Thermodynamic and vortic fine structures of real Schur flows

Abstract

A two-component-two-dimensional coupled with one-component-three-dimensional (2C2Dcw1C3D) flow may also be called a real Schur flow (RSF), as its velocity gradient is uniformly of real Schur form, the latter being the intrinsic local property of any general flows. The thermodynamic and `vortic' fine structures of RSF are exposed and, in particular, the complete set of equations governing a (viscous and/or driven) 2C2Dcw1C3D flow are derived. The Lie invariances of the decomposed vorticity 2-forms of RSFs in $d$-dimensional Euclidean space ${\mathbb{E}}^d$ for any interger $d\ge 3$ are also proven, and many Lie-invariant fine results, such as those of the combinations of the entropic and vortic quantities, including the invariances of the decomposed Ertel potential vorticity (and their multiplications by any interger powers of entropy) 3-forms, then follow.

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Cited by in corpus (3)

• The Role of Normal and Non-Normal Contributions to Enstrophy Production in the Near-Wall Region of a Turbulent Channel Flow
• Turbulence compressibility reduction with helicity
• Real Schur flow computations, helicity fastening effects and Bagua-pattern cyclones