Invariant recurrent solutions embedded in a turbulent two-dimensional Kolmogorov flow

By Gary J. Chandler, Rich R. Kerswell. Journal of Fluid Mechanics, 2013

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How researchers see this paper

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A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction (2022, methodology): “The dataset we considered is the 2-dimensional Kolmogorov ﬂow, 69 governed by the Navier-Stokes equation for incompressible ﬂow.”
Enhancing computational fluid dynamics with machine learning (2021, background): “[25] for the twodimensional Kolmogorov flow [26], which maintains fluctuations via a forcing term.”
Factorized Fourier Neural Operators (2021, methodology): “PDEs on regular grids The four Torus datasets on regular grids (TorusLi, TorusKochkov, TorusVis, and TorusVisForce, summarized in Table 1) are simulations based on Kolmogorov ﬂows which have been extensively studied in the literature (Chandler & Kerswell, 2013).”
Machine learning–accelerated computational fluid dynamics (2021, unknown): “In particular, we first consider Kolmogorov flow [41], a parametric family of forced turbulent flows obeying the Navier-Stokes equation [(1)], with forcing f = sin(4y)x̂− 0.”