By Radyadour Kh. Zeytounian

For the fluctuations round the potential yet really fluctuations, and showing within the following incompressible procedure of equations: on any wall; at preliminary time, and are assumed recognized. This contribution arose from dialogue with J. P. Guiraud on makes an attempt to push ahead our final co-signed paper (1986) and the most suggestion is to place a stochastic constitution on fluctuations and to spot the massive eddies with part of the chance house. The Reynolds stresses are derived from one of those Monte-Carlo strategy on equations for fluctuations. these are themselves modelled opposed to a method, utilizing the Guiraud and Zeytounian (1986). The scheme is composed in a collection of like equations, regarded as random, simply because they mimic the massive eddy fluctuations. The Reynolds stresses are bought from stochastic averaging over a kin in their recommendations. Asymptotics underlies the scheme, yet in a slightly free hidden approach. We clarify this in relation with homogenizati- localization approaches (described in the §3. four ofChapter 3). Ofcourse the mathematical good posedness of the scheme isn't recognized and the numerics will be bold! no matter if this try will motivate researchers within the box of hugely advanced turbulent flows isn't really foreseeable and we've got wish that the belief will end up worthy.

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**Sample text**

Flow which occurs within a closed cavity, the walls of which deform with motion very slowly in comparison to the speed of sound (low Mach number internal flow) is a very interesting singular asymptotic problem related to acoustic phenomena. In this case we see the impossibility of matching an approximation of the starting process with the approximation resulting from the (outer) classical approach, as a consequence of the persistence of acoustic oscillations in the deformable cavity and the application of a Multiple Scale Method (MSM) is necessary, with an “homogenization” procedure.

5) a classical solution for the free surface is and, in fact, NEWTONIAN FLUID FLOW: EQUATIONS AND CONDITIONS 39 for a flat bottom simulated by the equation: z = - h° = const. 59a), a° is the characteristic amplitude for the initial elevation of a free surface characterized by the function and l° is the characteristic wavelength in the horizontal x-direction. 6), the asymptotic theory an axial compressor relies on inviscid, incompressible flow equations and slip boundary conditions on the blades and is derived from the assumption that the number of blades per row, N, is much greather than one.

The second type of situation corresponds to the case when the small parameter is built into the particular solution one looks for without being directly apparent into the formulation of the problem. This is the case in the theory of small amplitude waves of any kind, surface waves for example. Here the small parameter is a ratio of lengths, namely the amplitude divided by the wavelength. Of course the parameter may be built into the model, in order to carry over expansions, but it is basically a property of the solution considered, rather than a parameter existing beforehand.