Eur. Phys. J. E (2017) 40: 103
https://doi.org/10.1140/epje/i2017-11594-4

Regular Article

Existence of the passage to the limit of an inviscid fluid

¹ Institute of Continuous Media Mechanics, UB RAS, 614013, Perm, Russia
² Department of Theoretical Physics, Perm State University, 614990, Perm, Russia

^* e-mail: Denis.Goldobin@gmail.com

Received: 17 July 2017
Accepted: 7 November 2017
Published online: 24 November 2017

Abstract

In the dynamics of a 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 the description of the flow of an inviscid fluid, does not possess proper turbulent behaviour. This raises the question of the existence of the passage to the limit of an 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 the flow of low-viscosity fluids, and obtain the small parameter quantifying accuracy of this description for real fluids.