Search results for "Stokes' law"
showing 5 items of 5 documents
Measurement of the velocity and attenuation of fourth sound in helium II
1979
The velocity and the attenuation of fourth sound have been measured in liquid helium at temperatures between 0.8 K and the λ point, along the vapor pressure curve. The measurements were made using the resonance technique and the helium was contained between small pores in packed powder specimens. From the velocity, it could be determined that the sound propagates under “adiabatic” conditions. According to theory, the attenuation of fourth sound consists of two contributions: surface losses due to heat exchange with the resonator body and volume losses due to dissipative processes associated with the viscosity coefficients η and ζ3. The results of our attenuation measurements are in agreemen…
VORTEX LAYERS IN THE SMALL VISCOSITY LIMIT
2006
In this paper we suppose that the initial datum for the 2D Navier–Stokes equations are of the vortex layer type, in the sense that there is a rapid variation in the tangential component across a curve. The variation occurs through a distance which is of the same order of the square root of the viscosity. Assuming the initial as well the matching (with the outer flow) data analytic, we show that our model equations are well posed. Another necessary assumption is that the radius of curvature of the curve is much larger than the thickness of the layer.
Zero Viscosity Limit for Analytic Solutions of the Navier-Stokes Equation on a Half-Space.¶ II. Construction of the Navier-Stokes Solution
1998
This is the second of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space in either 2D or 3D. Under the assumption of analytic initial data, we construct solutions of Navier-Stokes for a short time which is independent of the viscosity. The Navier-Stokes solution is constructed through a composite asymptotic expansion involving the solutions of the Euler and Prandtl equations, which were constructed in the first paper, plus an error term. This shows that the Navier-Stokes solution goes to an Euler solution outside a boundary layer and to a solution of the Prandtl equations within the boundary layer. The error term is written as a sum of firs…
ASYMPTOTIC ANALYSIS OF THE LINEARIZED NAVIER–STOKES EQUATION ON AN EXTERIOR CIRCULAR DOMAIN: EXPLICIT SOLUTION AND THE ZERO VISCOSITY LIMIT
2001
In this paper we study and derive explicit formulas for the linearized Navier-Stokes equations on an exterior circular domain in space dimension two. Through an explicit construction, the solution is decomposed into an inviscid solution, a boundary layer solution and a corrector. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction term is shown to be of the same order of magnitude as the square root of the viscosity. Copyright © 2001 by Marcel Dekker, Inc.
Non-Local Scattering Kernel and the Hydrodynamic Limit
2007
In this paper we study the interaction of a fluid with a wall in the framework of the kinetic theory. We consider the possibility that the fluid molecules can penetrate the wall to be reflected by the inner layers of the wall. This results in a scattering kernel which is a non-local generalization of the classical Maxwell scattering kernel. The proposed scattering kernel satisfies a global mass conservation law and a generalized reciprocity relation. We study the hydrodynamic limit performing a Knudsen layer analysis, and derive a new class of (weakly) nonlocal boundary conditions to be imposed to the Navier-Stokes equations.