Genrih R. Grek

Physics of Transitional Shear Flows

A summary of recently published book on hydrodynamic stability and transition phenomena in incompressible shear layers with the same title as that of the present contribution to the EUCASS proceedings is given. The objective is to emphasize the milestones of the edition which is aimed, most of all, at university and postgraduate students starting with the problem and may be of interest for the experienced “transition” community, as well.

Transition to turbulence in separation bubbles

This chapter focuses on instability and laminar—turbulent transition in local regions of boundary layer separation or ‘separation bubbles’ in the steady flow of an incompressible fluid. The present topic applies to aerodynamics of aerofoils and wings at low Reynolds numbers, boundary layers affected by steps, humps and other surface imperfections, flow separation at sharp edges, etc.

Transition prediction and control

In this chapter we consider some applications of the unstable-flow physics for laminar—turbulent transition prediction and control. Basically the purpose of transition prediction is to clarify whether the transition takes place in a flow under consideration and to find (calculate or measure) the Reynolds number of transition, ReT. If inside the neutral stability curve the disturbance becomes strong enough at its propagation in the streamwise direction, nonlinear mechanisms come to play which lead to the flow turbulization at ReT. Below we show how the linear stability approach in combination with empirical correlations can be used to predict the location of laminar—turbulent transition with a reasonable accuracy in certain practical situations.

Fundamentals of stability theory

A general and indicative definition of stability was given by Betchov and Criminale (1967): ‘the stability can be defined as quality of immunity to small disturbances.’ An illustration of this general property to the stability of mechanical systems is served by the elementary examples shown in Fig. 1.1.

Secondary instabilities of shear layers

When a linear instability mode reaches a large-enough amplitude, it enters the region of its essentially nonlinear, but still deterministic development. Usually the disturbance amplitude saturates in this region, which resembles the formation of a new quasi-steady state that opens in some cases the door for mechanisms of secondary instabilities discussed below.

Excitation of shear flow disturbances

Turbulence in convectively unstable shear flows subjected to extrinsic dynamics results from amplification of their perturbations, which are generated by external disturbances and usually start to grow far upstream of the turbulent flow region. In the previous chapters, we considered consecutively the transitional events in far-field and near-field regions of disturbance sources and emphasized the importance of the regions for different laminar–turbulent transition scenarios. Now we concentrate on the disturbance excitation in shear layers. This process is referred to as ‘receptivity’ and is the main concern in this chapter.

Some other basic factors of shear-layer stability

This chapter describes the results of theoretical, numerical and experimental studies to show how different isolated factors affect the linear stability of parallel and quasi-parallel flows. The palette of these factors includes surface geometry, volume forces, temperature effects, presence of particles in the fluid, wall permeability and compliance. Certainly, this set is not exhaustive. In particular, the stability of magnetohydrodynamic, unsteady flows, etc. is beyond the present scope. However, the set is diverse enough to provide a general view of the basic aspects of the stability analysis as applied to some problems related to engineering applications.

Nonlinear effects during the laminar–turbulent transition

There is a variety of nonlinear processes taking place at flow breakdown to turbulence. Competing with each other, they occur more or less individually only with special adjustment of the initial conditions. Below we consider some prototypical mechanisms of the laminar flow breakdown originating from the preceding amplification of linear instability waves and streaks in boundary layers.

Instability of the flat-plate boundary layer

The linear stability of the Blasius boundary layer which is a quasi-parallel rather than a strictly parallel flow is addressed in this chapter. At high Reynolds numbers, the wall-normal velocity V is small and the growth of the boundary layer is slow compared to distances characteristic for the laminar–turbulent transition induced by small disturbances. Hence, it is not too much surprising that the parallel-flow approximation works quite satisfactorily for two-dimensional waves observed in experiments.

Linear wave packets of instability waves

The ability to observe monochromatic instability waves in laboratory experiments is stipulated by controlled application of special disturbance sources, which excite small-amplitude oscillations at a single frequency with a predominant transverse wavenumber. In contrast, natural disturbances are mostly localized in space and/or time. In such cases, the wave packet concept discussed in this chapter can be used, which appears highly valuable for the general analysis of flow instability properties.