Dynamics-augmented cluster-based network model

In this study, we propose a novel data-driven reduced-order model for complex dynamics, including nonlinear, multi-attractor, multi-frequency, and multiscale behaviours. The starting point is a fully automatable cluster-based network model (CNM) (Li et al. J. Fluid Mech. vol.906, 2021, A21) which kinematically coarse-grains the state with clusters and dynamically predicts the transitions in a network model. In the proposed dynamics-augmented CNM (dCNM), the prediction error is reduced with trajectory-based clustering using the same number of centroids. The dCNM is first exemplified for the Lorenz system and then implemented for the three-dimensional sphere wake featuring periodic, quasi-periodic and chaotic flow regimes. For both plants, the dCNM significantly outperforms the CNM in resolving the multi-frequency and multiscale dynamics. This increased prediction accuracy is obtained by stratification of the state space aligned with the direction of the trajectories. Thus, the dCNM has numerous potential applications to a large spectrum of shear flows, even for complex dynamics

Network community-based analysis of complex vortical flows: Laminar and turbulent flows

The nonlinear interactions amongst vortical structures in fluid flows make their characterization and control a challenge, particularly in turbulence. In this work, a network (graph) community-based framework is introduced to formulate reduced-order models and perform flow-modification of complex laminar and turbulent vortical flows. The present framework represents the vortical interactions on a network, where the vortical elements are viewed as the nodes and the vortical interactions are regarded as edges weighted by induced velocity from the Biot--Savart law. This formulation enables the use of circulation and spatial arrangement of vortical elements for structure extraction from a flow field. The network-based community detection algorithm is used to identify closely interacting vortical elements, called communities. The methodology is used to extract communities of vortical elements in two- and three-dimensional flows, namely for a collection of discrete point vortices, laminar cylinder and airfoil wakes, and decaying two- and three-dimensional isotropic turbulence.We introduce a community-based reduced-order modeling formulation to capture key interactions amongst coherent structures in high-dimensional unsteady vortical flows. The overall interaction-based physics of the high-dimensional flow field is distilled into the vortical community centroids, considerably reducing the system dimension. Taking advantage of the vortical interactions, the proposed methodology is applied to formulate reduced-order models for the inter-community dynamics of vortical flows and predict lift and drag forces on bodies in wake flows. We demonstrate the capabilities of these models by accurately capturing the macroscopic dynamics of a collection of discrete point vortices, and the complex unsteady aerodynamic forces on a circular cylinder and an airfoil with a Gurney flap. The present formulation is found to be robust against simulated experimental noise and turbulence due to its integrating nature of the system reduction.Furthermore, we show that the inter- and intra-community interactions can be used to identify the communities which have the strongest and weakest interactions amongst them. These vortical communities are referred to as the connector and peripheral communities, respectively. We demonstrate the influence of the network-based structures to modify the dynamics of a collection of discrete point vortices. Taking advantage of the strong inter-community interactions, connector community can significantly modify the collective dynamics of vortices through the application of multiple impulse perturbations. We then apply the community-based framework to extract influential structures in isotropic turbulence. The connector and peripheral communities extracted from turbulent flows resemble shear-layer and vortex-core like structures, respectively. The influence of the connector structures on the flow field and their neighboring vortical structures is analyzed by adding impulse perturbations to the connectors in direct numerical simulations. The findings are compared with the cases of perturbing the strongest vortex tube and shear-layer regions. We find that perturbing the connector structures enhances local turbulent mixing beyond what are achieved by the other cases