Fast rotating flows in high spatial dimensions

Abstract

The central result about fast rotating-flow structures is the Taylor-Proudman theorem (TPT) which connects various aspects of the dynamics. Taylor's geometrical proof of TPT is reproduced and extended substantially, with Lie's theory for general frozen-in laws and the consequent generalized invariant circulation theorems, to compressible flows and to $d$-dimensional Euclidean space (${\mathbb{E}}^d$) with $d\ge 3$. The TPT relatives, the reduced models (with particular interests on passive-scalar problems), the inertial (resonant) waves and the higher-order corrections, are discussed coherently for a comprehensive bird view of rotating flows in high spatial dimensions.

plasmas are neutralized, for the time being, and the bibliography is greatly enriched with in particular many more relevant references of mathematical analyses

References in corpus (2)

• Rotations in three, four, and five dimensions
• On the exact solutions of (magneto)hydrodynamic systems and the superposition principles of nonlinear helical waves

Cited by in corpus (3)

• Compressible helical turbulence: Fastened-structure geometry and statistics
• Thermodynamic and vortic fine structures of real Schur flows
• Real Schur flow computations, helicity fastening effects and Bagua-pattern cyclones