Abstract
Large scale structures have been observed in many turbulent wall bounded flows, such as pipe, Couette or square duct flows. Many efforts have been made in order to capture such structures to understand and model them. However, commonly used methods have their limitations, such as arbitrariness in parameter choice or specificity to certain setups. In this manuscript we attempt to overcome these limitations by using two variants of Dynamic Mode Decomposition (DMD). We apply these methods to (rotating) Plane Couette flow, and verify that DMD-based methods are adequate to detect the coherent structures and to extract the distinct properties arising from different control parameters. In particular, these DMD variants are able to capture the influence of rotation on large-scale structures by coupling velocity components. We also show how high-order DMD methods are able to capture some complex temporal dynamics of the large-scale structures. These results show that DMD-based methods are a promising way of filtering and analysing wall bounded flows.
Highlights
Turbulent flows are generally characterized by chaotic motion and abundant mixing
Before introducing the results obtained with Dynamic Mode Decomposition (DMD) methods, we report here a visualization of the velocity flow fields of 2D slices in the x − z plane taken at fixed wall-normal distance: at the centerline y = h and close to the wall at y+ ≈ 15
4.1. multi-resolution DMD (mrDMD) We first applied the mrDMD method to a collection of 1000 snapshots of 2D slices in the x − z plane taken at fixed wall-normal distance: at the centerline y = h and close to the wall at y+ ≈ 15
Summary
Turbulent flows are generally characterized by chaotic motion and abundant mixing. But within certain canonical systems, experiments and simulations have detected coherent large scale structures [1, 2]. Direct numerical simulations (DNS) of PC flow have found extremely long structures that are far larger than the inter-plate distance [3, 4, 5, 6]. To accurately capture these structures, we require computational boxes that are large enough to fit them. Large-scale structures have some important practical impact, having the general role of redistributing friction and heat flux along the walls and across the flow [2]. Small computational boxes that fail to capture these large-scale structures can considerably alter the flow behaviour and statistics [3]
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