![]() ![]() low wave speed) and very small wave amplitude expansion of the three dimensional incompressible Euler equations in a basin with a free upper surface and a spatially varying bottom topography. These equations arise to first order in a low aspect ratio, low Froude number (i.e. We prove global well-posedness for the great lake equations. The physical velocity is replaced by the seepage velocity, being the velocity average over a representative pore volume. ![]() Introduction It is well-known that averaging of the equation describing an incompressible flow through a porous medium leads to Darcy's law. Beavers and Joseph's law, homogenization, effective interface law AMS subject classifications. Furthermore, the coefficient in the law is determined through an auxiliary boundary-layer type problem. It is valid when the pore size of the porous medium tends to zero. After studying the corresponding boundary layers, we obtain rigorously Saffman's modification of the interface condition observed by Beavers and Joseph. It is supposed, as in the experiment by Beavers and Joseph, that a uniform pressure gradient is maintained in the longitudinal direction in both the channel and the porous medium. We consider the laminar viscous channel flow over a porous surface. We compare ɛ and for realistic data and our results lead to the conclusion that the riblets reduce significantly tangential drag, which mayĮxplain their presence on the skin of Nektons. Is found that for the riblets of the characteristic size ɛ, being of the order smaller or equal to, the approximation obtained for the tangential drag could be applied. Then the result is applied to the viscous sub-layers around immersed bodies, strictly containing the surface riblets. Also the uniqueness of the solution is expressed through a non-linear algebraic condition linking and L The velocity of the upper plate and the distance between the plates L In all estimates explicit dependence on the kinematic viscosity ν, ) approximation for the tangential drag force is found. With the matrix coefficient in front of the effective shear stress, calculated using a boundary layer problem. In the effective solution the effect of roughness enters through the Navier slip condition ) approximation for the effective mass flow and an O(ɛ In the limit ɛ → 0 we find the effective Couette-Navier flow as an O(ɛ The lower plate is fixed and has periodically placed riblets of the characteristic We consider the Couette flow between two plates. ![]()
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