Chapter 58: τ-Euler: Inviscid Flow

The Euler equations of classical fluid dynamics describe the motion of an inviscid fluid: no friction, no dissipation, no viscosity. In τ³, the Euler equations are not postulated. They emerge from defect budget conservation on T² in the regime where vorticity dissipation and compression are negligible: d₂ ≈ d₃ ≈ 0. This chapter derives the τ-Euler equation, establishes the Kelvin circulation theorem as a topological invariant of T², and shows how Bernoulli’s principle is a consequence of defect energy conservation.