On existence of passage to the limit of inviscid fluid

Abstract

With the dynamics of viscous fluid, the case of vanishing kinematic viscosity is actually the case of Reynolds number tending to infinity. Hence, in the limiting case 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. The latter rises the question of existence of the passage to the limit of inviscid fluid for real weakly-viscous fluids. To address this question, one should employ the theory of turbulent boundary layer near an uninflectable 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 weakly-viscous fluids, and derive the small parameter quantifying accuracy of this description for real fluids.Received 16.05.2016; accepted 30.06.2016