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In averaging the Navier-Stokes equations the problem of closure arises. Scale similarity models address closure by (roughly speaking) extrapolation from the (known) resolved scales to the (unknown) unresolved scales. In a posteriori tests scale similarity models are often the most accurate but can prove to be unstable when used in a numerical simulation. In… (More)

We consider four turbulent models to simulate the boundary mixing layer of the ocean. We show the existence of solutions to these models in the steady-state case then we study the mathematical stability of these solutions.

We consider a deconvolution model for 3D periodic flows. We show the existence of a global attractor for the model.

We consider a system of equations that models the stationary flow of two im-miscible turbulent fluids on adjacent subdomains. The equations are coupled by nonlinear boundary conditions on the interface which is here a fixed given surface. We propose a spectral discretization of this problem and perform its numerical analysis. The convergence of the method… (More)

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