3D Intermittent Flows

• 3D intermittent flows are three-dimensional states characterized by localized, bursty motions embedded within a stable background, observed across granular, shear, MHD, and PDE studies.
• Researchers use spatio-temporal analysis, direct numerical simulations, and convex integration to quantify events such as puffs, chaotic transients, and localized jets.
• Key findings reveal that despite pronounced local intermittency, global metrics like mass flow or energy remain constant, with localized events driving large-scale transport and field amplification.

Three-dimensional intermittent flows are flow states in which the active motion is neither uniformly steady nor uniformly space-filling. In the literature surveyed here, intermittency denotes regularly spaced cessation and restart of a granular plug, sustained local fluctuations of wetting and non-wetting occupancy at fixed macroscopic forcing, localized turbulent structures such as puffs or oblique stripes, burst-like episodes of magnetic-energy amplification, chaotic transients with on-off statistics, intermittent jets in magnetized accretion, and mathematically constructed high-frequency flow packets concentrated on sets of small volume (Mersch et al., 2010, Karabasova et al., 12 May 2026, Ishida et al., 2017, Pratt et al., 2013, Garcia et al., 2023, Chatterjee et al., 2023, Novack et al., 2022, Peng et al., 15 Aug 2025). Across these settings, the central issue is not merely unsteadiness, but the organization of transport, dissipation, or field amplification into localized episodes embedded within a broader background state.

1. Conceptual scope and diagnostic language

The term intermittent flow is used with different but related meanings. In porous media, it denotes “sustained, local fluctuations of wetting and non-wetting phase occupancy at fixed macroscopic forcing” (Karabasova et al., 12 May 2026). In the silo experiment of Mersch et al., it denotes “regularly spaced cessation and restart of the central plug” identified from a high-speed spatio-temporal diagram (Mersch et al., 2010). In annular Poiseuille flow, intermittency is organized by localized turbulent structures, notably puffs and helical stripes (Ishida et al., 2017). In the magnetised spherical Couette problem, chaotic transients display “on-off intermittent behaviour” near a nearly invariant subspace (Garcia et al., 2023). In the convex-integration literature, intermittency refers to highly concentrated building blocks—“intermittent pipe-flows” or “intermittent Mikado flows”—chosen so that large amplitudes occupy only a small fraction of physical space (Novack et al., 2022, Peng et al., 15 Aug 2025).

Domain	Intermittent manifestation	Representative diagnostic
Granular and porous flow	Restart/cessation; disconnection/reconnection	$P_{\rm int}(V)$; $\nabla P$-Ca
Shear and MHD flow	Puffs, stripes, meanders, bursts, on-off transients	PDFs, $\alpha$, $K_*$
PDE construction	Concentrated pipe/Mikado packets	$R_q$, $w_{q+1}$

These usages share a structural feature: the dynamically relevant activity is localized in space, time, or both. This suggests that “3D intermittent flow” is less a single mechanism than a family of mechanisms whose common signature is sparse activation against a stable, weakly active, or statistically stationary background. The differences are equally important. Some cases are experimentally observed physical flows, some are DNS of fully resolved geometry, some are symmetry-constrained dynamical systems, and some are analytic constructions for weak solutions.

2. Granular and porous-media realizations

In the quasi–three-dimensional rectangular silo studied by Mersch et al., a DC high electric field is applied perpendicularly to the silo to tune cohesion. The outlet mass flow is measured, the flow geometry is visualized by successive-frame subtraction, and the flow dynamics is analyzed by spatio-temporal methods (Mersch et al., 2010). Four mutually exclusive geometrical regimes are reported at fixed voltage: Funnel-flow, Avalanche-flow, Rathole, and Blocked. The transition from funnel flow to rathole flow is probabilistic, and at a given voltage two kinds of flow dynamics can occur: a continuous flow or an intermittent flow. The intermittent-flow probability is fitted by

$$P_{\rm int}(V)=1-\exp(-V/V_0), \qquad V_0\approx 600\,{\rm V},$$

and grows from $0$ at $V\approx 0$ to $\approx 1$ above $\nabla P$0 (Mersch et al., 2010).

A striking feature of that experiment is that the mean outlet mass flow remains unchanged despite the geometric and dynamical transitions. Over $\nabla P$1, excluding the blocked region, the fitted slope is

$\nabla P$2

and no systematic voltage dependence of $\nabla P$3 is observed (Mersch et al., 2010). The intermittent cycle is decomposed into an onset phase $\nabla P$4, a fully flowing phase $\nabla P$5, and an abrupt cessation, with

$\nabla P$6

$\nabla P$7

$\nabla P$8

The duty cycle decreases from $\nabla P$9 at $\alpha$0 to $\alpha$1 at $\alpha$2, while the onset of intermittent behavior occurs around $\alpha$3–$\alpha$4 and saturates above $\alpha$5 (Mersch et al., 2010). The 6 mm thickness corresponds to $\alpha$6 grain diameters, so true 3D flow and depth-wise heterogeneity can in principle develop, but no explicit depth-resolved data are reported.

The pore-scale DNS of Karabasova et al. moves from quasi-3D behavior to fully 3D resolved geometry. The simulations use a micro-CT-derived Bentheimer sandstone geometry with 28 pores and 39 throats, discretized into 157,784 hexahedral finite-volume cells, and capillary numbers spanning $\alpha$7 to $\alpha$8 (Karabasova et al., 12 May 2026). Three regimes are identified: Regime I (Darcy, $\alpha$9), Regime II (intermittent, $K_*$0), and Regime III (ganglion dynamics). The capillary number is

$K_*$1

In the Darcy regime, the computed pressure-gradient-capillary-number relationship is linear with fitted exponent $K_*$2, while in the intermittent regime the fit is

$K_*$3

for $K_*$4 (Karabasova et al., 12 May 2026).

The local intermittency mechanism is described as a periodic sequence of drainage and imbibition displacements triggered by local pressure fluctuations. The elementary events are Haines jumps, snap-off, and cooperative pore filling. Using a topology-aware snap-off detector, a voxel is counted as intermittent only if at least three full disconnect–reconnect cycles occur at that location, with each half-phase persisting at least 1 ms (Karabasova et al., 12 May 2026). In a representative cluster at $K_*$5, disconnection consistently occurs once $K_*$6, linking local capillary destabilisation to network-scale flux redistribution. The intermittent set grows from 7.5% to 17.6% of pore-space voxels as capillary number increases, and the intermittent elements organize into connected conduits embedded within a stable backbone of fixed flow pathways (Karabasova et al., 12 May 2026). This directly counters the common simplification that intermittency in porous flow is purely local.

3. Wall-bounded shear flow and near-wall intermittency

In pressure-driven annular pipe flow, Ishida, Duguet, and Tsukahara study incompressible pressure-driven annular flow in long domains and analyze the transition from puffs to oblique stripes statistically by focusing on the axisymmetry properties of the associated large-scale flows (Ishida et al., 2017). For small radius ratio $K_*$7, turbulence at marginal $K_*$8 appears as axisymmetric, streamwise-localized puffs. For large $K_*$9, one observes regular helical stripes inclined at an angle $R_q$0 to the streamwise direction. At intermediate $R_q$1–$R_q$2, straight puffs and helical puffs coexist stochastically in space and time. The large-scale inclination is defined by

$R_q$3

The unimodal-to-bimodal transition in the PDF of $R_q$4 yields an estimated critical radius ratio $R_q$5 (Ishida et al., 2017).

The significance of that result is mechanistic rather than taxonomic. The transition is gradual, not abrupt, and is controlled by the emergence of a transverse large-scale flow component once azimuthal confinement is relaxed sufficiently (Ishida et al., 2017). In this case, intermittency is carried by localized turbulent structures, but the orientation and persistence of those structures are selected by global mass-conservation constraints. This is closely aligned with the porous-media picture in which intermittent events are embedded in a larger network.

A complementary near-wall manifestation appears in the digital Fresnel reflection holography measurements of Kumar et al. in a smooth-wall turbulent channel at $R_q$6 (Sankar et al., 2020). The measurements resolve the viscous sublayer, $R_q$7, with 3 kHz sampling, 1 $R_q$8m/pixel spatial resolution, and a lowest measurement height of $R_q$9. Two intermittent flow families are identified. The first consists of nearly uniform high-speed and low-speed events, occupying $w_{q+1}$0 of all trajectories below $w_{q+1}$1, with $w_{q+1}$2, $w_{q+1}$3, and $w_{q+1}$4–$w_{q+1}$5. The second consists of small-scale spanwise meandering motions, also about $w_{q+1}$6 of sublayer data, with spanwise excursion $w_{q+1}$7–$w_{q+1}$8, streamwise excursion $w_{q+1}$9–$$P_{\rm int}(V)=1-\exp(-V/V_0), \qquad V_0\approx 600\,{\rm V},$$0 per meander, and occasional peak accelerations exceeding $$P_{\rm int}(V)=1-\exp(-V/V_0), \qquad V_0\approx 600\,{\rm V},$$1 (Sankar et al., 2020).

The statistical signature is strongly non-Gaussian. The PDFs of wall shear stress follow stretched-exponential tails, and the one-point PDF of the magnitude of Lagrangian acceleration is fitted by

$$P_{\rm int}(V)=1-\exp(-V/V_0), \qquad V_0\approx 600\,{\rm V},$$2

with $$P_{\rm int}(V)=1-\exp(-V/V_0), \qquad V_0\approx 600\,{\rm V},$$3 and $$P_{\rm int}(V)=1-\exp(-V/V_0), \qquad V_0\approx 600\,{\rm V},$$4 in units of $$P_{\rm int}(V)=1-\exp(-V/V_0), \qquad V_0\approx 600\,{\rm V},$$5 (Sankar et al., 2020). Defining a meandering indicator $$P_{\rm int}(V)=1-\exp(-V/V_0), \qquad V_0\approx 600\,{\rm V},$$6 for trajectories whose net $$P_{\rm int}(V)=1-\exp(-V/V_0), \qquad V_0\approx 600\,{\rm V},$$7–$$P_{\rm int}(V)=1-\exp(-V/V_0), \qquad V_0\approx 600\,{\rm V},$$8 deflection exceeds $$P_{\rm int}(V)=1-\exp(-V/V_0), \qquad V_0\approx 600\,{\rm V},$$9, one finds

$0$0

Here the intermittent events are neither isolated laminar-turbulent patches nor pore-scale topological switches, but localized, strongly accelerated near-wall motions that substantially populate the high-tail statistics.

4. Magnetohydrodynamic and astrophysical forms of intermittency

In statistically steady, convectively driven Boussinesq MHD turbulence, direct numerical simulations reveal intermittent large-scale high-shear flows that occur frequently and spontaneously (Pratt et al., 2013). The system is sustained by convective driving of the velocity field and small-scale dynamo action, but the intermittent emergence of coherent, sheet- or ribbon-like streams generates magnetic energy at an elevated rate over time-scales longer than the characteristic time of the large-scale convective motion. The magnetic stretching term

$0$1

is used as a core diagnostic. Each burst typically lasts $0$2 to $0$3 buoyancy times $0$4, with some events as short as $0$5 or beyond $0$6; in a run of length $0$7, 15 distinct shear bursts are recorded, on average one every $0$8 (Pratt et al., 2013). During a strong isolated burst, the global magnetic energy rises by a factor of $0$9–$V\approx 0$0 over its pre-burst value.

Garcia et al. study a different MHD route to intermittency in the magnetised spherical Couette problem (Garcia et al., 2023). There, symmetry-breaking Hopf bifurcations lead to high-dimensional invariant tori, then to chaotic attractors, and finally to chaotic transients after a boundary crisis. For one sequence of bifurcations, the chaotic transients display on-off intermittent behaviour. Defining

$V\approx 0$1

the “off” state corresponds to very small non-axisymmetric energy outside the nearly invariant $V\approx 0$2 subspace, while the “on” state corresponds to bursts in $V\approx 0$3 (Garcia et al., 2023). The reported statistics are characteristic:

$V\approx 0$4

the set of burst times has box-counting fractal dimension $V\approx 0$5, and the inter-burst distribution scales as $V\approx 0$6 (Garcia et al., 2023). In this setting, unstable invariant tori organize the transient dynamics.

Astrophysical accretion provides a third MHD variant. In “Misaligned magnetized accretion flows onto spinning black holes: magneto-spin alignment, outflow power and intermittent jets” (Chatterjee et al., 2023), numerical simulations show that rapidly spinning, prograde black holes in the magnetically-arrested disk state force the inner accretion flow into alignment with the black-hole spin via the magneto-spin alignment mechanism for initial misalignment angles $V\approx 0$7. Extremely misaligned MAD disks exhibit intermittent jets that blow out parts of the disk to $V\approx 0$8 gravitational radii before collapsing, leaving behind hot cavities and magnetized filaments. The intermittent jet mechanism forms a mini-feedback cycle and could explain some cases of X-ray and radio quasi-periodic eruptions observed in dim AGN (Chatterjee et al., 2023). The same study further reports that geometrically-thick, misaligned accretion flows do not undergo sustained Lense-Thirring precession and suggests instead that magnetic flux eruptions can mimic precession-like motion by driving large-scale surface waves in the jets.

Taken together, these MHD examples show distinct organizations of intermittency: shear bursts in turbulent convection, on-off chaotic transients near unstable tori, and eruption-collapse cycles in magnetized accretion. The commonality is the episodic release or concentration of magnetic and kinetic activity; the mechanisms range from magnetic stretching to crisis-mediated dynamics to black-hole magnetic-flux eruptions.

5. Intermittent flows as analytical building blocks in 3D PDE theory

In the analytical literature on the 3D incompressible Euler equations, intermittency is encoded directly into the construction of weak solutions. Novack and Vicol prove that for any $V\approx 0$9 there exist non-conservative weak solutions in

$\approx 1$0

and by interpolation these solutions belong to $\approx 1$1 for $\approx 1$2 approaching $\approx 1$3 as $\approx 1$4 approaches $\approx 1$5 (Novack et al., 2022). The construction uses an Euler–Reynolds iteration with higher-order Reynolds stresses and intermittent pipe-flows of optimal relative intermittency. At stage $\approx 1$6,

$\approx 1$7

with

$\approx 1$8

The corrective perturbation is a superposition of concentrated pipe-like flows, and the intermittency parameter is chosen as

$\approx 1$9

The authors describe this balance as a “one-half intermittency rule” (Novack et al., 2022).

The conceptual point is explicit in that work: the intermittent nature of the constructed solutions matches that of turbulent flows, which are observed to possess an $\nabla P$00-based regularity index exceeding $\nabla P$01 (Novack et al., 2022). The result does not imply, and is not implied by, Isett’s proof of the Hölder-based Onsager conjecture. Thus mathematical intermittency here is not a secondary stylistic feature of convex integration; it is the mechanism that permits a distinct regularity class and a distinct geometry of the building blocks.

A closely related construction appears in the Hall-MHD setting. Peng, Wang, and Zhang prove non-uniqueness of weak solutions with non-trivial magnetic fields to the 3D Hall-MHD equations on the plane through convex integration and by constructing new errors and new intermittent flows (Peng et al., 15 Aug 2025). Their perturbations are written as

$\nabla P$02

with principal and corrector parts built from projected 3D intermittent Mikado flows. The elementary packet is

$\nabla P$03

with $\nabla P$04, $\nabla P$05, and average stress $\nabla P$06 (Peng et al., 15 Aug 2025). The profile is concentrated in a slab of width $\nabla P$07 orthogonal to $\nabla P$08 and oscillates at frequency $\nabla P$09 along $\nabla P$10. This is intermittency in the strongest geometric sense: each packet is huge on a set of very small volume and vanishing elsewhere.

These PDE constructions should not be conflated with laboratory or DNS intermittency, but neither are they disconnected from it. They formalize concentration, sparse support, and shell-wise energy transfer using explicit building blocks whose geometry is chosen to control norms and error terms. A plausible implication is that the mathematical theory has adopted “intermittent flow” not metaphorically, but as a geometrically precise analogue of sparse activation in turbulent cascades.

6. Cross-cutting mechanisms, distinctions, and recurrent misconceptions

Several recurrent mechanisms emerge across the surveyed literature. One is localized activation within a stable background. In porous media, intermittent conduits are embedded within a stable backbone of fixed flow pathways (Karabasova et al., 12 May 2026). In annular Poiseuille flow, localized puffs or stripes coexist with laminar regions (Ishida et al., 2017). In magnetised spherical Couette flow, chaotic bursts alternate with long visits near a nearly invariant manifold (Garcia et al., 2023). In convex integration, the perturbation fields are concentrated in tubes or slabs occupying a small fraction of space (Novack et al., 2022, Peng et al., 15 Aug 2025).

A second mechanism is global organization of apparently local events. The pore-scale DNS shows that intermittent disconnection and reconnection are accompanied by strongly coupled local pressure redistribution and non-wetting phase flow, and explicitly concludes that intermittency is “network-coupled rather than purely local” (Karabasova et al., 12 May 2026). The puff-to-stripe transition in annular flow is controlled by the emergence of a large-scale azimuthal flow component, not by a purely local change of the turbulent patch (Ishida et al., 2017). The on-off intermittent transients in the magnetised spherical Couette problem are organized by unstable invariant tori (Garcia et al., 2023). This suggests that 3D intermittency is often constrained by long-range geometry, network connectivity, or phase-space structure.

Several misconceptions are directly contradicted by the cited work. Intermittency does not necessarily imply a changed mean throughput: in the silo experiment, $\nabla P$11 is constant within experimental uncertainty even though the flow becomes intermittent and the geometry changes from funnel flow toward rathole flow (Mersch et al., 2010). Intermittency does not necessarily produce sharp spectral lines: in the pore-scale DNS, the median PSD over intermittent elements is broadband, with a low-frequency plateau and high-frequency decay, and no sharp peaks (Karabasova et al., 12 May 2026). In low-luminosity accreting black holes, quasi-periodic variability does not need to be attributed to sustained Lense-Thirring precession: geometrically-thick, misaligned accretion flows do not undergo sustained LT precession in the reported simulations, while magnetic flux eruptions may mimic precession-like motion (Chatterjee et al., 2023). And in PDE theory, the intermittent Onsager theorem is complementary to rather than a corollary of Hölder-based constructions (Novack et al., 2022).

The literature also shows that “3D intermittent flow” does not select a single observable. Depending on the context, the appropriate observables are regime probabilities, onset-front velocities, duty cycle, capillary-number scaling, connectivity maps, premultiplied spectra, stretched-exponential PDFs, magnetic stretching, burst-time fractal dimension, or Reynolds-stress estimates. The topic is therefore best understood as a unifying description of sparse, bursty, or localized activity in three-dimensional flow systems, rather than as a single phenomenological law.