Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (1): 243-256.
Received:
2018-03-22
Online:
2020-02-26
Published:
2020-04-08
Supported by:
CLC Number:
Heyuan Wang. Dynamical Mechanism and Energy Conversion of Couette-Taylor Flow[J].Acta mathematica scientia,Series A, 2020, 40(1): 243-256.
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r值范围 | 0<acr<σ0 r1=1.4685 | acr>σ re=1.7532 rg=27.5452 rh=31.6102 | |||
定点O | 稳定结点 | 鞍结点(一个方向不稳,另两个方向稳定) | |||
定点P+和P- | 不存在 | 稳定结点 | 稳定结点 | 稳定结点 | 鞍点 |
系统(2.4)相空间中的运动情况 | 趋于稳定定态O | 趋于稳定定态P+或P- | 运动最终按螺旋线趋于P+或P- | 同左,但越靠近rh,轨线在P+和P-之间来回跳动的越频繁,出现暂态混沌,最终趋于P+或P- | 不稳定极限环(亚临界霍普夫分岔) |
动能 | 最小值 | 逐渐增大 | 保持增大 | 增长 | |
Casimir函数 | 最小值 | 逐渐增大 | 保持增大 | 增长 | |
D1与D2之和 | 不存在 | 逐渐递增 | 递增 | 逐渐增大 | |
Coutte-Talor流的实际流动 | Couette流 | 形成规则的Talor涡流及Talor行进波等如图 1(a)(b)(c) | 经过波状涡流等达到暂态混沌如图 1(d) | 不规则湍流(混沌)如图 1(d) |
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