Linear And Nonlinear Instabilities Of Blasius Boundary Layer Perturbed By Streamwise Vortices

Linear and Nonlinear Instabilities of Blasius Boundary Layer Perturbed by Streamwise Vortices

Linear and Nonlinear Instabilities of Blasius Boundary Layer Perturbed by Streamwise Vortices. Part II: Intermittent Instability Induced by Long-wavelength Klebanoff Modes

This report presents theoretical results on the stability properties of a Blasius boundary layer perturbed by Klebanoff distortions with a relatively long spanwise scale. Even relatively weak Klebanoff modes can alter the near-wall curvature of the underlying flow by O(1) and, hence, introduce linear instabilities with larger characteristic growth rates and frequencies than those of the Tollmien-Schlichting waves in an unperturbed Blasius flow. A localised distortion supports both sinuous and varicose modes of instability, with the growth rates of the sinuous modes being likely to be larger, in general. Overall, the instability is intermittent in time and localised in space, being confined to a finite part of the Klebanoff mode cycle and to a specific window(s) along the streamwise direction. A spanwise periodic distortion supports spatially quasi-periodic modes (via the parametric resonance mechanism), which may be viewed as modified T-S waves with excess growth rates when the Klebanoff modes are weak. In spite of the simplifications involved in this theory, its predictions appear qualitatively consistent with some of the unusual characteristics of the high-frequency wavepackets observed during previous experiments. The nonlinear development of a localised sinuous mode is followed across a sequence of asymptotic regimes using the non-equilibrium critical-layer theory.

Seventh IUTAM Symposium on Laminar-Turbulent Transition

The origins of turbulent ?ow and the transition from laminar to turbulent ?ow are the most important unsolved problems of ?uid mechanics and aerodynamics. - sides being a fundamental question of ?uid mechanics, there are numerous app- cations relying on information regarding transition location and the details of the subsequent turbulent ?ow. For example, the control of transition to turbulence is - pecially important in (1) skin-friction reduction of energy ef?cient aircraft, (2) the performance of heat exchangers and diffusers, (3) propulsion requirements for - personic aircraft, and (4) separation control. While considerable progress has been made in the science of laminar to turbulent transition over the last 30 years, the c- tinuing increase in computer power as well as new theoretical developments are now revolutionizing the area. It is now starting to be possible to move from simple 1D eigenvalue problems in canonical ?ows to global modes in complex ?ows, all - companied by accurate large-scale direct numerical simulations (DNS). Here, novel experimental techniques such as modern particle image velocimetry (PIV) also have an important role. Theoretically the in?uence of non-normality on the stability and transition is gaining importance, in particular for complex ?ows. At the same time the enigma of transition in the oldest ?ow investigated, Reynolds pipe ?ow tran- tion experiment, is regaining attention. Ideas from dynamical systems together with DNS and experiments are here giving us new insights.