The overall goal of this project is to significantly enhance the speed, accuracy, and spatiotemporal prediction capabilities of large eddy simulations of turbulent flows using a new modeling framework. Such enhancements in prediction of large-scale eddy interactions across multiple points in space at multiple time instances are of importance in several applications including (i) statistical prediction of the path of a destructive tornado and (ii) prediction and control of jet-noise intensities at various locations away from the source. While the development of such models for turbulent flows requires a fundamental understanding of the statistical nature of spatiotemporal interactions in turbulence, sufficient knowledge in this context (e.g., regarding multi-point space-time correlations at high Reynolds numbers) is currently lacking. To address this knowledge gap for isotropic and wall-bounded turbulent flows and to develop the proposed framework based on space-time structure, the PIs will focus on achieving the following objectives: (1) conduct a comprehensive study of statistical properties of spatiotemporal fluctuations in (1D) Burgers turbulence, (3D) isotropic turbulence and turbulent channel flow configurations at high Reynolds numbers using traditional and novel computational approaches, (2) develop new, optimal turbulence models for Burgers and isotropic turbulence with highly improved prediction capabilities, based on space-time structure of turbulence, and (3) generalize the proposed framework for turbulent channel flows. The proposed framework would significantly advance the state of the art in turbulence modeling by addressing a major drawback of existing models arising from their inability to accurately capture the large-scale spatiotemporal structure of turbulent flows. The hypothesis is that the speed and accuracy of large eddy simulations can be significantly improved if the relevant subgrid-scale stress models are constructed based on information that is consistent with the underlying spatiotemporal statistics of the turbulent flow. In accordance with this hypothesis, the effects of unresolved spatial and temporal scales on the resolved scales are carefully considered in the filtered (or coarse-grained) governing equations via new subgrid scale models, based on the optimal prediction formalism, principles of error minimization, stochastic estimation, and relevant information on spatiotemporal correlations. The resulting subgrid scale models will not only attempt to preserve the spatiotemporal structure of the turbulent flow but will also enable faster simulations of turbulent flows by allowing for larger time steps in numerical simulations due to inclusion of coarse-grained temporal information contained in the space-time correlations. The proposed framework appears to be promising for fast and reliable turbulent flow simulations, as preliminary studies by the PIs demonstrated that the method was successful when applied to a broad range of other canonical nonlinear dynamical systems. Through the proposed test problems and objectives, the PIs also plan to demonstrate the utility of the proposed framework for turbulent flows and gain insights for applications for more complex flows. In terms of the broader impacts, this project is not only expected to make important contributions to the fundamental understanding of turbulence, but is also expected to have an impact on fast and reliable turbulence simulations in various scientific and engineering applications and product innovations relevant to jet noise acoustics, fluid-structure interaction, turbulence control, gas turbines, pollutant dispersion, and weather phenomena. In order to disseminate knowledge about the underlying basic concepts and research results to students from different disciplines, the PIs plan to offer a new graduate level multi-disciplinary course on turbulence simulation and reduced order modeling, with lecture notes to be made available to the general public through a website. For further impact, the PIs also propose to organize a minisymposium on recent advances in turbulence modeling at the US National Congress on Computational Mechanics to communicate the framework and results to other researchers in the field. This project will support the training of researchers including Ph.D. and undergraduate students, who will be actively recruited from underrepresented groups through Diversity Enrichment Programs at U. Oklahoma.
