Showing papers by "E. A. Kuznetsov published in 1994"

Nonlinear interaction between long inertio-gravity and rossby waves

Abstract: The equations describing the interaction of long inertio-gravity (IG) waves with the Rossby waves are derived. Due to remarkable cancellations, the interaction is shown to be anomalously weak. As a result, an inverse cascade of turbulence produces wave condensate of large amplitude so that wave breaking with front creation can occur.

Phase Gradient Mechanism of Self-Focusing and Collapse in Non-Linear Dispersive Travelling Waves

Abstract: We present experimental, theoretical and numerical results of a new mechanism of self-focusing and collapse of travelling-wave pulses originating from large non-linear dispersion. We discovered a transition between the mechanism of Bretherton and Spiegel (Bretherton C.S. and Spiegel E. A., Phys. Lett. A, 96 (1983) 152) and the new mechanism, as a function of the initial pulse width. These dynamics have been observed in travelling-wave convection in binary mixtures and are described in the framework of the complex Ginzburg-Landau equation. We also present, for the first time, a quantitative experimental study of the role of phase winding in renormalizing the amplitude growth rate.

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.