Linear and Nonlinear Instabilities of Blasius Boundary Layer Perturbed by Streamwise Vortices. Part II: Intermittent Instability Induced by Long-wavelength Klebanoff Modes
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 2001
- Accession Number
- ADA400173
Entities
People
- Meelan M. Choudhari
- Xuesong Wu