Extraction of invariant manifolds and application to turbulence with a passive scalar

TL;DR

This paper introduces a method to identify invariant manifolds in reduced fluid dynamics models, demonstrating its application to turbulence with a passive scalar to extract physical insights.

Contribution

A novel method for identifying invariant manifolds in reduced models of fluid systems, applied to turbulence with passive scalar fields.

Findings

Identification of invariant manifolds in turbulence models

Application to Lagrangian evolution of field gradients

Enhanced understanding of turbulence dynamics

Abstract

The reduction of dimensionality of physical systems, specially in fluid dynamics, leads in many situations to nonlinear ordinary differential equations which have global invariant manifolds with algebraic expressions containing relevant physical information of the original system. We present a method to identify such manifolds, and we apply it to a reduced model for the Lagrangian evolution of field gradients in homogeneous and isotropic turbulence with a passive scalar.