Journal of Applied Mathematics

Existence of weak solutions for a scale similarity model of the motion of large eddies in turbulent flow

Meryem Kaya

Abstract

In turbulent flow, the normal procedure has been seeking means $\overline{u}$ of the fluid velocity $u$ rather than the velocity itself. In large eddy simulation, we use an averaging operator which allows for the separation of large- and small-length scales in the flow field. The filtered field $\overline{u}$ denotes the eddies of size $O(\delta)$ and larger. Applying local spatial averaging operator with averaging radius $\delta$ to the Navier-Stokes equations gives a new system of equations governing the large scales. However, it has the well-known problem of closure. One approach to the closure problem which arises from averaging the nonlinear term is the use of a scale similarity hypothesis. We consider one such scale similarity model. We prove the existence of weak solutions for the resulting system.

Article information

Source
J. Appl. Math., Volume 2003, Number 9 (2003), 429-446.

Dates
First available in Project Euclid: 15 September 2003

https://projecteuclid.org/euclid.jam/1063629204

Digital Object Identifier
doi:10.1155/S1110757X03301111

Mathematical Reviews number (MathSciNet)
MR2005050

Zentralblatt MATH identifier
1084.35059

Subjects