From the application of composite DMD to turbulent channel flow databases at ReT~200 and ReT~932, we find that a dozen modes suffice to reconstruct the Reynolds stresses profiles.
Skin friction coefficient skin#
In this work, we have considered combining skin friction (C_f(t_j)) and either the streamwise perturbation velocity field (u’(x, t_j)) or the Reynolds shear stress field (u’v‘(x, t_j)). The first category of the techniques introduces multiple variables into the snapshots sequence and proposes a weighted β factor to classify the modes of close relevance with weighted variable, which highly reduce the number of modes that needed to reconstruct the flow filed. The techniques applied can be classified into three categories: (i) composite DMD to help extract DMD modes from composite variables that are closely related to the physics of interest, (ii) agglomeration strategies applied with DMD that highly compress the large databases while retaining the accuracy of feature detection, and (iii) a new θ-DMD to deal with non-uniformly sampled databases from numerical or experimental results. In this thesis, we develop several techniques for Dynamic Mode Decomposition (DMD) method to deal with the problem of large flow database analysis. Finally, the current analysis also revealed w's trivial role in this convection-dominated free-shear flow, Reynolds stresses' spectral description of cascading eddies, vortices' sensitivity to dilation and indifference to distortion, and structure responses' origin in vortex activities. The complete revelation of the prism wake essentially comes down to understanding the six mechanisms, which Part 2 (Li et al., 2022) will address by investigating the physical interpretations of the duplets' in-synch, phenomenological features. The downstream wall remains a distinct interface and is dominated by four other mechanisms. The upstream and crosswind walls constitute a dynamically unified interface dominated by only two mechanisms. The LTI reduced the subcritical prism wake during shear layer transition II into only six dominant excitation-response Koopman modal duplets. The DMD also approximated the Koopman modes with O-8 error. Through a pedagogical demonstration on a prism wake and the rudimentary Dynamic Mode Decomposition algorithm, results show a near-exact linearization of nonlinear turbulence, with mean and rms errors of O-12 and O-9, respectively. The architecture is data-driven and modular, accommodating all types of data and Koopman algorithms. It also develops the Koopman-LTI architecture-a systematic procedure to associate fluid excitation and structure surface pressure by matching Koopman eigen tuples, solving a longstanding problem for fluid-structure interactions. This work proposes a Linear-Time-Invariance (LTI) notion to the Koopman analysis, finding an invariant subspace on which Koopman modes are consistent and physically meaningful. Preliminary studies of the two-dimensional skin-friction data through the late transitional regime, using DMD (, showed that the plateau that appears at Re x ≈ 5.7 × 10 5, where Re x is the Reynolds number based on the distance from the leading edge of the plate, coincides with the first appearance of hairpin-like structures, and that the trace of these structures is successfully reproduced using a few low-frequency DMD modes. Therefore, the application of DMD to the late transitional regime, which is marked by a significant rise in the skin-friction coefficient, as shown in figure 1, would help in identifying the coherent structures associated with this rise and provide a reduced-order representation of the flow structures. is of particular relevance as coherent structures can be extracted from wall-bounded flows using different techniques however, any such effort would be of limited use unless it can be shown that these extracted structures contribute notably to the dynamics of the underlying turbulent flow.
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