Pseudo-Rotating Spiral Jet Dynamics

• Pseudo-Rotating Spiral Jet is a phenomenon where spiral patterns appear due to deterministic forcing and sequential vortex generation, rather than true angular momentum.
• The concept spans multiple fields, from fluid dynamics to optics and plasma physics, revealing mechanisms like axis-switching and propagation-encoded effects.
• Researchers can quantify this effect using control parameters and forcing ratios, which clarify vortex detachment, spiral arm visibility, and the underlying kinematic origins.

A pseudo-rotating spiral jet is a jet-like or beam-like structure that exhibits a spiral, helical, or apparently rotating morphology without necessarily undergoing bulk solid-body rotation or carrying classical swirl in the usual sense. In the most explicit recent fluid-mechanical usage, it denotes an actively forced round-jet pattern in which separate branches, disconnected from the main jet stream, are formed by vortical structures aligned along curved paths around the initial jet axis; the apparent arm rotation has a well-defined frequency, but it is an observational effect produced by how successive vortical structures are generated and visually grouped rather than by the bodily rotation of coherent spiral arms (Wawrzak et al., 31 Aug 2025). Related literature supports a broader, cross-domain interpretation in which pseudo-rotation arises from propagation-encoded structure, traveling azimuthal deformations, axis-switching, twist transfer, or plasma motion along helical fields, depending on the physical system.

1. Conceptual definition and distinguishing features

The defining distinction is between apparent spiral or rotational organization and true azimuthal transport of matter or energy around an axis. In several hydrodynamic and plasma contexts, the visible structure rotates or twists as a pattern, while the underlying mechanism is instead a traveling deformation, a propagating interference geometry, cross-sectional reorientation, or field-guided motion.

This distinction is explicit in twisted liquid jets from non-circular orifices. There, the jet surface can show a twisted appearance because a single azimuthal capillary ripple propagates around the circumference, yet the jet has no angular momentum around the axis, and “the apparent rotation of the surface curve does not mean the actual rotation of the surface particles around the center” (Kageyama et al., 2020). A similar separation appears in free jets from cornered nozzles: the jet cross-section rotates downstream, but no angular momentum is imposed at the inlet; the phenomenon is instead geometry-induced apparent rotation or axis-switching driven by corner-generated streamwise vorticity (D'Addio et al., 2015).

Solar-jet literature reaches the same conceptual boundary from magnetized plasma. One recent active-region study concludes that the observed rotation results from plasma spiral motion along twisted magnetic fields rather than from untwisting of the field lines themselves, so the visible spin is a kinematic manifestation of field-guided flow rather than evidence of a rigidly rotating plasma column (Huang et al., 24 Feb 2026). A pseudo-rotating spiral jet is therefore best understood as a class of organized spiral appearances whose rotation belongs primarily to the pattern, the geometry, or the field topology.

2. Actively controlled round jets: the explicit fluid-mechanical realization

The most direct formulation of the topic appears in the actively controlled turbulent round jet studied at $Re=3000$, where the pseudo-rotating spiral jet is defined as a jet pattern consisting of “separate branches disconnected from the main jet stream, formed by vortical structures aligned along curved paths rotating around the initial jet axis” (Wawrzak et al., 31 Aug 2025). The nozzle forcing combines axisymmetric axial excitation and an azimuthally traveling radial excitation, with inlet decomposition

$$U_a(r,t)=U_m(r)+u_a(r,t)+u_{turb}(r,t), \qquad U_r(r,t)=u_r(r,t),$$

and control law

$$u_a(r,t)=A_a \sin(2\pi f_a t)\, g_a(r), \qquad u_r(r,t)=A_r \cos(\theta-2\pi f_r t)\, g_r(r),$$

where $\theta=\arctan(z/y)$. In the reported simulations,

$$A_a=A_r=0.08U, \qquad St_a=0.5, \qquad u_{turb}\sim 0.01U.$$

The physical picture is highly specific. Axial forcing generates toroidal vortices, while radial forcing biases them radially and azimuthally. Farther downstream, typically after about $4.5D$ to $5D$, these vortices detach from the main stream and move along inclined paths at about $\alpha \approx 40^\circ$ to the jet axis. The visible branches are therefore not continuous helical tubes of fluid, but sequences of detached vortical structures. Side views can look scattered or chaotic, whereas top views can suggest two or more spiral arms.

The governing control parameter is the frequency ratio

$\mathcal R = \frac{f_a}{f_r}=\frac{St_a}{St_r}.$

For integer $\mathcal R$, the system recovers familiar controlled-jet topologies such as bifurcating and trifurcating jets. For rational non-integer $$U_a(r,t)=U_m(r)+u_a(r,t)+u_{turb}(r,t), \qquad U_r(r,t)=u_r(r,t),$$0, the flow belongs to a broader multi-armed jet family with nominal arm spacing

$$U_a(r,t)=U_m(r)+u_a(r,t)+u_{turb}(r,t), \qquad U_r(r,t)=u_r(r,t),$$1

Spiral jets are not a separate family; they are a perceptual and kinematic subset of these rationally forced multi-armed jets.

3. Kinematic origin of the apparent rotation

The control mechanism is organized by joint excitation peaks (JEPs), the spacetime events at which the maxima of the axial and radial forcings coincide. These events determine where a vortex is generated under especially favorable off-axis conditions. For the first JEP,

$$U_a(r,t)=U_m(r)+u_a(r,t)+u_{turb}(r,t), \qquad U_r(r,t)=u_r(r,t),$$2

For rational $$U_a(r,t)=U_m(r)+u_a(r,t)+u_{turb}(r,t), \qquad U_r(r,t)=u_r(r,t),$$3, the JEP sequence advances deterministically in azimuth, so the vortex source locations form an arithmetic progression modulo $$U_a(r,t)=U_m(r)+u_a(r,t)+u_{turb}(r,t), \qquad U_r(r,t)=u_r(r,t),$$4.

The apparent spiral-arm rotation is then a pattern effect. If vortices separated by some index increment $$U_a(r,t)=U_m(r)+u_a(r,t)+u_{turb}(r,t), \qquad U_r(r,t)=u_r(r,t),$$5 are close enough in azimuth and coexist long enough within the observable domain, they are visually grouped into a continuous curved arm. The azimuthal spacing between such events is

$$U_a(r,t)=U_m(r)+u_a(r,t)+u_{turb}(r,t), \qquad U_r(r,t)=u_r(r,t),$$6

and their time separation is

$$U_a(r,t)=U_m(r)+u_a(r,t)+u_{turb}(r,t), \qquad U_r(r,t)=u_r(r,t),$$7

The corresponding apparent angular speed and apparent rotation frequency are

$$U_a(r,t)=U_m(r)+u_a(r,t)+u_{turb}(r,t), \qquad U_r(r,t)=u_r(r,t),$$8

In Strouhal form,

$$U_a(r,t)=U_m(r)+u_a(r,t)+u_{turb}(r,t), \qquad U_r(r,t)=u_r(r,t),$$9

The reduced kinematic model used to reproduce the LES assumes infinite vortex lifetime, point-like vortex centers, neglect of turbulence, vortex detachment at $$u_a(r,t)=A_a \sin(2\pi f_a t)\, g_a(r), \qquad u_r(r,t)=A_r \cos(\theta-2\pi f_r t)\, g_r(r),$$0, inclination angle $$u_a(r,t)=A_a \sin(2\pi f_a t)\, g_a(r), \qquad u_r(r,t)=A_r \cos(\theta-2\pi f_r t)\, g_r(r),$$1, and convection speed $$u_a(r,t)=A_a \sin(2\pi f_a t)\, g_a(r), \qquad u_r(r,t)=A_r \cos(\theta-2\pi f_r t)\, g_r(r),$$2 (Wawrzak et al., 31 Aug 2025). Within those assumptions, the model reproduces the apparent two-spiral, five-spiral, and other spiral patterns reported in the 3D simulations. The key conclusion is that the large-scale motion generated by the forcing is deterministic, even when the flow imagery looks visually irregular.

Observability is itself constrained. For a domain of effective length $$u_a(r,t)=A_a \sin(2\pi f_a t)\, g_a(r), \qquad u_r(r,t)=A_r \cos(\theta-2\pi f_r t)\, g_r(r),$$3, the paper gives criteria such as

$$u_a(r,t)=A_a \sin(2\pi f_a t)\, g_a(r), \qquad u_r(r,t)=A_r \cos(\theta-2\pi f_r t)\, g_r(r),$$4

for straight-arm visibility, and

$$u_a(r,t)=A_a \sin(2\pi f_a t)\, g_a(r), \qquad u_r(r,t)=A_r \cos(\theta-2\pi f_r t)\, g_r(r),$$5

for curved-arm visibility. This is why a nominally high-order multi-armed jet can be perceived as a low-arm spiral: the true topology exists, but only a subset of it is simultaneously visible.

4. Related hydrodynamic mechanisms in non-swirling and capillary jets

Several adjacent hydrodynamic systems exhibit pseudo-rotating spiral-jet behavior through mechanisms other than active forcing.

A non-circular liquid jet with $$u_a(r,t)=A_a \sin(2\pi f_a t)\, g_a(r), \qquad u_r(r,t)=A_r \cos(\theta-2\pi f_r t)\, g_r(r),$$6-fold symmetry usually undergoes axis switching, which the literature interprets as a standing azimuthal wave. By prescribing a radial velocity in quadrature with the shape perturbation, one can preferentially excite only one of the two counter-propagating azimuthal ripples. The resulting cross-sectional deformation travels around the jet circumference, and axial advection maps this temporal azimuthal phase propagation into a twisted three-dimensional jet surface. The paper’s practical forcing law is

$$u_a(r,t)=A_a \sin(2\pi f_a t)\, g_a(r), \qquad u_r(r,t)=A_r \cos(\theta-2\pi f_r t)\, g_r(r),$$7

with $$u_a(r,t)=A_a \sin(2\pi f_a t)\, g_a(r), \qquad u_r(r,t)=A_r \cos(\theta-2\pi f_r t)\, g_r(r),$$8, and the jet remains a non-swirling twisted jet with no angular momentum around the axis (Kageyama et al., 2020). Its capillary oscillation frequency is

$$u_a(r,t)=A_a \sin(2\pi f_a t)\, g_a(r), \qquad u_r(r,t)=A_r \cos(\theta-2\pi f_r t)\, g_r(r),$$9

and the downstream wavelength is

$\theta=\arctan(z/y)$0

This is an exact hydrodynamic prototype of a pseudo-rotating spiral jet produced by traveling azimuthal phase rather than swirl.

Free jets from cornered nozzles provide a second mechanism. Direct numerical simulation shows that square, fractal, and star-like nozzles produce downstream rotation of the jet cross-section even though the inlet has a uniform axial velocity profile. The reported law is

$\theta=\arctan(z/y)$1

and the mechanism is the generation of paired positive and negative streamwise-vorticity layers $\theta=\arctan(z/y)$2 at the nozzle corners (D'Addio et al., 2015). The flow rotates as a deforming pattern: the jet does not acquire classical swirl, but the short and long directions of the cross-section invert through self-induced stretching and axis-switching.

Binary disk-jet systems extend the same logic to MHD outflows. In 3D resistive MHD simulations of a circumstellar disk in a binary, the spiral structure that develops in the disk is launched into the outflow as a “jet spiral wall” (Sheikhnezami et al., 2021). The authors show that the disk spiral is a pattern, not material corotation; at $\theta=\arctan(z/y)$3, its speed is

$\theta=\arctan(z/y)$4

while the local Keplerian speed is

$\theta=\arctan(z/y)$5

The jet spiral is therefore a tidally forced, magnetically launched pattern embedded in a rotating flow rather than a simple solid-body spiral jet. Quantitatively, the binary increases disk accretion rate by $\theta=\arctan(z/y)$6 and disk-wind mass flux by $\theta=\arctan(z/y)$7 relative to a single-star case (Sheikhnezami et al., 2021).

A still more reduced analogue appears in the rotating-plate experiment on secondary-vortex shedding. There, a curved shear layer rolls up into a primary vortex and, for $\theta=\arctan(z/y)$8, sheds discrete secondary vortices from the tip. Both the shear-layer roll-up and the paths of the secondary vortices are described by a modified Kaden spiral,

$\theta=\arctan(z/y)$9

with shedding times following

$$A_a=A_r=0.08U, \qquad St_a=0.5, \qquad u_{turb}\sim 0.01U.$$0

This is a useful reduced model for pseudo-rotating spiral jets that consist of a spiral backbone populated by discrete vortical packets rather than a continuous rotating filament (Francescangeli et al., 2020).

5. Optical and wave analogues

Structured-light research contains some of the clearest non-fluid analogues of pseudo-rotating spiral jets. The optical tornado wave is generated by interfering two ring-Airy beams carrying orbital angular momentum of opposite helicity. In the focal region, “the intensity pattern outlines a spiral of decreasing radius and pitch,” and the bright lobes trace a three-dimensional funnel-like structure (Mansour et al., 15 Sep 2025). The relevant lobe positions are given by

$$A_a=A_r=0.08U, \qquad St_a=0.5, \qquad u_{turb}\sim 0.01U.$$1

In the monochromatic case, $$A_a=A_r=0.08U, \qquad St_a=0.5, \qquad u_{turb}\sim 0.01U.$$2, so the structure is static in time at fixed $$A_a=A_r=0.08U, \qquad St_a=0.5, \qquad u_{turb}\sim 0.01U.$$3; the apparent rotation arises only because the lobe angle changes with propagation distance. The paper explicitly interprets this as a static three-dimensional spiral structure rather than time-domain spinning, making the single-color optical tornado a direct optical analogue of a pseudo-rotating spiral jet (Mansour et al., 15 Sep 2025).

The same work distinguishes this from genuine time rotation. When $$A_a=A_r=0.08U, \qquad St_a=0.5, \qquad u_{turb}\sim 0.01U.$$4, the two-color beating term induces actual temporal rotation with full-rotation period

$$A_a=A_r=0.08U, \qquad St_a=0.5, \qquad u_{turb}\sim 0.01U.$$5

which the authors describe as an optical analog of a drill. The important encyclopedic point is that the same spiral morphology can therefore exist in both pseudo-rotating and truly rotating forms, depending on whether the twist is encoded in propagation or in time.

A second optical analogue is the rotating soliton trapped in a single spiral waveguide. In the laboratory frame, the soliton center follows a corkscrew path because the guide itself spirals in $$A_a=A_r=0.08U, \qquad St_a=0.5, \qquad u_{turb}\sim 0.01U.$$6, but in a suitable transformed frame the state is stationary or periodically self-reproducing. The reported oscillation period is

$$A_a=A_r=0.08U, \qquad St_a=0.5, \qquad u_{turb}\sim 0.01U.$$7

This is another precise realization of pseudo-rotation: the localized packet appears to spiral through space, while the motion is fundamentally a guided state in a moving refractive geometry (Petrovic et al., 2017).

6. Magnetized plasma and solar spiral jets

Magnetized plasma jets exhibit both pseudo-rotating and genuinely untwisting spiral structures, and recent solar work has sharpened the distinction.

A data-constrained 3D MHD simulation of a tiny spiral jet in a moss region attributes the spiral appearance to a fan-spine configuration containing an unstable flux rope. The rope rises, the pre-existing magnetic null collapses into a curved 3D current sheet, and external reconnection transfers both twist and cool material from the rope to the outer spine (Li et al., 14 Mar 2025). The twist-propagation speed is reported as

$$A_a=A_r=0.08U, \qquad St_a=0.5, \qquad u_{turb}\sim 0.01U.$$8

close to the local Alfvén speed estimate of

$$A_a=A_r=0.08U, \qquad St_a=0.5, \qquad u_{turb}\sim 0.01U.$$9

The jet then displays rolling dark and bright threads. The physical picture is not rigid-body rotation of the whole jet column, but twist transfer and untwisting along reconnected helical field lines.

A later active-region event reaches a different conclusion. Combining spectroscopy, a time-dependent magnetofrictional model, and MHD simulation, the authors argue that the observed rotation is driven primarily by plasma motion along helical open magnetic field lines rather than by untwisting of the field lines themselves (Huang et al., 24 Feb 2026). They report a roughly constant width of $4.5D$0 Mm at projected heights of $4.5D$1, $4.5D$2, and $4.5D$3 Mm, while the rotational speed decreases from

$4.5D$4

to

$4.5D$5

to

$4.5D$6

and the rotation period increases from

$4.5D$7

to

$4.5D$8

to

$4.5D$9

The same study reports that both linear and rotational velocities decrease with altitude, which it treats as evidence against a classical untwisting interpretation (Huang et al., 24 Feb 2026). In encyclopedic terms, this is one of the clearest plasma examples of a pseudo-rotating spiral jet: the spiral is real, but the rotation is carried by plasma tracing a persistent helical field.

For contrast, a limb event involving a broken flux rope and a fan-spine topology is interpreted as a genuine rotating helical blowout jet. In that case, the untwisting southern leg of the flux rope becomes a rotating jet, with blob speeds of $5D$0–$5D$1, radial jet speed of about $5D$2, and a narrow CME later reaching about $5D$3 at $5D$4 (Joshi et al., 2018). This comparison is important: spiral appearance alone does not specify whether a jet is pseudo-rotating or genuinely untwisting.

7. Interpretation, observability, and recurrent misconceptions

The main recurrent misconception is to equate any spiral or rotating-looking jet with bulk swirl. The literature surveyed here consistently warns against that inference. In actively controlled round jets, the apparent arm rotation is explicitly described as an illusion created by connecting neighboring moving vortices into continuous patterns (Wawrzak et al., 31 Aug 2025). In twisted liquid jets, the apparent surface rotation coexists with zero angular momentum about the axis (Kageyama et al., 2020). In optical tornadoes, the monochromatic beam is static in time at fixed $5D$5, even though successive transverse planes look rotated (Mansour et al., 15 Sep 2025). In solar jets, projected redshift/blueshift asymmetries and spiral threads may arise either from field untwisting or from plasma flowing along already helical fields (Huang et al., 24 Feb 2026).

Observability is therefore part of the phenomenon, not merely an experimental nuisance. In the active-flow-control case, the visible number of arms depends on the observable domain and vortex lifetime; the true multi-armed topology may be inaccessible even when it is fully determined by the forcing ratio (Wawrzak et al., 31 Aug 2025). In solar observations, projection effects and the coexistence of radial and lateral motion mean that tracked features do not isolate pure azimuthal velocity (Joshi et al., 2018). In optical realizations, the distinction between pseudo-rotation and true temporal rotation depends on whether one fixes $5D$6 or follows the propagation geometry (Mansour et al., 15 Sep 2025).

A plausible general implication is that the pseudo-rotating spiral jet is best treated as a pattern class rather than a single dynamical mechanism. Across fluids, optics, and plasma, the shared structure is a spiral or helical organization with a rotation-like appearance, while the underlying cause may be deterministic vortex sequencing, traveling azimuthal capillary modes, cross-sectional axis-switching, propagation-encoded interference, twist transfer, or field-guided plasma motion. What unifies these cases is not a universal constitutive law, but a common separation between spiral appearance and classical rigid or swirling rotation.