Existence of weak solutions for a scale similarity model of the motion of large eddies in turbulent flow (Q2570857)

Summary: 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.