Session: Rising Stars of Mechanical Engineering Celebration & Showcase

Paper Number: 150020

150020 - Modal Decomposition for Physical Discovery and Model Reduction of Turbulent Flows 

Modal decomposition techniques are at the forefront of scientific discovery from large experimental and numerical datasets of complex flow fields. Arguably the most prominent of these techniques are the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), which extract the energetically and dynamically most relevant flow features, respectively. Both methods yield accurate low-dimensional representations of complex flow dynamics. However, neither POD nor DMD provide direct and quantitative insight into the nonlinear interactions that dictate these dynamics. The common practice remains to use peaks in power or cross spectra as ad-hoc indicators for the presence of nonlinear interactions. The proposed work on bispectral mode decomposition (BMD) directly addresses the broader need for the capability to systematically identify and quantify nonlinear phenomena in aeroscience, natural science, and environmental engineering. Applications range from vortex shedding, unsteady separation, and acoustic aerodynamic resonances to studying turbulent convection in oceanography and modes of climate variability in atmospheric science. 

BMD is a recently developed modal decomposition technique that extracts flow structures associated with triadic nonlinear interactions, the fundamental mechanism of energy transfer in turbulent flows. First, the two classical transition scenarios of the zero-pressure-gradient boundary layer are revisited. The initial stages of these paths to turbulence are well understood, both on a phenomenological and theoretical level. By unambiguously separating from high-fidelity numerical data the temporal and spatial scales involved in the nonlinear breakdown process, this work aims at completing our understanding of the transition processes. For instance, vortex shedding, a common nonlinear phenomenon in aerodynamics, can be thoroughly analyzed using BMD to reveal its intricate coupling with other flow features.

By either confirming or refuting the hypothesis that nonlinearity is at the root of early transition in streamwise corner flows, the proposed work addresses a long-standing discrepancy between theoretical predictions by linear models and experimental observations of this ubiquitous flow. Part of this effort is the computation of direct numerical simulation (DNS) databases for each flow under investigation. These high-fidelity simulations provide the detailed data necessary for BMD to effectively isolate and quantify nonlinear interactions.

Furthermore, the application of BMD extends to studying turbulent convection in oceanography and modes of climate variability in atmospheric science. The exploratory study of BMD as a means of estimating nonlinear transfer functions aims at enabling future generations of reduced-order models of complex flows. These models, grounded in a more precise characterization of nonlinear interactions, will be crucial for advancing our ability to simulate and predict the behavior of complex systems in engineering and the natural sciences.

Presenting Author: Oliver Schmidt UC San Diego

Presenting Author Biography: Oliver T. Schmidt is an Associate Professor in the Department of Mechanical and Aerospace Engineering at UC San Diego's Jacobs School of Engineering. Before joining UCSD, he was a Postdoctoral Scholar in Mechanical and Civil Engineering at the California Institute of Technology. He received his Ph.D. in Aeronautical Engineering from the University of Stuttgart, Germany, in 2014. His research focuses on physics-based modeling and computational fluid mechanics. He is a recipient of the NSF CAREER award, and his research is currently supported by the AFOSR, ONR, DOE, and NSF.

Authors:

Oliver Schmidt UC San Diego