Open-Air Vortex-Toroid Formation by Counter-Flow Arrest of Orbitally Moving Swirled Jets: A Preliminary Experimental and Dimensional Study

I present a preliminary experimental and dimensional study of open-air vortex-toroid formation by counter-flow arrest of orbitally moving swirled jets. The flow is produced by a custom S-block device in which two diametrically opposed outlets, each emitting a swirled jet, are rotated about a vertical axis at 800–1200 rpm in open atmosphere. Smoke visualisation reveals a localised, sustained tracer organisation in an annular region around the rotor; six thermocouples record local temperature reductions of 0.3–0.8 K relative to ambient. Four operating conditions are proposed and quantitatively evaluated: (i) a counter-flow balance Λ = U_j/U_c = O(1) (with U_c ≈ U_orb in the S-block frame), under which the axial component of the swirled jet is locally arrested by the orbital motion of its source; (ii) a temporal overlap K = τ_d · f_pass > 1, ensuring that the next orbital pass re-excites the same azimuthal sector before vortex decay; (iii) a momentum-symmetry condition P_net ≈ 0, eliminating net translational drift of the structure; and (iv) a non-zero angular-momentum input dL_z/dt, sustaining circulation against viscous loss. For the documented reference regime (n ≈ 1000 rpm, D_S = 0.30 m, two outlets) the four conditions are simultaneously satisfied: Λ ≈ 1.40, K ≈ 3.3–6.7, P_net ≈ 0 by construction, and dL_z/dt ≈ 8.6 × 10⁻³ N·m. The local helical pitch is found to compress to p ≈ 1 mm, distinguishing the present structure from classical impulsive vortex rings (where formation number L/D ≈ 4) by L_pass/D_eff ≈ 60Dynamic-pressure, kinetic-power and adiabatic temperature scales are derived and agree among themselves within ±15–25 %. Smoke visualisation reveals a localised, sustained tracer organisation in an annular region around the rotor; six thermocouples placed near the rotation axis and in the annular region record local temperature shifts of approximately −1 K near the axis and +2 K in the annular region, against an ambient reference near 21 °C. A nine-point verification programme (PIV, pressure mapping, mass-flow calibration, thermal imaging, parameter sweeps, control geometries, CFD and energy-balance closure) is listed for subsequent validation. The contribution of this preprint is to establish a self-consistent dimensional and operational framework for open-air vortex-toroid formation by counter-flow arrest of orbitally moving swirled jets as a testable hypothesis.