2025/03/02 by Paolo Bernuzzi, Christian Kuehn, Bernuzzi, Paolo +1
Engineering · #60H15 (Primary) 37A50 #76F06 #76M35 (Secondary) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Probability (math.PR) #Water Systems and Optimization
paper · pdf · doi:10.48550/arxiv.2503.00987
openalex publication_date 2025/03/02 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28
We study the phenomenon of turbulence initiation in pipe flow under different noise structures by estimating the probability of initiating metastable transitions. We establish lower bounds on turbulence transition probabilities using linearized models with multiplicative noise near the laminar state. First, we consider the case of stochastic perturbations by Itô white noise; then, through the Stratonovich interpretation, we extend the analysis to noise types such as white and red noise in time. Our findings demonstrate the viability of detecting the onset of turbulence as rare events under diverse noise assumptions. The results also contribute to applied SPDE theory and offer valuable methodologies for understanding turbulence across application areas.