Wall-resolved large-eddy simulations are performed to study the impact of spanwise traveling transversal surface waves in zero-pressure gradient turbulent boundary layer flow. Eighty variations of wavelength, period, and amplitude of the space-and time-dependent sinusoidal wall motion are considered for a boundary layer at a momentum thickness based Reynolds number of Re θ = 1000. The results show a strong decrease of friction drag of up to 26 % and considerable net power saving of up to 10 %. However, the highest net power saving does not occur at the maximum drag reduction. The drag reduction is modeled as a function of the actuation parameters by support vector regression using the LES data. A substantial attenuation of the near-wall turbulence intensity and especially a weakening of the near-wall velocity streaks are observed. Similarities between the current actuation technique and the method of a spanwise oscillating wall without any normal surface deflection are reported. In particular, the generation of a directional spanwise oscillating Stokes layer is found to be related to skin-friction reduction.

Abstract

We propose a universal method for data-driven modeling of complex nonlinear dynamics from time-resolved snapshot data without prior knowledge. Complex nonlinear dynamics govern many fields of science and engineering. Data-driven dynamic modeling often assumes a low-dimensional subspace or manifold for the state. We liberate ourselves from this assumption by proposing cluster-based network modeling (CNM) bridging machine learning, network science, and statistical physics. CNM describes short- and long-term behavior and is fully automatable, as it does not rely on application-specific knowledge. CNM is demonstrated for the Lorenz attractor, ECG heartbeat signals, Kolmogorov flow, and a high-dimensional actuated turbulent boundary layer. Even the notoriously difficult modeling benchmark of rare events in the Kolmogorov flow is solved. This automatable universal data-driven representation of complex nonlinear dynamics complements and expands network connectivity science and promises new fast-track avenues to understand, estimate, predict, and control complex systems in all scientific fields.

We present the first general metric for attractor overlap (MAO) facilitating an unsupervised comparison of flow data sets. The starting point is two or more attractors, i.e., ensembles of states representing different operating conditions. The proposed metric generalizes the standard Hilbert-space distance between two snapshots to snapshot ensembles of two attractors. A reduced-order analysis for big data and many attractors is enabled by coarse-graining the snapshots into representative clusters with corresponding centroids and population probabilities. For a large number of attractors, MAO is augmented by proximity maps for the snapshots, the centroids, and the attractors, giving scientifically interpretable visual access to the closeness of the states. The coherent structures belonging to the overlap and disjoint states between these attractors are distilled by few representative centroids.We employ MAO for two quite different actuated flow configurations: a two-dimensional wake with vortices in a narrow frequency range and three-dimensional wall turbulence with broadband spectrum. In the first application, seven control laws are applied to the fluidic pinball, i.e., the two-dimensional flow around three circular cylinders whose centers form an equilateral triangle pointing in the upstream direction. These seven operating conditions comprise unforced shedding, boat tailing, base bleed, high-and low-frequency forcing as well as two opposing Magnus effects. In the second example, MAO is applied to three-dimensional simulation data from an open-loop drag reduction study of a turbulent boundary layer. The actuation mechanisms of 38 spanwise traveling transversal surface waves are investigated. MAO compares and classifies these actuated flows in agreement with physical intuition. For ‡ Present address : 2 R. Ishar and others instance, the first feature coordinate of the attractor proximity map correlates with drag for the fluidic pinball and for the turbulent boundary layer. MAO has a large spectrum of potential applications ranging from a quantitative comparison between numerical simulations and experimental particle-image velocimetry data to the analysis of simulations representing a myriad of different operating conditions.

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