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Prime Role of the Curvature of Potentials in Physics; Application to Inertia

The curvature of the inertial or gravitational potentials defined as a Hodge-Helmholtz decomposition of acceleration into an irrotational and a solenoidal components, enable to federate certain domains of macroscopic physics. After two verifications in physics, one on the calculation of the curvatures for capillary effects and the second on the deflection of light by a gravitational effect, the concept of curvature of the potential is applied to the inertia. The physical analysis of each of the contributions of the decomposition is carried out on a classic example of fluid mechanics, the backward-facing step flow where inertia plays a preponderant role on the recirculation length.