Data-Driven Discovery of a New Ginzburg-Landau Reduced-Order Model for Vortex Shedding

TL;DR

This paper introduces a data-driven approach to discover a new Landau variable and reduced-order models for vortex shedding, enhancing understanding and control of fluid dynamics phenomena.

Contribution

It develops a novel Landau variable for the Ginzburg-Landau equation and constructs interpretable local and global reduced-order models from simulation data.

Findings

Discovered a new Landau variable for vortex shedding.

Built interpretable PDE models with SINDy that capture wake dynamics.

Validated models across different regions of the wake.

Abstract

Vortex shedding is an important physical phenomenon observed across many spatial and temporal scales in fluids. Previous experimental and theoretical studies have established a hierarchy of local and global reduced-order models for vortex shedding based on the Stuart-Landau and Ginzburg-Landau equations. In this work, we employ data-driven methods to discover a new Landau variable for the complex Ginzburg-Landau equation (CGLE) for periodic two-dimensional vortex shedding past a cylinder. We first coarse grain vorticity field data from direct numerical simulations of the fluid by integrating over the vertical spatial dimension, and then time-delay embed this new variable to obtain phase information necessary for CGLE analysis. Finally, we use the sparse identification of nonlinear dynamics (SINDy) to learn an interpretable system of coupled real partial differential equations that balance model complexity and prediction error. We develop local homogeneous models in key regions of the wake, as well as global heterogeneous models that are parameterized by the streamwise coordinate across the entire wake. After computing the normal-form parameters from the discovered equations, we classify the different models and determine behavior and stability in the different regions of the wake, demonstrating the validity of these models across a range of spatiotemporal subdomains. Different dynamics are found to dominate at different stations within the wake. In addition to introducing a novel Landau variable for vortex shedding, this work may also help characterize other vortex shedding systems and inform the design of control schemes.