A soliton on a vortex filament

Journal of Fluid Mechanics - Tập 51 Số 3 - Trang 477-485 - 1972
Hidenori Hasimoto1
1Institute of Space and Aeronautical Science University of Tokyo

Tóm tắt

The intrinsic equation governing the curvature K and the torsion τ of an isolated very thin vortex filament without stretching in an incompressible inviscid fluid is reduced to a non-linear Schrödinger equation \[ \frac{{\rm l}}{i}\frac{\partial \psi}{\partial t} = \frac{\partial^2\psi}{\partial s^2}+{\textstyle\frac{1}{2}}(|\psi|^2+A)\psi, \] where t is the time, s the length measured along the filament, ψ is the complex variable \[ \psi = \kappa\exp\left(i\int_0^{s}\tau \,ds\right) \] and is a function oft. It is found that this equation yields a solution describing the propagation of a loop or a hump of helical motion along a line vortex, with a constant velocity 2τ. The relation to the system of intrinsic equations derived by Betchov (1965) is discussed.

Từ khóa


Tài liệu tham khảo

Hama F. R. 1963 Phys. Fluids,6,526.

Hasimoto H. 1971 J. Phys. Soc. Japan,31,293.

Yajima, N. & Outi A. 1971 Prog. Theor. Phys. (Kyoto) 45,1997.

Asano N. , Taniuti, T. & Yajima N. 1969 J. Math. Phys. 10,2020.

Hama F. R. 1962 Phys. Fluids,5,1156.

Taniuti, T. & Yajima N. 1969 J. Math. Phys. 10,1369.

Batchelor G. K. 1967 An Introduction to Fluid Dynamics , p.509.Cambridge University Press.

Kambe, T. & Takao T. 1971 J. Phys. Soc. Japan, 31. 591.

Betcrov R. 1965 J. Fluid Mech. 22,471.

Karpman, V. I. & Krushkal E. M. 1969 Soc. Phys. J.E.T.P.,28,277.

Thông tin
Thông tin xuất bản

Journal of Fluid Mechanics

Tập 51 Số 3

477-485

Thông tin tác giả