Investigation of transition to turbulence using white-noise excitation and local analysis techniques

Abstract

Weak free-stream turbulence excites modulated Tollmien–Schlichting (T–S) waves in a laminar boundary layer that grow in magnitude with downstream distance and ultimately lead to the formation of turbulent spots and then fully turbulent flow. Hot-wire experiments have indicated that the development of localized large-amplitude ‘events’ in the velocity records are the essential precursor to the eventual formation of turbulent spots in the flow field. Traditional global Fourier techniques are unable to resolve the localized nature of these events and hence provide little useful information concerning the physical processes responsible for this breakdown process.

This investigation used sequences of computer-generated deterministic white noise to excite a laminar boundary layer via a loudspeaker embedded in a flat-plate model. This form of excitation generated the modulated disturbance waves of interest a short distance downstream from the source in a repeatable and deterministic manner. Further downstream the pattern of flow breakdown and subsequent generation of turbulent spots was similar to that observed in naturally excited situations. By repeatedly exciting the boundary layer with a single white-noise sequence it was possible to examine the highly nonlinear stages of ‘event’ development and breakdown with a single hot-wire probe.

Two local analysis techniques, the wavelet transform (WT) and singular spectrum analysis (SSA), were used in conjunction with the white-noise excitation technique to examine the highly nonlinear flow mechanisms responsible for the localized formation of events that lead to the eventual breakdown to turbulence.