Lagrangian Dynamical Theory of the Velocity Gradient Tensor: Real Schur Form, Schur Frame, Characteristic Vorticity Modes, and Commutative Vorticity Operators

The present work proposes a novel Lagrangian dynamical theory for the velocity gradient tensor (VGT) $\bm{A}\equiv\bm{\nabla}\bm{u}$, formulated on the basis of its canonical real Schur form in the traditional vortex region with positive discriminant. Starting from the Navier-Stokes equations for co