Coupled dynamics of chiral waves and gyroscopic systems with applications to atmospheric phenomena

TL;DR

This paper introduces chiral gravitational elastic waves and examines their behavior in gyroscopic systems and atmospheric phenomena, revealing how gravity and Coriolis forces influence wave dynamics and control.

Contribution

It presents a novel concept of chiral gravitational waves and analyzes their interactions with gyroscopic and atmospheric systems, including control mechanisms via orientation and gravity effects.

Findings

Gravity affects stop band frequencies in waveguides.

Wave direction can be controlled by spinner orientation.

Polar vortex shapes can be modeled by gyropendulum equations.

Abstract

The present paper introduces the notion of chiral gravitational elastic waves and explores their connections to equatorial and planetary waves. The analysis of the gravity-induced waveforms in gyroscopic systems composed of gyropendulums provides important insights into the dynamics of waves in the vicinity of the equatorial belt. We show that the direction of motion of the chiral waveforms can be controlled by choosing the orientation of the spinners. The presence of gravity is shown to affect the stop band frequencies for such structures, providing an additional control parameter for the chiral waveguides. The effect of the Coriolis force is demonstrated for chiral continuum models describing waves in the equatorial region and the polar regions on a rotating sphere. Additional asymptotic features of equatorial waves are presented in this paper. We show that the shape of a ridge of a polar vortex can be approximated by the governing equations of a gyropendulum. The theoretical work is accompanied by illustrative examples.