Ensemble Input-output Analysis For Turbulent Flows- Application To Optimal Harmonic Response
Abstract
Turbulence encountered in many aeronautical engineering applications is commonly with various forms of external disturbances and perturbations- e.g. surface roughness, wind gust, rain, ice and acoustic noise. Understanding and characterization of how such perturbations affect the dynamics and statistics of turbulence are of crucial importance for prediction and modeling of the flow, and they ultimately offer valuable physical insights into controlling turbulence in a robust way. Despite the importance, turbulence is an extremely high-dimensional chaos which makes achieving this task fundamentally difficult due to what is popularly known as the ‘butterfly effect’ (i.e. the sensitivity of chaotic dynamical system to initial condition). Focussing on wall-bounded shear flows, the proposed research aims to develop a novel inputoutput analysis framework that characterizes the effect of ‘perturbation’ embedded to turbulence. Based on ensemble average which enables one to bypass the difficulty associated with ‘butterfly effect’ at high Reynolds numbers, the proposed research will develop a theoretical and computational framework that rigorously examines the spatio-temporal dynamics of perturbations in turbulent flows. Two specific issues are proposed to explore- 1) chaotic resonance, a phenomenon that the given dynamical system responds to the weak input perturbation through engaging the effects of intrinsic chaotic activities; 2) ensemble resolvent analysis, a data-driven optimization framework searching for the perturbation leading to the most energetic ensemble-averaged response of the flow. The former is essential to create a theoretical model that describes the ensemble-averaged perturbation dynamics in turbulence in terms of the classical triple decomposition, and the latter is equivalent to the popular resolvent analysis for the perturbation dynamics without any ad-hoc model (e.g. eddy viscosity model). The outcome of this proposal will provide fundamental physical insights into the perturbation dynamics in wall-bounded turbulence, which is, to the best of the knowledge of the applicant, very rarely studied. Ultimately, it will play an important role in modeling and controlling the precise physical mechanisms of turbulent skin-friction generation, heat transfer, and noise generation, the central processes underpinning many aeronautical design processes.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 22, 2024
- Source ID
- FA86552317023
Entities
People
- Yongyun Hwang
Organizations
- Air Force Office of Scientific Research
- Imperial College London
- United States Air Force