One-Dimensional Approximation of Viscous Flows

TL;DR

This paper derives simplified one-dimensional equations from Navier-Stokes to analyze viscous fluid flows, enabling study of instability behaviors and self-similarity in fluid dynamics and their connections to gravitational phenomena.

Contribution

It introduces a (1+1)-dimensional model for viscous flows, extending drop formation theory to explore instability evolution and self-similarity in fluid/gravity correspondence.

Findings

Derivation of simplified (1+1)-D equations from Navier-Stokes.

Potential to analyze instability evolution and self-similar behaviors.

Framework for exploring fluid/gravity duality in viscous flows.

Abstract

Attention has been paid to the similarity and duality between the Gregory-Laflamme instability of black strings and the Rayleigh-Plateau instability of extended fluids. In this paper, we derive a set of simple (1+1)-dimensional equations from the Navier-Stokes equations describing thin flows of (non-relativistic and incompressible) viscous fluids. This formulation, a generalization of the theory of drop formation by Eggers and his collaborators, would make it possible to examine the final fate of Rayleigh-Plateau instability, its dimensional dependence, and possible self-similar behaviors before and after the drop formation, in the context of fluid/gravity correspondence.