The problem of turbulence onset in shear flows has attracted the attention of investigators for more than a century. Despite its complexity, interest in the laminar-turbulent transition has increased during the past few decades owing to i ts importance in both fundamental and applied aspects of fluid mechanics . The physical mechanisms of the transition phenomenon depend essen­ tially on the specific type of flow and the character of environmental disturbances. For boundary-layer flows two main classes of transition are known (Morkovin 1 968, 1 984; Morkovin & Reshotko 1 990). The first of them is connected with boundary-layer instabilities (described initially by linear stability theories), amplification, and interaction of different instability modes resulting in the laminar flow breakdown. This class is usually observed when environmental disturbances are rather small. The second class of transition, usually called bypass, is connected with "direct" nonlinear laminar-flow breakdown under the influence of external dis­ turbances . This is observed when high enough levels of environmental perturbations (free-stream disturbances, surfacc roughness, etc) are pre­ sent. This article focuses on the first class of transition because of its fun­ damental and practical importance in problems involving moving vehicles

Physical mechanisms of laminar-boundary-layer transition

On the görtler instability of boundary layers

The interactions between longitudinal vortices and accompanying waves considered are strongly nonlinear, in the sense that the mean-flow profile throughout the boundary layer is completely altered from its original undisturbed state. Nonlinear interactions between vortex flow and Tollmien-Schlichting waves are addressed first, and some analytical and computational properties are described. These include the possibility in the spatial-development case of a finite-distance break-up, inducing a singularity in the displacement thickness. Second, vortex/Rayleigh wave nonlinear interactions are considered for the compressible boundary-layer, along with certain special cases of interest and some possible solution properties. Both types, vortex/Tollmien-Schlichting and vortex/Rayleigh, are short-scale/long-scale interactions and they have potential applications to many flows at high Reynolds numbers. The strongly nonlinear nature is believed to make them very relevant to fully fledged transition to turbulence.

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On strongly nonlinear vortex/wave interactions in boundary-layer transition

Abstract Gortler instability occurs due to the action of centrifugal forces in boundary layers over curved surfaces, where it most commonly results in the generation of steady streamwise vortices. This study provides a summary of the current knowledge of this phenomenon. All existing experimental evidence is discussed. Experimental facts that bear on the theoretical modelling of the instability are pointed out. Linear theory is discussed in details and compared critically with the available experiments. The nonlinear evolution of the vortices and their effect on the laminar-turbulent transition process are reviewed. The available nonlinear theories and direct numerical simulations are critically compared with the experiments. Centrifugal instability of turbulent boundary layers is discussed in detail. Effects of the instability on heat transfer and the associated buoyancy forces on the instability are discussed. A summary of some outstanding questions is given.

On the Goertler instability of boundary layers

The relationship between asymptotic descriptions of vortex–wave interactions and more recent work on ‘exact coherent structures’ is investigated. In recent years immense interest has been focused on so-called self-sustained processes in turbulent shear flows where the importance of waves interacting with streamwise vortex flows has been elucidated in a number of papers. In this paper, it is shown that the so-called ‘lower branch’ state which has been shown to play a crucial role in these self-sustained processes is a finite Reynolds number analogue of a Rayleigh vortex–wave interaction with scales appropriately modified from those for external flows to Couette flow, the flow of interest here. Remarkable agreement between the asymptotic theory and numerical solutions of the Navier–Stokes equations is found even down to relatively small Reynolds numbers, thereby suggesting the possible importance of vortex–wave interaction theory in turbulent shear flows. The relevance of the work to more general shear flows is also discussed.

P. Hall

Papers

The nonlinear interaction of Tollmien-Schlichting waves and Taylor-Goertler vortices in curved channel flows