# Bulletin of the American Physical Society

# 75th Annual Meeting of the Division of Fluid Dynamics

## Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.

### Session Q26: General Fluid Dynamics: Theory

1:25 PM–3:22 PM,
Monday, November 21, 2022

Room: 234

Chair: Carlo Casciola, Univ of Rome La Sapienza

### Abstract: Q26.00002 : New Families of Conservation Laws based on Extended Formulations of the Reynolds Transport Theorem*

1:38 PM–1:51 PM

#### Presenter:

Robert K Niven

(University of New South Wales)

#### Author:

Robert K Niven

(University of New South Wales)

*n*-dimensional manifold or coordinate space, based on general coordinates X, parameters C and tensor field V. These can be used to derive new integral conservation laws in different spaces, including for volumetric, velocimetric and velocivolumetric spaces based on the ordered triples (u,x,t), where u is the Eulerian velocity and x is position. These require different fluid densities, here labelled ρ(x,t) in volumetric space [SI units: kg m

^{-3}], д(u,t) in velocimetric space [kg (m s

^{-1})

^{-3}] and ζ(u,x,t) in velocivolumetric space [kg (m s

^{-1})

^{-3}m

^{-3}]. Such fluid densities can be defined from their underlying probability density functions p(x|t), p(u|t) and p(u,x|t) by convolution. The extended formulation is used to derive 11 tables of conservation laws for different choices of X and C, for the eight common conserved quantities of fluid mechanics (fluid mass, species mass, linear and angular momentum, energy, charge, entropy and probability). The findings considerably expand the set of known conservation laws of fluid mechanics.

*Funded by The University of New South Wales, Australia, and Institut Pprime / CNRS, France.

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