Numerical studies on the regularity properties of the fluid dynamical equations
| Project/Area Number |
16540103
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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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) |
2004 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2005: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2004: ¥2,300,000 (Direct Cost: ¥2,300,000)
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| Keywords | Navier-Stokes equations / regularity of solutions / megneto-hydrodynamics / Euler-Lagrange formalism / magnetic reconnection / 乱流 / オイラーラグランジュ定式化 / 特異点 / 特異摂動 |
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| Research Abstract |
In order to clarify fast reconnection phenomena in magnetohydrodynamics, we performed numerical experiments on the basis of the Eulerian-Lagrangian formalism.
In 2004, we extended the Eulerian-Lagrangian formalism for the Navier-Stokes equations to magnetohydrodynamical equations. There are two Weber transforms corresponding to conservation of two kinds of helicities. For the case of unit Prandtl number, we have shown that one connection tensor is sufficient to reformulate the magnetohydrodynamical system. By using it, direct numerical simulations of 2D Orszag-Tang were done and it was found that correspondence between diffusive labels A and spatial positions x becomes non-invertible (resetting phenomena). We showed that it is related with magnetic reconnection. Furthermore, numerical simulations were done with initial conditions of 3D generalized O-T vortices and orthogonally offset magnetic flux tubes. Resetting phenomena also take place for these cases.
In 2005, more practical numerical simulations with twisted magnetic flux tubes were performed. Parallel/anti-parallel flux tubes and linked flux rings were used as initial conditions. It was confirmed that magnetic reconnections are associated with resetting phenomena. The time scales defined by the resetting intervals are smaller that those estimated by global characteristics and are closer to time-scales of fast reconnections. In this sense we showed that this method can quantify fast reconnections. We also found by visualizations that a spatial correspondence between reconnecting magnetic fields and the resetting phenomena.
A regularity criterion for ideal magnetohydrodynamical equations is known to be given in terms of the vorticity and the current density fields A simple argument respecting helicity invariants shows that if the magnetic field is smooth, then so is the velocity field, thereby suggesting some room for improving the above criterion.
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Report
(3 results)
Research Products
(16 results)
