Same physics as the 3D ASMR honey-pour engine, seen from the side. Two real effects, stacked:
- Free-fall tapering ā volume flux Q is conserved, so as the stream accelerates under gravity (v(s) = ā(vāĀ²+2gs)) its cross-section must shrink: r(s) = ā(Q / (Ļv(s))). That's why a poured stream is always fatter at the nozzle than where it lands.
- Viscous rope-coiling instability ā a thin, very viscous jet falling onto a surface buckles once the fall height clears a viscosity- and flow-dependent threshold Hcrit (higher viscosity lowers the threshold; higher flow rate raises it). Below threshold the stream falls straight; above it, it folds back and forth ā the classic honey/syrup "sewing-machine" pattern, seen from the side as a side-to-side sine wave instead of the true 3D spiral.
- Viscosity ā thin the fluid toward water-like and the coiling folds shrink or vanish even from a tall pour; thicken it toward honey/molasses and folding starts from a much shorter drop.
- Pour height ā raise it past Hcrit to trigger folding; the fold amplitude grows with how far height exceeds threshold.
- Flow rate ā a faster pour needs more height before it starts coiling, and lands as a thicker stream.