## 11 Citations

Surfaces Which Behave Like Vortex Lines

- MathematicsTrends in Mathematics
- 2019

In general setting of theory of integral invariants, due to Poincare and Cartan, one can find a d-dimensional integrable distribution (given by a possibly higher-rank form) whose integral surfaces…

2 . 1 Flows in the inertial frame : integral surface , ( high-order ) Kelvin theorems

- Mathematics, Physics
- 2020

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…

Fast rotating flows in high spatial dimensions.

- Mathematics
- 2020

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…

Hierarchies of new invariants and conserved integrals in inviscid fluid flow

- Mathematics
- 2018

A vector calculus approach for the determination of advected invariants is presented for inviscid fluid flow. This approach describes invariants by means of Lie dragging of scalars, vectors, and…

Geometrical and topological description of chirality-relevant flow structures

- Physics
- 2019

Issues relevant to the flow chirality and structure are focused, while the new theoretical results, including even a distinctive theory, are introduced. However, it is hope that the presentation,…

The geometry and physics of the Taylor-Proudman theorems in E d ( ≥ 3 ) , the compressible flows and the plasma analogues

- Physics
- 2019

The Taylor-Proudman theorem (TPT) is a result of the Kelvin theorem, according to Taylor’s own idea, which can be extended to general frozen-in laws and the consequent generalised circulation…

Vortex Extraction Method Based on Compact Ratio

- PhysicsGSES
- 2016

The compact ratio method for extracting vortex is less affected by data resolution, and incorporates the idea of mathematical morphology to provide a new idea for ocean vortex extraction.

Taylor-Proudman theorems in $\mathbb{E}^{3,4\ and\ 5}$

- Mathematics
- 2019

Taylor's circulation-invariance proof of the theorem after Proudman is reinstated in the new derivation in $\mathbb{E}^3$ and in the Taylor-Proudman-type theorems in $\mathbb{E}^{5}$ and…

Research on Semantic Analysis of Ocean Flow Field Based on Feature Similarity Collaborative Filtering

- Computer ScienceJournal of Coastal Research
- 2020

A quadruple-based organization is proposed for ocean flow field features, in which by expanding the concept features, attribute features, and relationship features, a basic structure-based approach is formed, which provides semantic support for the integration and management of spatiotemporal data in the ocean flow fields.

On passive scalars advected by two-, three- and $d$-dimensional incompressible flows

- Physics
- 2018

When a passive scalar in the incompressible two-dimensional (2D) flow is so smart as to track the vorticity field to have a rugged correlation, it may form large scale patterns as the vortex with…

## References

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Invariants of the Euler equations for ideal or barotropic hydrodynamics and superconductivity in D dimensions

- Mathematics, Physics
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New Conserved Vorticity Integrals for Moving Surfaces in Multi-Dimensional Fluid Flow

- Mathematics
- 2013

For inviscid fluid flow in any n-dimensional Riemannian manifold, new conserved vorticity integrals generalizing helicity, enstrophy, and entropy circulation are derived for lower-dimensional…

Coadjoint orbits, vortices, and Clebsch variables for incompressible fluids

- Mathematics, Physics
- 1983

Conserved integrals for inviscid compressible fluid flow in Riemannian manifolds

- MathematicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2015

An explicit determination of all local conservation laws of kinematic type on moving domains and moving surfaces is presented for the Euler equations of inviscid compressible fluid flow in curved…

Geometric formulation of the Cauchy invariants for incompressible Euler flow in flat and curved spaces

- MathematicsJournal of Fluid Mechanics
- 2017

Cauchy invariants are now viewed as a powerful tool for investigating the Lagrangian structure of three-dimensional (3D) ideal flow (Frisch & Zheligovsky, Commun. Math. Phys., vol. 326, 2014, pp.…

Semidirect products and reduction in mechanics

- Mathematics
- 1984

This paper shows how to reduce a Hamiltonian system on the cotangent bundle of a Lie group to a Hamiltonian system in the dual of the Lie algebra of a semidirect product. The procedure simplifies,…

The Hamiltonian formalism and a many-valued analogue of Morse theory

- Mathematics
- 1982

CONTENTS Introduction § 1. The Hamiltonian formalism. Simplest examples. Systems of Kirchhoff type. Factorization of the Hamiltonian formalism for the B-phase of 3He § 2. The Hamiltonian formalism of…

Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits

- Mathematics
- 1966

© Annales de l’institut Fourier, 1966, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions…