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Journal of Applied Mathematics
Volume 2003, Issue 9, Pages 429-446

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

Department of Mathematics, Faculty of Arts and Sciences, Gazi University, Teknikokullar, Ankara 06500, Turkey

Received 28 January 2003; Revised 5 May 2003

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In turbulent flow, the normal procedure has been seeking means 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 u¯ denotes the eddies of size O(δ) and larger. Applying local spatial averaging operator with averaging radius δ 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.