New Conservation Laws Based on Generalised Reynolds Transport Theorems

Robert Niven , Laurent Cordier (1, 2) , Eurika Kaiser (3) , Michael Schlegel (4) , Bernd R. Noack (5)

1 PPrime [Poitiers] - Institut Pprime [UPR 3346]
2 TIC - Turbulence Incompressible et Contrôle [Institut Pprime]
3 University of Washington [Seattle]
4 TU - Technical University of Berlin / Technische Universität Berlin
5 HIT - Harbin Institute of Technology

The Reynolds transport theorem gives a generic conservation law for a conserved quantity carried by fluid flow through a continuous control volume, providing the foundation for all conservation laws of fluid mechanics. We present new spatial and parametric multivariate generalisations of this theorem, each of which provides a continuous mapping of the contents of a domain within a coordinate space. The most general form involves mappings on a manifold, presented in a multivariate extension of exterior calculus. These theorems are used to generate tables of new conservation laws in integral form in different spaces, including Eulerian velocity space and velocity-volume phase space, based on fluid densities defined in these spaces.

Mots clés: Reynolds transport theorem; exterior calculus; conservation laws; velocity space; phase space; density

Domaines: Sciences de l'ingénieur [physics]; Mécanique des fluides [physics.class-ph]

Robert Niven, Laurent Cordier, Eurika Kaiser, Michael Schlegel, Bernd R. Noack. New Conservation Laws Based on Generalised Reynolds Transport Theorems. 22nd Australasian Fluid Mechanics Conference AFMC2020, Dec 2020, Brisbane, Australia. ⟨10.14264/380a993⟩. ⟨hal-03088600⟩