| Budget Amount *help |
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,200,000 (Direct Cost: ¥1,200,000)
|
|---|
| Research Abstract |
1.Three-dimensional instability of an elliptic vortex and a vortex ring was investigated from the viewpoint of the Hamiltonian spectral theory.
(1)A pure shear breaks the SO(2)xO(2)-symmetry of the Rankine vortex and deforms the circular core into an ellipse.We have succeeded in explicitly writing down the infinitesimal disturbances in terms of the Bessel functions.The relation with the elliptical instability is clarified.
(2)For a vortex ring, symmetry-bresking perturbation is the curvature effect. The infinitesimal disturbances on Kelvin's vortex ring are written out in a closed form.We have found a possibility of parametric resonance between pairs of Kelvin waves whose azimuthal wavenumbers are separated by two.A local stability analysis is also made, using the WKB method It is clarified that the structure of unstable modes on a Gaussian core is very different from that on Kelvin's vortex ring.
(3)We have derived weakly nonlinear evolution equations of amplitudes of several unstable mo
… More
des on a vortex tube subjected to a pure shear, with the aid of equivariant vector fields associated with Z2xO(2) symmetry.
2.When a pulse of excimer laser of a few ten nanoseconds is irradiated on a Co-coated substrate, vortex filaments are created, quenched and frozen at once.By estimating the time scales from a stability analysis in the localized induction approximation, we have extracted a dynamical picture from the micrographs of the frozen pictures.(2)By repeating the irradiation, of pulses several times, unstable vortex rings are obtained.
3.For the side-band instability of a plane wave, it is proven that, near the linear critical point, the methods based on envelope equations, on amplitude equations and on a secondary-instability analysis are all equivalent.
4.For the Rayleigh-Benard convection, the fifth-order amplitude equations are derived, using the center-manifold reduction, and their bifurcation analysis is made near the degeneracy point with quadratic dependence on temperature of the density being an unfolding parameter It is clarified that right-hexagonal, right-triangle and patch-work quilt patterns are unstable as a primary bifurcation solution of the generic normal form equations. Less
|
