## Journal of Applied Mathematics

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

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

#### 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 $O\left(\delta \right)$ 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

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1155/S1110757X03301111

**Mathematical Reviews number (MathSciNet)**

MR2005050

**Zentralblatt MATH identifier**

1084.35059

**Subjects**

Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 35Q35

Secondary: 76D03

#### Citation

Kaya, Meryem. Existence of weak solutions for a scale similarity model of the motion of large eddies in turbulent flow. J. Appl. Math. 2003 (2003), no. 9, 429--446. doi:10.1155/S1110757X03301111. https://projecteuclid.org/euclid.jam/1063629204