Energy dissipation in flows through curved spaces

TL;DR

This paper demonstrates that fluid flows in curved spaces inherently experience energy loss due to curvature-induced viscous stresses, even without obstacles or walls, revealing a fundamental dissipation mechanism.

Contribution

It uncovers a novel energy dissipation process in fluid dynamics caused solely by the intrinsic curvature of the space, independent of traditional viscous effects.

Findings

Curvature induces viscous stresses in fluid flows without obstacles.

Energy dissipation occurs solely due to space curvature effects.

The process may significantly impact physical systems involving curved geometries.

Abstract

Fluid dynamics in intrinsically curved geometries is encountered in many physical systems in nature, ranging from microscopic bio-membranes all the way up to general relativity at cosmological scales. Despite the diversity of applications, all of these systems share a common feature: the free motion of particles is affected by inertial forces originating from the curvature of the embedding space. Here we reveal a fundamental process underlying fluid dynamics in curved space: the free motion of fluids, in the complete absence of solid walls or obstacles, exhibits loss of energy due exclusively to the intrinsic curvature of space. We find that local sources of curvature generate viscous stresses as a result of the inertial forces. The curvature-induced viscous forces are shown to cause hitherto unnoticed and yet appreciable energy dissipation, which might play a significant role for a variety of physical systems involving fluid dynamics in curved spaces.