Unified Geometric Axiom of Rectilinear and Circulating Flow

Axiomatic Statement

Unified Flow Axiom: For any steady or asymptotically stable flow, its trajectory satisfies the following in a local coordinate system:

(i) Normal Boundedness – Displacements and velocity components deviating from the mainstream direction are always bounded by a finite constant.

(ii) Tangential Convergence – The projection of velocity along the mainstream direction, or the path length, tends to converge smoothly (no infinite oscillations or blowup occur).

This axiom does not distinguish between rectilinear flow and circulating flow; it only constrains the geometric structure of the flow.

Geometrically speaking, a straight line can be regarded as a special case of curves, which is logically self‑consistent.