The value of the permeability in fluid flow through porous media is important for process investigation. In low Reynolds number, the classic Darcy’s law is suitable for simulation of fluid flow. In this paper, an experimental study for evaluation of preformed fiber permeability has been done. Also, the deviations from the classical Darcy law by experimental and numerical simulation of the N...

In this paper, we study the dynamic stability of the three-dimensional axisymmetric Navier-Stokes Equations with swirl. To this purpose, we propose a new one-dimensional model that approximates the Navier-Stokes equations along the symmetry axis. An important property of this one-dimensional model is that one can construct from its solutions a family of exact solutions of the threedimensionaFin...

We study the asymptotic behavior, at small viscosity ε, of the NavierStokes equations in a 2D curved domain. The Navier-Stokes equations are supplemented with the slip boundary condition, which is a special case of the Navier friction boundary condition where the friction coefficient is equal to two times the curvature on the boundary. We construct an artificial function, which is called a corr...

In this paper, the jump conditions for the normal derivative of the pressure have been derived for two-phase Stokes (and Navier-Stokes) equations with discontinuous viscosity and singular sources in two and three dimensions. While different jump conditions for the pressure and the velocity can be found in the literature, the jump condition of the normal derivative of the pressure is new. The de...

The Stokes equations are the linearization of the incompressible Navier-Stokes equations about zero. They may be derived directly from the Boltzmann equation as the formal limit of moment equations for an appropriately scaled family of Boltzmann solutions. The present paper establishes this limit for the Boltzmann equation considered over a periodic spatial domain for bounded collision kernels....

We consider both the effect of particle inertia on stochastic Stokes’ drift, and also a related process which could be considered as a crude model of stochastic Stokes’ drift driven by an eddy diffusivity. In the latter, the stochastic forcing is a stable Ornstein–Uhlenbeck process rather than Brownian motion. We show that the eddy Stokes’ drift velocity has a peak at a non-zero value of the co...

This paper details a theoretical modeling of Brillouin ring fiber laser which incorporates the interaction between multiple Brillouin Stokes signals. The ring cavity was pumped at several Brillouin pump (BP) powers and the output was measured through an optical coupler with various coupling ratios. The first-order Brillouin Stokes signal was saturated with the presence of the second-order Stoke...

We present a well-posed model for the Stokes/Brinkman problem with jump embedded boundary conditions (J.E.B.C.) on an immersed interface. It is issued from a general framework recently proposed for fictitious domain problems. Our model is based on algebraic transmission conditions combining the stress and velocity jumps on the interface Σ separating the fluid and porous domains. These condition...

Stokes phenomenon refers to the fact that an asymptotic expansion of complex functions can differ in different regions of the complex plane, and that beyond the so-called Stokes lines the expansion has an unphysical divergence. An important special case is when the Stokes lines emanate from phase space caustics of a complex trajectory manifold. In this case, symmetry determines that to second o...

In [14], S. Montgomery-Smith provides a one dimensional model for the three dimensional, incompressible Navier-Stokes equations, for which he proves the blow up of solutions associated to a class of large initial data, while the same global existence results as for the Navier-Stokes equations hold for small data. In this note the model is adapted to the case of two and three space dimensions, w...