Defects of One - Dimensional Vortex Lattices

Abstract

In the framework of the equation

$${{\psi }_{t}} = {{\psi }_{{xx}}} + \psi - {{\left| \psi \right|}^{2}}\psi ,$$

the dynamics of one-dimensional lattices of Taylor vortices in Couette flow and of rolls in weak supercritical convection is studied. It is shown that the propagation of the defects as transition areas between stable (according to Eckhaus) and unstable lattices depends significantly on the topological properties of the field ψ(x), i.e. the degree of mapping R ¹ → S ¹. The velocity of such defects has been determined. It has been clarified that the defects between stable lattices spread diffusively due to the conservation of the topological invariant.