Geometric Stability of Pseudo-plane Ideal Flows

TL;DR

This paper investigates the geometric stability of steady pseudo-plane ideal flows, revealing conditions for vertical coherence and providing a topological explanation for observed vortex behaviors.

Contribution

It introduces a geometric stability theory contrasting traditional dynamical stability, linking flow topology to vertical alignment and stability in pseudo-plane flows.

Findings

Vertical alignment exists only in straightline jets and circular vortices.

All vertical-aligned flows are geometrically stable.

Non-aligned flows are geometrically unstable.

Abstract

Geometric analysis of steady pseudo-plane ideal flow reveals a fundamental relation between vertical coherence and streamline topology. It shows vertical alignment only exists in straightline jet and circular vortex. A geometric stability theory is then developed as a structural stability in contrast to traditional dynamical stability, suggesting all vertical-aligned pseudo-plane flows are geometrically stable and all non-aligned non-straightline flows are unstable. It provides a topological explanation for the tendency of axisymmetrization and vertical alignment observed in vortex experiments.