Finite amplitude stability of internal steady flows of the Giesekus viscoelastic rate-type fluid

TL;DR

This paper develops a thermodynamically-based Lyapunov functional to analyze the finite amplitude stability of steady internal flows in Giesekus viscoelastic fluids, providing bounds on flow parameters for guaranteed stability.

Contribution

It introduces a novel Lyapunov functional approach for stability analysis of Giesekus fluids, deriving explicit bounds on Reynolds and Weissenberg numbers for unconditional asymptotic stability.

Findings

Derived bounds on Reynolds and Weissenberg numbers for stability

Applied stability analysis to Taylor–Couette flow

Established unconditional asymptotic stability criteria

Abstract

Using a Lyapunov type functional constructed on the basis of thermodynamical arguments we investigate the finite amplitude stability of internal steady flows of viscoelastic fluids described by the Giesekus model. Using the functional we derive bounds on the Reynolds and the Weissenberg number that guarantee the unconditional asymptotic stability of the corresponding steady internal flow, wherein the distance between the steady flow field and the perturbed flow field is measured with the help of the Bures--Wasserstein distance between positive definite matrices. The application of the theoretical results is documented in the finite amplitude stability analysis of Taylor--Couette flow.