Applicability of the hodograph method for the problem of longscale nonlinear dynamics of a thin vortex filament near a flat boundary
Abstract
Hamiltonian dynamics of a thin vortex filament in an ideal incompressible fluid near a flat fixed boundary is considered under the conditions that at any point of the curve, determining the shape of the filament, the angle between tangent vector and the boundary plane is small. Also the distance from a point on the curve to the plane is small in comparison with the curvature radius. The dynamics is shown to be effectively described by a nonlinear system of two (1+1)dimensional partial differential equations. The hodograph transformation reduces this system to a single linear differential equation of the second order with separable variables. Simple solutions of the linear equation are investigated for real values of spectral parameter λ, when the filament projection on the boundary plane has shape of a twobranch spiral or a smoothed angle, depending on the sign of λ.
 Publication:

Physical Review E
 Pub Date:
 June 2003
 DOI:
 10.1103/PhysRevE.67.066301
 arXiv:
 arXiv:physics/0302064
 Bibcode:
 2003PhRvE..67f6301R
 Keywords:

 47.15.Ki;
 47.32.Cc;
 47.10.+g;
 Physics  Fluid Dynamics
 EPrint:
 9 pages, revtex4, 6 epsfigures