Existence of the passage to the limit of inviscid fluid

TL;DR

This paper investigates whether the behavior of low-viscosity fluids can be accurately described by the Euler equation as viscosity approaches zero, using turbulent boundary layer theory to bridge the gap between viscous and inviscid flow models.

Contribution

It introduces a framework based on turbulent boundary layer theory to analyze the passage to the limit of inviscid fluid flow for real low-viscosity fluids.

Findings

Establishes conditions under which Euler equations approximate low-viscosity fluid flow.

Quantifies the accuracy of inviscid models for real fluids with small viscosity.

Provides a theoretical basis for understanding turbulence emergence in the inviscid limit.

Abstract

In the dynamics of viscous fluid, the case of vanishing kinematic viscosity is actually equivalent to the Reynolds number tending to infinity. Hence, in the limit of vanishing viscosity the fluid flow is essentially turbulent. On the other hand, the Euler equation, which is conventionally adopted for description of flow of inviscid fluid, does not possess proper turbulent behaviour. This raises the question of the existence of the passage to the limit of inviscid fluid for real low-viscosity fluids. To address this question, one should employ the theory of turbulent boundary layer near an inflexible boundary (e.g., rigid wall). On the basis of this theory, one can see how the solutions to the Euler equation become relevant for the description of flow of low-viscosity fluids, and obtain the small parameter quantifying accuracy of this description for real fluids.