We develop specialized forcing terms to adjust the conservation properties of the governing fluid flows. These modifications introduce new dynamics (e.g. twisting of vortical structures), selectively speeding up or slowing down the turbulent flow cascades, and contribute to the stabilization of turbulent flows.

1. G. Kumar and A. G. Nair, “Stabilizing two-dimensional turbulent Kolmogorov flow via selective modification of inviscid invariants,” Physics of Fluids 35(12), 2023 (link)(arXiv).
2. A. G. Nair, J. Hanna & M. Aureli, “Selective energy and enstrophy modification of two-dimensional decaying turbulence,” Journal of Fluid Mechanics 956, A12, 2023 (link)(arXiv).

We abstract the complex interactions in unsteady fluid flows into a network model, simplifying the mathematical representation. This approach not only highlights crucial spatio-temporal structures but also facilitates the development of rapid and interpretable fluid dynamics models.

1. A. G. Nair, S. Douglass and N. Arya, “Network-theoretic modeling of fluid-structure interactions,” Theoretical and Computational Fluid Dynamics, 37, 707–723, 2023 (link)(arXiv).
2. K. Taira & A. G. Nair, “Network-based analysis of fluid flows: Progress and outlook,” Progress of Aerospace Sciences 131, 100823, 2022 (link)(arXiv).
3. P. Woerner, A. G. Nair, K. Taira & W. S. Oates, “Sparsification of long-range force networks for molecular dynamics simulations,” PLoS ONE 14(4), 2019 (link) (code).
4. A. G. Nair, S. L. Brunton, & K. Taira, “Networked oscillator-based modeling and control of unsteady wake flows,” Physical Review E, 97 (063107), 2018 (link) (arXiv) (code).
5. M. G. Meena, A. G. Nair, & K. Taira, “Network community-based model reduction for vortical flows,” Physical Review E, 97 (063103), 2018 (link) (arXiv) (code).
6. K. Taira, A. G. Nair, & S. L. Brunton, “Network structure of two-dimensional decaying isotropic turbulence,” Journal of Fluid Mechanics 795, R2, 2016 (link) (arXiv) (code).
7. A. G. Nair & K. Taira, “Network-theoretic approach to sparsified discrete vortex dynamics,” Journal of Fluid Mechanics 768, 549-571, 2015 (link) (arXiv) (code).

Ph.D. Thesis: A. G. Nair, “Network-theoretic and data-based analysis and control of unsteady fluid flows,” 2018 (link).

We leverage phase information for accurate reconstruction of flow fields from large-scale, spatio-temporal experimental data. We also focus on modeling and adjusting the phase characteristics in fluid flows, aiming to significantly improve transient aerodynamic performance.

1. A. G. Nair, K. Taira, B. W. Brunton & S. L. Brunton, “Phase-based control of periodic fluid flows,” Journal of Fluid Mechanics 927, A30, 2021 (link)(arXiv) (code).
2. A. G. Nair, B. Strom, B. W. Brunton & S. L. Brunton, “Phase-consistent dynamic mode decomposition from multiple overlapping spatial domains,” Physical Review Fluids 5(7), p.074702, 2020 (link) (arXiv) (code).

We employ centroid-based unsupervised clustering algorithms for the coarse-grained modeling of time-series data. Our focus is on manipulating the dynamics of fluid flows to align with predetermined cluster states.

1. N. Arya and A. G. Nair, “Cluster regression model for control of nonlinear dynamics,” in review, 2023 (arXiv).
2. A. G. Nair, B. R. Noack, C. A. Yeh, E. Kaiser, S. L. Brunton & K. Taira, “Cluster-based feedback control of turbulent post-stall separated flows,” Journal of Fluid Mechanics 875, 345-375, 2019 (link) (arXiv) (code).

Our goal is to develop empirical models that accurately predict fluid flow dynamics, incorporating specialized domain knowledge for enhanced precision and relevance.

1. M. Hickner, U. Fasel, A. G. Nair, B. W. Brunton, & S. L. Brunton, “ Data-driven unsteady aeroelastic modeling for control,” AIAA Journal, pp1-14, 2022 (link)(arXiv).
2. M. Morimoto, K. Fukami, K. Zhang, A. G. Nair & K. Fukagata, “Convolutional neural networks for fluid flow analysis: toward effective metamodeling and low-dimensionalization,” Theoretical and Computational Fluid Dynamics, 2021 (link)(arXiv)(code).
3. S. Pawar, O. San, A. G. Nair, A. Rasheed & T. Kvamsdal, “Model Fusion with physics-guided machine learning,” Physics of Fluids 33(6), p.067123, 2021 (link) (arXiv) (code).