Divorticity and Dihelicity In Two-Dimensional Hydrodynamics

TL;DR

This paper introduces a novel theoretical framework for 2D hydrodynamics based on divorticity and dihelicity, revealing invariants that constrain the evolution of flow structures.

Contribution

It develops a new formulation using divorticity and dihelicity concepts, establishing invariants that influence 2D hydrodynamic evolution.

Findings

Identifies global and Lagrange invariants in 2D hydrodynamics.

Provides a theoretical basis for understanding divorticity line evolution.

Offers constraints on flow dynamics through invariants.

Abstract

A framework is developed based on the concepts of {\it divorticity} ${\textbf B}$($\equiv\nabla\times\bfo$, $\bfo$ being the vorticity) and $\textit{dihelicity} g \lp \equiv\bfv\cdot\textbf{B}\rp$ for discussing the theoretical structure underlying two-dimensional (2D) hydrodynamics. This formulation leads to the global and Lagrange invariants that could impose significant constraints on the evolution of divorticity lines in 2D hydrodynamics.