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

  • Tao Chen
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Abstract

The present work proposes a novel Lagrangian dynamical theory for the velocity gradient tensor (VGT) A≡∇u, formulated on the basis of its canonical real Schur form.... The proposed theory is expected to be useful for understanding the evolution dynamics of the VGT rotational invariants and intrinsic vorticity modes in a variety of vortical flows.

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Cite

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BibTeX
@misc{chen2026lagrangian,
  title = {{Lagrangian Dynamical Theory of the Velocity Gradient Tensor: Real Schur Form, Schur Frame, Characteristic Vorticity Modes, and Commutative Vorticity Operators}},
  author = {Tao Chen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.14034},
  eprint = {2609.14034},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14034},
}
RIS
TY  - UNPB
TI  - Lagrangian Dynamical Theory of the Velocity Gradient Tensor: Real Schur Form, Schur Frame, Characteristic Vorticity Modes, and Commutative Vorticity Operators
AU  - Tao Chen
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.14034
UR  - https://arxiv.org/abs/2609.14034
AB  - The present work proposes a novel Lagrangian dynamical theory for the velocity gradient tensor (VGT) A≡∇u, formulated on the basis of its canonical real Schur form.... The proposed theory is expected to be useful for understanding the evolution dynamics of the VGT rotational invariants and intrinsic vorticity modes in a variety of vortical flows.
ER  -