Wave-number dependence of the transitions between traveling and standing vortex waves and their mixed states in the Taylor-Couette system

TL;DR

This paper explores how vortex wave transitions in the Taylor-Couette system depend on wave number, revealing new bifurcation scenarios and the existence of standing waves with oscillating amplitudes, enhancing understanding of vortex dynamics.

Contribution

It extends previous studies by analyzing the wave-number dependence of vortex transitions, uncovering new bifurcation behaviors and standing wave states in the Taylor-Couette system.

Findings

Wave-number influences vortex transition stability.

Discovery of backward bifurcating standing waves.

Identification of oscillating amplitude states.

Abstract

Previous numerical investigations of the stability and bifurcation properties of different nonlinear combination structures of spiral vortices in a counterrotating Taylor-Couette system that were done for fixed axial wavelengths are supplemented by exploring the dependence of the vortex phenomena waves on their wavelength. This yields information about the experimental and numerical accessability of the various bifurcation scenarios. Also backwards bifurcating standing waves with oscillating amplitudes of the constituent traveling waves are found.