CAREER: Bispectral mode decomposition for discovery of triadic interactions in laminar-turbulent transition

Modal decomposition techniques are at the forefront of scientific discovery from large experimental and numerical datasets of complex flow fields. These techniques include the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), which extract the energetically and dynamically most relevant flow features. Both methods yield accurate low-dimensional representations of complex flow dynamics.

However, neither POD nor DMD give direct and quantitative insight into the nonlinear interactions that dictate these dynamics, and 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.

The research activities are tightly interwoven with a comprehensive education and outreach plan that targets early-career researchers, nonspecialists, and students at the high-school and college levels. The broad dissemination of the research methodology and outcomes is facilitated by providing a free, open-source numerical tool for bispectral mode analysis.

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 research aims at completing our understanding of the transition processes. By either confirming or refuting the hypothesis that nonlinearity is at the root of early transition in streamwise corner flows, the proposed work furthermore 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. The exploratory study of BMD as a means of estimating nonlinear transfer functions, lastly, aims at enabling future generations of reduced-order models of complex flows.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.