2007 Fiscal Year Final Research Report Summary
Accurate Analysis of Turbulence Dynamics using Unstable Periodic Flow
| Project/Area Number |
17340118
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Kyoto University |
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Principal Investigator |
KIDA Shigeo Kyoto University, Graduate School of Engineering, Professor (70093234)
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| Co-Investigator(Kenkyū-buntansha) |
KAWAHARA Genta Osaka Univ., School of Engineering Science, Professor (50214672)
GOTO Susumu Kyoto Univ, Graduate School of Engineering, Assistant Professor (40321616)
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| Project Period (FY) |
2005 – 2007
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| Keywords | Unstable periodic flow / Couette system / Turbulent mixing / Passive vector |
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| Research Abstract |
Fluid mixing is one of the most prominent characteristics of turbulence. In order to understand the mixing dynamics and to develop a quantitative description of its statistical properties we performed the unstable-periodic-flow (UPF) analysis of the passive vectors advected in a Couette system. The unrepeatability of turbulence is one of the main causes which make the turbulence research difficult. In contrast the UPF discovered by Kawahara and Kida (2001), which has positive Lyapunof number, repeats exactly the same state for ever. Therefore, by using the UPF, we can calculate the statistics associated with flows as accurately as desired in proportion to the time devoted. We distribute many passive vectors in this UPF, and compare their stretching rate and orientation with the flow structures. It is found that those passive vectors which start at the same position but with different orientation, will align in direction in a finite time (of order of the period of UPF). This suggests th
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at the directional field of passive vectors may be uniquely defined as a function of the time and position of the UPF. We examine then how are those passive vectors that are distributed uniformly in space will rearrange as the time progresses. We divide the flow field into many small cubes, and calculate the statistics of the direction of passive vectors in each cube. The passive vectors are aligned in a line in most of the cubes. On the other hand, there are quite a few cubes in which the directions of passive vectors are aligned in a plane. We confirmed that such planes are parallel to the vorticity vector and that it is caused by the advection due to strong tubular vortices in the flow. The fluid mixing is enhanced around such places where the direction of passive vectors is diverse. The main organized structure in the Couette turbulence is the streamwise vortex, which creates the ejection and sweep regions near the wall boundary. The linear alignment of passive vectors is found in the interior of the streamwise vortices as well as in the ejection region. The planar distribution, on the other hand, is observed in the periphery of the streamwise vortices and in the sweep region. Such correspondence between the directional distribution of passive vectors and the flow structure depends on the near-past (between the present time and the past about a half of the period of UPF). The passive vectors lose their memory in the characteristic time of the turbulence. This is of essential importance in considering turbulence mixing and in developing turbulence model. Less
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