with the expectation that this discussion might mark the beginning of their resolution.

An extensive set of experimental data, for zero pressure gradient boundary layers, over a wide range of Reynolds number is re-evaluated with the help of a composite profile fitted to the mean-velocity data. Boundary layer parameters such as , H and the time scale ratio, , are then carefully examined for consistency among the various experiments and their dependence on Reynolds number. Based on the predictions of the classical theory for these parameters, several criteria are established to evaluate whether a data set can be classified as 'well-behaved', i.e. representative of the desired 'canonical' state. We find that, when carefully applied, the different criteria are very consistent between themselves and can effectively be used interchangeably. The analysis can furthermore help identify the causes for deviations from the desired TBL state and hence serve as a guide in the design of future experiments.

Low-dimensional empirical Galerkin models are developed for spatially evolving laminar and transitional shear layers, based on a Karhunen-Loève decomposition of incompressible two-and three-dimensional Navier-Stokes simulations. It is shown that the key to an accurate Galerkin model is a novel analytical pressure-term representation. The effect of the pressure term is elucidated by a modal energy-flow analysis in a mixing layer, which generalizes the framework developed by Rempfer (1991). In convectively unstable shear layers, it is shown in particular that neglecting small energy terms leads to large amplitude errors in the Galerkin model. The effect of the pressure term and small neglected energy flows is very important for a twodimensional mixing layer, is less pronounced for the three-dimensional analogue, and can be considered as small in an absolutely unstable wake flow.