Fluid Gauge Theory
anisotropic stress field, gauge principle, fluid gauge theory, current conservation, Euler equation
Abstract
According to the general gauge principle, Fluid Gauge Theory is presented to cover a wider class of flow fields of a perfect fluid without internal energy dissipation under anisotropic stress field. Thus, the theory of fluid mechanics is extended to cover time dependent rotational flows under anisotropic stress field of a compressible perfect fluid, including turbulent flows. Eulerian fluid mechanics is characterized with isotropic pressure stress fields. The study is motivated from three observations. First one is experimental observations reporting large-scale structures coexisting with turbulent flow fields. This encourages a study of how such structures observed experimentally are possible in turbulent shear flows, Second one is a theoretical and mathematical observation: the "General solution to Euler's equation of motion" (found by Kambe in 2013) predicts a new set of four background-fields, existing in the linked 4d-spacetime. Third one is a physical query, "what symmetry implies the current conservation law ?". The latter two observations encourage a gauge-theoretic formulation by defining a differential one-form representing the interaction between the fluid-current field jμ and a background field aμ.
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2021-12-06
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