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Proceedings of the 22nd Australasian Fluid Mechanics Conference AFMC2020
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 ofdoi:10.14264/380a993 fatcat:5qqcg4imsncmxfc4j4xbu56wcu