Looking back on what we have learned about TVF since Taylor’s[2] original paper, what seems to be most impressive is the tremendous progress that has been made in the experimental field. Foremost among the modern experimental discoveries is the observation of the WVF by Coles[31].
This study analyzes both the fluid flow of rotating cylinders and the stability of the modulated Couette flow by numerical methods; under different modulated amplitudes and frequencies, the unstable behavior caused by fluid flow influences the Couette flow to become TVF.
Then this study investigates the instability analysis of modulated TVF by utilizing a numerical method. Based on the consideration that the outer cylinder is fixed and the inner cylinder rotates at a non-zero averaged speed under varying modulated amplitudes and frequencies, the flow is converted from one-dimension Couette flow to TVF. When the modulated amplitude is greater than one and the rotation speed of the inner cylinder exceeds the threshold value for one-dimensional flow, the flow will be more stable at intermediate and high frequencies. When the modulated amplitude is sufficiently large and the inner cylinder rotates at medium frequency, subharmonic flow arises.
When the rotational speed of cylinders exceeds the threshold value of stable TVF, the flow will be transformed from TVF to WVF. First, we numerically investigate the lowest stability boundary of TVF for flows with different wavenumbers and for various radius ratios under the inner cylinder rotates at a fixed speed and outer cylinder is stationary. The variation in the wavenumber of a supercritical TVF will cause the various stability of the flow and the wavenumber of Taylor vortices is constant only as long as the flow is quasi-static. The variation in the wavenumber is examined and found to be important when the radius ratio is less than 0.7842. And then we consider the case
wherein η = 0.88, α = 2.7–3.5, and k = 1–3, and we solve the lowest instability 1 boundary of TVF for two concentric rotating cylinders.
One may ask whether it is worth the effort to pursue these obviously very difficult nonlinear aspects of the Taylor vortex problem. The answer to this question seems to be yes, because in the case of TVF we can pursue the formation of turbulence from laminar flow to full turbulent with great precision in all detail through a number of very characteristic stages. In other words, basic theoretical work can be done on this problem, which, in the end, rank as high as the pioneering studies that we have examined in this study.
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自傳
姓 名：林豪傑 性 別：男
出生年月：民國58 年 05 月 19 日 出 生 地：高雄市
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