Divorticity and Dihelicity In Two-Dimensional Hydrodynamics

A framework is developed based on the concepts of {\it divorticity} ${\textbf B}$($\equiv\nabla\times\bfo$,$\bfo$beingthevorticity)and$$\mathit{\text{dihelicity}}$ g \lp \equiv\bfv\cdot$\mathbf{\text{B}}$\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.