テイラー渦流れの不安定性に関するカオス理論による数値解析

抄録

Taylor vortex flow bifurcates to multiple modes depending on the two variables Reynolds number (Re) and aspect ratio (Γ). One example of the bifurcation phenomenon is transition from the Taylor vortex flow to the Wavy Taylor vortex flow with increasing Reynolds number. Through experiment, the critical Reynolds number at which the Taylor vortex flow bifurcated to the wavy Taylor vortex flow has been clarified. In addition, that of the numerical analysis also has been done. However, verification between the numerical results and experimental values is not necessary enough. In this study, the critical Reynolds number in Taylor vortex flow fixed at both ends with the aspect ratio was clarified. In the numerical analysis, the axial velocity change of the Taylor vortex flow which located to the bottom layer was embedded as an attractor in 3-dimensional topological space. The trajectory of attractor made a determination the mode whether the Taylor vortex flow or the wavy Taylor vortex flow. Finally the critical Reynolds number was clarified with the Reynolds number and the aspect ratio from 1.0 to 6.5. The numerical results and experimental results were similar for the two-cell mode, but the quantitative difference were found in the specific region of the aspect ratio for the four- and six- cell modes in the Taylor vortex flow.