Background. Active flow control devices that impose unsteady boundary conditions on fluid flows — pulsed-jet arrays, fluidic oscillators, sweeping jets — have been extensively studied for mixing enhancement, separation control and noise reduction. A less-explored configuration is one in which an array of apertures imposes not merely an unsteady, but a travelling (spatially phased) excitation pattern at the boundary. Whether such a travelling boundary condition can selectively organise vortex wavepackets and circulation statistics beyond those produced by ordinary pulsed jets remains an open question. Scope of this preprint. Building on the kinematic framework introduced in Part I, this Part II develops a classical fluid-dynamical formulation for the Mechanical Spiral-Phased Transducer (MSPT) — a rotor-stator aperture system in which the spatial phase of jet openings travels along the rotor azimuth, generating a controlled travelling boundary condition on the fluid. The preprint is purely theoretical and methodological; no experimental data are reported. Its purpose is to define rigorous, falsifiable hypotheses and quantitative measurement protocols suitable for future experimental and numerical investigation. Theoretical formulation. The framework explicitly distinguishes input/design quantities — parameters that are prescribed or measured during the experimental setup — from measured response metrics obtained from the resulting flow. The input/design set comprises the orifice Reynolds number Reⱼ, the local forcing Strouhal number Stf, the vortex formation number F, the aperture spacing ratio s/d, and the travelling-phase ratio Π_ξ, defined as the ratio between the rotor-induced travelling-pattern speed and the jet exit velocity. The discharge coefficient Cd, the Mach number Ma and the cavitation number σ are treated as calibration and limitation quantities that delimit the operating envelope. Crucially, the coherence parameter is not prescribed a priori: it is treated as a measured output, extracted from pressure transducers, particle image velocimetry (PIV), hydrophone records and computational fluid dynamics (CFD) data, depending on the experimental context. Three falsifiable hypotheses. The preprint formulates three independent, testable hypotheses with explicit rejection criteria. H1 addresses forced convective resonance: it tests whether the imposed travelling boundary condition selects coherent vortex wavepackets at the forcing frequency, beyond what is produced by stationary pulsed-jet arrays of equivalent energy input. H2 addresses circulation statistics: it tests whether the probability distribution of vortex circulation samples becomes statistically multimodal relative to lognormal- and gamma-type stochastic baselines characteristic of unforced or randomly forced flows. The proposed near-equispaced peak model is explicitly stated as a working hypothesis rather than a proven law. H3 addresses coherent modal dominance: it tests, using proper orthogonal decomposition (POD), spectral POD and dynamic mode decomposition (DMD), whether forced configurations exhibit a small set of energetically dominant modes relative to matched control cases. Methodological safeguards. Throughout, the text maintains an explicit separation between hydrodynamic response and acoustic resonance phenomena, requires uncertainty quantification for all measured quantities, and states quantitative rejection boundaries that would falsify each hypothesis. The framework is intended to be reproducible across water-tunnel, wind-tunnel and numerical implementations. Significance. By providing falsifiable hypotheses and measurement protocols for a travelling-boundary-condition flow control device, this preprint establishes a foundation for empirical investigation of MSPT-class systems. Potential applications, subject to experimental verification, include enhanced mixing in industrial processes, controlled vortex generation in propulsion and acoustic shaping in underwater and aeronautical systems.
Vladimir Khaustov (2026) studied this question.