Numerical study on the fluid dynamical equations on the basis of the Eulerian-Lagrangian formalism
| Project/Area Number |
14540203
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
OHKITANI Koji KYOTO UNIVERSITY, Research Institute for Mathematical Sciences, Associate Professor, 数理解析研究所, 助教授 (70211787)
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| Project Period (FY) |
2002 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2003: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2002: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | Navier-Stokes equations / Euler equations / turbulence / Eulerian-Lagrangian fomalism / singularity / singular perturbation / ナビエトークス方程式 / 渦のつなぎ替え |
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| Research Abstract |
We have studied the Navier-Stokes equations numerically on the basis of the Eulerian-Lagrangian formalism. In the first year we performed calculations of vortex reconnection by using two orthogonally off-set vortex tubes. The grid points used are 256^3 and 512^3. We first showed that the Jacobian determinant of the diffusive labels becomes zero because of viscous effects. To assure invertibility of labels, we reset labels as A = x when the determinant becomes close to O. It was found that the time interval over which frequent resetting takes, place corresponds to vortex reconnection. It was also found that resetting intervals are comparable to time scale of small scale turbulent motion. Thus, this method gives an objective criterion for monitoring vortex reconnection. Also, in physical space characteristics structure of iso-surfaces of vorticity |ω| and pseudo-vorticity |ζ| are compared.
In the second year, Navier-Stokes turbulence was studied by applying the above methodology to numerical experiments on homogeneous isotropic turbulence. It was found that resetting is also required in the case of turbulence and that this method is effective for monitoring small-scale vortex reconnection taking place in turbulence. We next turned our attention to the relationship between the Navier-Stokes equations and the Euler equations, their inviscid counterpart. The singular perturbation nature of the relationship was characterized by using connection tensor C, a second spatial derivative of labels. It was found that the behavior of C is anomalous in the inviscid limit. More precisely, some numerical evidence was obtained which support the existence of constants A_p such that
<lim>___<v→0>∫^<t_<j+1>_<t_j>||C||^2_pdt>A_p>0,||C||_p≡(1/<(2π)^3>∫|C|^pdx)^<1/p>
holds for the intervals of consecutive resetting times [t_j, t_<j+1>].
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Report
(3 results)
Research Products
(4 results)
