Viscosity variation in fluid flows across scale

TL;DR

This review explores how spatial and temporal viscosity variations across different scales influence fluid flow behaviors, stability, and transitions, revealing new physical mechanisms and implications for natural and engineered systems.

Contribution

It provides a comprehensive survey of viscosity variation effects across scales, highlighting novel mechanisms and identifying open research questions in fluid dynamics.

Findings

Viscosity gradients couple translation and rotation in low Reynolds number flows.

Viscosity variation alters stability and transition dynamics in shear flows.

Stratification affects energy production and instabilities at high Reynolds numbers.

Abstract

A wide range of natural and engineered fluid flows exhibit spatial or temporal viscosity variations, spanning scales from microbial locomotion to planetary mantle convection. These variations introduce qualitatively new physical mechanisms absent in constant-viscosity flows. This review surveys such phenomena across scales. In low Reynolds number (Stokes) flows, viscosity gradients couple translation and rotation, enabling novel particle responses to uniform forcing-- mechanisms that microorganisms may exploit. In shear flows, viscosity variation alters base flow profiles and breaks symmetries, modifying stability and transition dynamics. At high Reynolds numbers, stratification fundamentally changes the singular perturbation structure governing energy production, enhancing or suppressing canonical instabilities and introducing new ones. Viscosity variation also affects nonnormal growth and nonlinear interactions that drive transition to turbulence. While laminar and fully developed turbulence have been extensively studied, transitional processes remain poorly understood in variable-viscosity flows. In turbulent regimes, viscosity variation impacts jets, wall-bounded flows, and mixing layers. At geophysical scales, incorporating eddy viscosity stratification in climate models may improve predictions, while in Earth's mantle, viscosity contrasts drive large-scale convection and geological evolution. Particle-laden flows, common across contexts, can generate effective viscosity stratification through inhomogeneous loading. Throughout, we highlight cases where viscosity variation alters flow behavior qualitatively, and point to open questions. This review aims to guide graduate students and researchers toward tractable, cross-disciplinary problems.