L’équation stationnaire de Navier Stokes dans le système de coordonnées de coordonnées cylindriques, décrivant l’écoulement dans le domaine de W = {0. En mécanique des fluides le tourbillon de Lamb-Oseen est un écoulement tourbillonnaire de géométrie cylindrique et d’extension infinie, solution des équations de Navier-Stokes ainsi nommé d’après les travaux de Horace Lamb et de Carl Wilhelm Oseen. Il est décrit dans un système de coordonnées cylindriques par. Navier-Stokes equations in cylindrical coordinates which allows the incorporation of compressible and coordonnées cylindriques. Ceci permet l’incorporation.

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Tourbillon de Lamb-Oseen

Record 1 of 1. Waves on shear and vortex flows and the stability of the Moore-Saffman model for a trailing wingtip vortex.

This thesis comprises three papers. In the first, the eigenvalue problem governing the propagation of long nonlinear surface waves is investigated when there is a current u y beneath dw surface, y being the vertical coordinate.


Aux origines de la loi de Darcy ()

Cylindique consider specific velocity profiles such as boundary layer profiles of the Falkner-Skan similarity type, including the Blasius case. The singular solutions of the Rayleigh equation are examined to gain insight about the long wave limit of such solutions.

The second paper considers the inviscid linear stability of a trailing vortex using mean flow profiles given by an approximate solution of the Navier-Stokes equations.

The axial and tangential velocity profiles obtained from this solution, deduced by Moore and Saffmanagree well with experiments involving wings at slight angles of attack; in particular, they better describe the jet-like and wake-like axial flows near the center of the vortex than does the much-studied similarity solution found by Batchelor We numerically obtain growth rates for unstable perturbations for different values of n, a wingtip loading parameter.

Finally, we study the elliptical modes of instability in a pair of counter-rotating trailing wingtip vortices using the aforementioned Moore-Saffman vortex model. To this end, a direct numerical simulation is performed using a spectral method in cylindrical coordinates developed by Matsushima and Marcus We obtain growth rates and eigenmodes, several of which suggest the presence of a critical layer singularity in the radial coordinate r.


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Moreover, we compare our results to those for the Batchelor vortex, which is the model that most recent investigations have employed. As is clear from the above, the subject matter of this thesis is twofold: However distinct, both subjects have in common the presence of a critical layer singularity, which has a profound impact on the solutions of the equations governing each flow.

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