Background noise pushes azimuthal instabilities away from spinning states

Abstract

Azimuthal instabilities occur in rotationally symmetric systems, either as spinning (rotating) waves or standing waves. We make use of a novel ansatz to derive a differential equation characterizing the state of these instabilities in terms of their amplitude, orientation, nature (standing/spinning) and temporal phase. For the first time we show how source terms determine quantitatively the system preference for spinning and/or standing states. In particular we find that, when present, background noise pushes the system away from spinning states and towards standing states, consistently with experiments.