One-Dimensional Approximation of 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.

17 pages, 3 figures; v2: refs & comments added

References in corpus (16)

• Nonlinear Fluid Dynamics from Gravity
• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship
• Instabilities of Black Strings and Branes
• The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity
• Rayleigh-Plateau and Gregory-Laflamme instabilities of black strings
• The Incompressible Navier-Stokes Equations From Black Hole Membrane Dynamics
• Black Holes as Lumps of Fluid
• Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations
• High and Low Dimensions in The Black Hole Negative Mode
• Equilibrium configurations of fluids and their stability in higher dimensions
• Plasmarings as dual black rings
• Bifurcation of Plasma Balls and Black Holes to Lobed Configurations
• Black hole-black string phase transitions from hydrodynamics
• Liquid bridges and black strings in higher dimensions
• Curvature driven diffusion, Rayleigh-Plateau, and Gregory-Laflamme