[PDF] Rethinking the Reynolds Transport Theorem, Liouville Equation, and Perron-Frobenius and Koopman Operators: Spatial and Generalized Parametric Forms | Semantic Scholar

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Corpus ID: 53395823

Rethinking the Reynolds Transport Theorem, Liouville Equation, and Perron-Frobenius and Koopman Operators: Spatial and Generalized Parametric Forms

@article{Niven2018RethinkingTR,
title={Rethinking the Reynolds Transport Theorem, Liouville Equation, and Perron-Frobenius and Koopman Operators: Spatial and Generalized Parametric Forms},
author={R. K. Niven and L. Cordier and E. Kaiser and M. Schlegel and B. R. Noack},
journal={arXiv: Fluid Dynamics},
year={2018}
}

We exploit a lesser-known connection between the (temporal) Reynolds transport theorem, Reynolds averaging and the Liouville equation for the flow of a conserved quantity, to derive new spatial and parametric forms of these theorems and associated evolution operators, which provide maps between different domains (in various spaces) associated with a conserved quantity in a vector or tensor field. First, for a time-independent continuous flow field described by Eulerian velocity and positionâ€¦Â CONTINUE READING