A composite dynamic mode decomposition analysis of turbulent channel flows

Abstract

In this contribution, we consider the Dynamic Mode Decomposition (DMD) framework as a purely data-driven tool to investigate both standard and actuated turbulent channel databases via Direct Numerical Simulation (DNS). Both databases have comparable Reynolds number Re » 3600. The actuation consists in the imposition of a stream wise-varying sinusoidal spanwise velocity at the wall, known to lead to drag reduction. Specifically, a composite-based DMD analysis is conducted, with hybrid snapshots composed by skin friction and Reynolds stresses. A small number of dynamic modes (~3-9) are found to recover accurately the DNS Reynolds stresses near walls. Moreover, the DMD modes retrieved propagate at a range ofphase speeds consistent with those reported in the literature. We conclude that composite DMD is an attractive, purely data-driven tool to study turbulent flows. On the one hand, DMD is helpful to identify features associated with the drag, and on the other hand, it reveals the changes in flow structure when actuation is imposed.

Dynamic Mode Decomposition Analysis of Spatially Agglomerated Flow Databases

“…We will consider the temporal sequence formed by the Reynolds shear stress fields, u v x, t j . Following Reference [32], a simplified database that still represents the turbulent physics is obtained by removing every other point along the homogeneous x and z directions and retaining only either the lower or upper half of the domain. The resulting database, V ∈ R n p ×N with n p = 117,504 and N = 1200, is still large enough to pose a tough challenge for most workstations.…”

“…The first testcase considered is a toy model, a synthetic flow field studied already in References [16,30]. The second testcase considered is the Re D = 60 flow around the mid section of infinitely long cylinder [20], whereas the third testcase is the turbulent channel flow at Re τ ≈ 200 [31,32].…”

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“…Moreover, dynamic mode decomposition (DMD), originally used as a tool to identify patterns in fluid dynamics (see e.g. [32], [33], [34], [35]), was reused in the medical field. Tirunagari et al [36] incorporated different extensions of DMD to develop a novel automated, registration-free movement correction approach for kidney dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI).…”

Suppression of vortex shedding using a slit through the circular cylinder at low Reynolds number

“…Usually, the investigation of the complex interaction between wake features needs the use of the modal decomposition technique in such flows. Moreover, the POD also helps to evaluate the dominant shedding modes 44 .…”