Large-scale structures have been observed in many shear flows which are the fluid generated between two surfaces moving with different velocity. A better understanding of the physics of the structures (especially large-scale structures) in shear flows will help explain a diverse range of physical phenomena and improve our capability of modeling more complex turbulence flows. Many efforts have been made in order to capture such structures; however, conventional methods have their limitations, such as arbitrariness in parameter choice or specificity to certain setups. To address this challenge, we propose to use Multi-Resolution Dynamic Mode Decomposition (mrDMD), for large-scale structure extraction in shear flows. In particular, we show that the slow motion DMD modes are able to reveal large-scale structures in shear flows that also have slow dynamics. In most cases, we find that the slowest DMD mode and its reconstructed flow can sufficiently capture the large-scale dynamics in the shear flows, which leads to a parameter-free strategy for large-scale structure extraction. Effective visualization of the large-scale structures can then be produced with the aid of the slowest DMD mode. To speed up the computation of mrDMD, we provide a fast GPU-based implementation. We also apply our method to some non-shear flows that need not behave quasi-linearly to demonstrate the limitation of our strategy of using the slowest DMD mode. For non-shear flows, we show that multiple modes from different levels of mrDMD may be needed to sufficiently characterize the flow behavior.

Abstract Most existing unsteady flow visualization techniques concentrate on the depiction of geometric patterns in flow, assuming the geometry information provides sufficient representation of the underlying physical characteristics, which is not always the case. To address this challenge, this work proposes to analyse the time‐dependent characteristics of the physical attributes measured along pathlines which can be represented as a series of time activity curves (TAC). We demonstrate that the temporal trends of these TACs can convey the relation between pathlines and certain well‐known flow features (e.g. vortices and shearing layers), which enables us to select pathlines that can effectively represent the physical characteristics of interest and their temporal behaviour in the unsteady flow. Inspired by this observation, a new TAC‐based unsteady flow visualization and analysis framework is proposed. The centre of this framework is a new similarity measure that compares the similarity of two TACs, from which a new spatio‐temporal, hierarchical clustering that classifies pathlines based on their physical attributes, and a TAC‐based pathline exploration and selection strategy are proposed. A visual analytic system incorporating the TAC‐based pathline clustering and exploration is developed, which also provides new visualizations to support the user exploration of unsteady flow using TACs. This visual analytic system is applied to a number of unsteady flow in 2D and 3D to demonstrate its utility. The new system successfully reveals the detailed structure of vortices, the relation between shear layer and vortex formation, and vortex breakdown, which are difficult to convey with conventional methods.

Taylor-Couette flow (TCF) is the turbulent fluid motion created between two concentric and independently rotating cylinders. It has been heavily researched in fluid mechanics thanks to the various nonlinear dynamical phenomena that are exhibited in the flow. As many dense coherent structures overlap each other in TCF, it is challenging to isolate and visualize them, especially when the cylinder rotation ratio is changing. Previous approaches rely on 2D cross sections to study TCF due to its simplicity, which cannot provide the complete information of TCF. In the meantime, standard visualization techniques, such as volume rendering / iso-surfacing of certain attributes and the placement of integral curves/surfaces, usually produce cluttered visualization. To address this challenge and to support domain experts in the analysis of TCF, we developed a visualization framework to separate large-scale structures from the dense, small-scale structures and provide an effective visual representation of these structures. Instead of using a single physical attribute as the standard approach which cannot efficiently separate structures in different scales for TCF, we adapt the feature level-set method to combine multiple attributes and use them as a filter to separate large- and small-scale structures. To visualize these structures, we apply the iso-surface extraction on the kernel density estimate of the distance field generated from the feature level-set. The proposed methods successfully reveal 3D large-scale coherent structures of TCF with different control parameter settings, which are difficult to achieve with the conventional methods.

Despite significant advances in the analysis and visualization of unsteady flow, the interpretation of it's behavior still remains a challenge. In this work, we focus on the linear correlation and non-linear dependency of different physical attributes of unsteady flows to aid their study from a new perspective. Specifically, we extend the existing spatial correlation quantification, i.e. the Local Correlation Coefficient (LCC), to the spatio-temporal domain to study the correlation of attribute-pairs from both the Eulerian and Lagrangian views. To study the dependency among attributes, which need not be linear, we extend and compute the mutual information (MI) among attributes over time. To help visualize and interpret the derived correlation and dependency among attributes associated with a particle, we encode the correlation and dependency values on individual pathlines. Finally, to utilize the correlation and MI computation results to identify regions with interesting flow behavior, we propose a segmentation strategy of the flow domain based on the ranking of the strength of the attributes relations. We have applied our correlation and dependency metrics to a number of 2D and 3D unsteady flows with varying spatio-temporal kernel sizes to demonstrate and assess their effectiveness.