Three-dimensional distortions of a vortex filament with axial velocity

摘要: Three-dimensional motion of a thin vortex filament with axial velocity, embedded in an inviscid incompressible fluid, is investigated. The deflections the core centreline are not restricted to be small compared radius. We first derive equation motion, correct second order ratio radius that curvature, by matching procedure, which recovers results obtained Moore & Saffman (1972). An asymptotic formula for linear dispersion relation up order. Under assumption localized induction, governing self-induced reduced nonlinear evolution generalizing induction equation. This new equivalent Hirota integrable, including both Schrodinger and modified KdV certain limits. Therefore also integrable soliton surface approach gives N-soliton solution, identical if pertinent used. Among other exact solutions circular helix plane curve Euler's elastica. local model predicts that, owing existence flow, class helicoidal vortices become neutrally stable any perturbations. non-local influence entire perturbed on stability explored help cutoff method valid order, extends first-order scheme developed Widnall velocity found discriminate between right- left-handed helices long-wave instability mode disappear parameter range when successive turns too close together. Comparison reveals structure crucial making quantitative predictions.