Bypass transition and spot nucleation in boundary layers

TL;DR

This paper presents a new probabilistic cellular automaton model for boundary layer transition to turbulence, integrating spot nucleation and evolution, with parameters fitted from simulations, achieving accurate predictions across turbulence levels.

Contribution

It introduces a novel cellular automaton model for boundary layer transition, combining nucleation rates with nonlinear transition thresholds, extending recent theories to spatially developing flows.

Findings

Model accurately predicts spot nucleation distribution.

Quantitative agreement with turbulence statistics.

Applicable across different free-stream turbulence levels.

Abstract

The spatio-temporal aspects of the transition to turbulence are considered in the case of a boundary layer flow developing above a flat plate exposed to free-stream turbulence. Combining results on the receptivity to free-stream turbulence with the nonlinear concept of a transition threshold, a physically motivated model suggests a spatial distribution of spot nucleation events. To describe the evolution of turbulent spots a probabilistic cellular automaton is introduced, with all parameters directly fitted from numerical simulations of the boundary layer. The nucleation rates are then combined with the cellular automaton model, yielding excellent quantitative agreement with the statistical characteristics for different free-stream turbulence levels. We thus show how the recent theoretical progress on transitional wall-bounded flows can be extended to the much wider class of spatially developing boundary-layer flows.