In turbulent flow, the normal procedure has been seeking means of the fluid velocity 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 denotes the eddies of size and larger. Applying local spatial averaging operator with averaging radius 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.
Meryem Kaya. "Existence of weak solutions for a scale similarity model of the motion of large eddies in turbulent flow." J. Appl. Math. 2003 (9) 429 - 446, 7 August 2003. https://doi.org/10.1155/S1110757X03301111