Aditya Nair

Network structure of two-dimensional decaying isotropic turbulence

The present paper reports on our effort to characterize vortical interactions in complex fluid flows through the use of network analysis. In particular, we examine the vortex interactions in two-dimensional decaying isotropic turbulence and find that the vortical interaction network can be characterized by a weighted scale-free network. It is found that the turbulent flow network retains its scale-free behavior until the characteristic value of circulation reaches a critical value. Furthermore, we show that the two-dimensional turbulence network is resilient against random perturbations but can be greatly influenced when forcing is focused towards the vortical structures that are categorized as network hubs. These findings can serve as a network-analytic foundation to examine complex geophysical and thin-film flows and take advantage of the rapidly growing field of network theory, which complements ongoing turbulence research based on vortex dynamics, hydrodynamic stability, and statistics. While additional work is essential to extend the mathematical tools from network analysis to extract deeper physical insights of turbulence, an understanding of turbulence based on the interaction-based network-theoretic framework presents a promising alternative in turbulence modeling and control efforts.

Network-theoretic approach to sparsified discrete vortex dynamics

We examine discrete vortex dynamics in two-dimensional flow through a network-theoretic approach. The interaction of the vortices is represented with a graph, which allows the use of network-theoretic approaches to identify key vortex-to-vortex interactions. We employ sparsification techniques on these graph representations based on spectral theory for constructing sparsified models and evaluating the dynamics of vortices in the sparsified setup. Identification of vortex structures based on graph sparsification and sparse vortex dynamics are illustrated through an example of point-vortex clusters interacting amongst themselves. We also evaluate the performance of sparsification with increasing number of point vortices. The sparsified-dynamics model developed with spectral graph theory requires reduced number of vortex-to-vortex interactions but agrees well with the full nonlinear dynamics. Furthermore, the sparsified model derived from the sparse graphs conserves the invariants of discrete vortex dynamics. We highlight the similarities and differences between the present sparsified-dynamics model and the reduced-order models.

Numerical Simulations of Subsonic and Transonic Open-Cavity Flows

Two-dimensional open-cavity flows for free stream Mach number of 0.1 to 1.6 are investigated with direct numerical simulations for cavities of aspect ratio 2 and 6 to characterize the flow stability. We determine the neutral stability curve over a wide range of Mach numbers and Reynolds numbers. In particular, we examine the effects of compressibility on the flow in transonic regime at low Reynolds numbers. Rossiter modes are identified by spectral analysis. The corresponding spatial structures associated with the dominant and subdominant Rossiter modes are extracted with dynamic mode decomposition. The nature of these structures provides us insight to their contribution to instability of the flow. The interaction between the shock waves and the shear layer modes for the transonic flows are investigated.