Fluid Gauge Theory
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 largescale 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 and a background field . A known relativistic action of a perfect fluid is introduced together with the interaction action just mentioned, and furthermore, a third gauge invariant action is defined to govern the field linearly in its free-state. The general gauge principle is applied to the combined system of the three actions to describe general time-dependent rotational flow fields of an ideal compressible fluid. The combined system can be shown to be invariant under both global and local gauge transformations of variations of . The global gauge transformation is a diagnostic test whether the system is receptive to a new field . Since the test is cleared, a new internal stress field is introduced into the flow field of a perfect fluid, together with the current conservation = 0, where the stress is an anisotropic stress field which is an extension added to the Eulerian isotropic pressure-stress field jμ aμ aμ aμ aμ(xν ( Mik(xν ( ∂μjμ Mik p δik.
