| 概要 |
In this talk I will consider the Couette-Taylor problem, a flow between
two concentric cylinders, whose inner cylinder is rotating with uniform
speed and the outer one is at rest. If the rotating speed is
sufficiently small, the Couette flow (laminar flow) is stable. When the
rotating speed increases, beyond a certain value of the rotating speed,
a vortex flow pattern (Taylor vortex) appears. The Couette-Taylor
problem has been studied for viscous incompressible fluids and the
occurrence of the Taylor vortex was shown to solve a bifurcation problem
for the incompressible Navier-Stokes equations. In this talk, this
problem will be considered for viscous compressible fluids. We study the
spectrum of the linearized operator around the Couette flow and show the
bifurcation of the compressible Taylor vortex when the Mach number is
sufficiently small. It is also shown that the compressible Taylor vortex
converges to the incompressible one when the Mach number tends to zero.
This talk is based on a joint work with Prof. Takaaki Nishida (Kyoto
University) and Ms. Yuka Teramoto (Kyushu University).
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