Institute of Mathematics for Industry


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Bifurcation of the compressible Taylor vortex

Hold Date 2017-05-26 15:30~2017-05-26 17:00

Place 2nd floor room D, Seminar House, Fukuoka University

Object person  

Speaker Yoshiyuki KAGEI (Kyushu University)

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).