Relaminarization in Fluid Dynamics

• Relaminarization is the process by which turbulent flows return to a laminar state, driven by mechanisms like favorable pressure gradients, wall forcing, curvature and elasticity.
• The phenomenon encompasses complete or partial turbulence collapse, with studies showing diverse outcomes in pipes, channels, and curved geometries through DNS and experimental evidence.
• Practical applications of relaminarization include drag reduction, enhanced heat transfer, and improved flow control strategies in both industrial and academic settings.

Relaminarization is the return of a turbulent or turbulent-like flow toward a laminar or quasi-laminar state. In the literature covered here, the term includes complete collapse of turbulence in pipe, channel, curved-pipe, viscoelastic, and thermal-convection settings, but also weaker states in which turbulence persists while its contribution to the mean momentum balance becomes secondary, as in strongly accelerated turbulent boundary layers. The phenomenon is therefore not tied to a single geometry or mechanism: it can be induced by favorable pressure gradients, mean-profile modification, wall forcing, curvature changes, magnetic damping, stratification, elasticity, or rapid viscosity growth, and it may be complete, local, transient, or incomplete (Ranjan et al., 2017, Kühnen et al., 2018, Kumar et al., 2022).

1. Definitions and conceptual distinctions

A useful distinction is between hard relaminarization and soft relaminarization. In strong favorable-pressure-gradient boundary layers, the latter denotes a regime in which turbulence does not vanish in absolute terms, but its effect on the mean momentum balance becomes negligible because the imposed acceleration dominates and the Reynolds shear stress becomes effectively “frozen” along streamlines (Ranjan et al., 2017). By contrast, several pipe-flow studies report complete return to laminar Hagen–Poiseuille flow after turbulence collapse, with the downstream state remaining laminar in a smooth straight pipe unless a sufficiently large disturbance is reintroduced (Kühnen et al., 2018).

The same terminological breadth appears outside canonical Newtonian wall turbulence. In transitional pipe flow, relaminarization of a turbulent puff is the disappearance of a localized turbulent structure and return to the laminar base state (Khan et al., 16 Sep 2025). In elastic turbulence, relaminarization is identified by the normalized friction factor returning to unity, $f/f_{lam}\to 1$, together with disappearance of the fluctuating wake state (Kumar et al., 2022). In wall-sheared thermal convection, what relaminarizes is the plume-driven turbulent convective state, replaced by a steady or quasi-periodic coherent circulation (Xu et al., 2023).

The phenomenology is correspondingly varied. Some studies report complete and sustained relaminarization, some only a local laminarized region, and some an incomplete process followed by retransition. DNS over a Gaussian bump shows that strong favorable pressure gradient initiates relaminarization but does not complete it before adverse pressure gradient triggers partial retransition (Balin et al., 2020). In a curved $180^\circ$ bend, turbulence can collapse over a substantial portion of the bend but re-emerge after the geometry returns to a straight circular pipe (Bagheri et al., 21 Nov 2025).

2. Acceleration-driven relaminarization in boundary layers

The classical setting is an initially turbulent boundary layer subjected to strong streamwise acceleration, or equivalently a strong favorable pressure gradient. In that problem, onset is gradual rather than sharply localized, and several traditional parameters coexist: Launder’s acceleration parameter

$K=\frac{\nu}{U_e^2}\frac{dU_e}{dx},$

the pressure-gradient parameter

$\Delta_p=\frac{\nu}{\rho u_\tau^3}\frac{dP}{dx},$

the Narasimha–Sreenivasan parameter $\Lambda$, the shape factor $H=\delta^\ast/\theta$, and $Re_\theta=U_e\theta/\nu$. The same literature also emphasizes that no single universal onset criterion exists (Ranjan et al., 2017).

This ambiguity motivates the two-layer quasi-laminar theory. In that framework, the relaminarizing boundary layer consists of an outer stress-free, inviscid but rotational layer and an inner viscous laminar sub-boundary layer. Reassessment against higher-$Re$ experiments, including cases with $Re_{\theta0}$ up to about $4590$, showed that quasi-laminar theory gives a much better match to relaminarizing flows than standard turbulent boundary-layer codes, even when acceleration is high and $180^\circ$0 reaches about $180^\circ$1 (Ranjan et al., 2017). A central implication is that conventional equilibrium-style closures fail because the flow is no longer behaving as a fully turbulent boundary layer.

DNS over a Gaussian bump sharpens that picture. The strong favorable pressure gradient on the upstream side weakens near-wall turbulence, produces intermittency, reduces Reynolds shear stress, suppresses the wall-shear-normalized turbulent kinetic energy production rate, and drives the mean profile above the standard logarithmic law; however, relaminarization does not complete (Balin et al., 2020). At the bump peak, where favorable pressure gradient switches rapidly to adverse pressure gradient, the weakened inner layer undergoes partial retransition and generates a new highly energized internal layer. That internal layer then dominates the downstream adverse-pressure-gradient response. The same DNS argues that, under strong pressure gradients, inner and outer layers become largely independent: the near-wall region responds directly to the pressure gradient and determines skin friction, while the outer layer behaves more like a free-shear layer subject to pressure-gradient and curvature effects (Balin et al., 2020).

Unsteady propulsive flapping foils show a different but related acceleration-driven scenario. There, relaminarization is phase-dependent and appears as an extended laminar region in the wall-scaled profile, with departure from the standard log law and laminar-like behavior extending beyond $180^\circ$2 (Zurman-Nasution et al., 13 Aug 2025). At a representative mid-chord location, the relaminarizing favorable-pressure-gradient part of the cycle is associated with a 31% drop in the cyclic fluctuation of skin friction and an 8.5% rise in shape factor, and the effect intensifies rather than weakens as $180^\circ$3 increases from $180^\circ$4 to $180^\circ$5 (Zurman-Nasution et al., 13 Aug 2025). The same study explicitly finds that standard steady relaminarization criteria based on $180^\circ$6, $180^\circ$7, or $180^\circ$8 do not predict onset reliably in such a non-equilibrium, history-dependent flow.

3. Pipe, duct, and channel flows: profile engineering, wall forcing, and localized decay

A major modern theme is that turbulent pipe flow can be relaminarized by modifying the mean streamwise velocity profile so that the core decelerates and the near-wall region accelerates. Two steady devices realize that idea directly: a stationary obstacle insert and an annular near-wall injection system. Both produce complete relaminarization up to $180^\circ$9, and at $K=\frac{\nu}{U_e^2}\frac{dU_e}{dx},$0 the downstream pressure drop is reduced by a factor of 3.4 (Kühnen et al., 2018). The same interpretation underlies 3D-printed honeycomb flow-management devices: straight honeycombs mainly flatten the profile, whereas shaped honeycombs can create an M-shaped profile with centerline depression and near-wall overspeed. With these devices, complete relaminarization is achieved up to Reynolds numbers of order $K=\frac{\nu}{U_e^2}\frac{dU_e}{dx},$1, downstream skin friction is reduced almost by a factor of 5, and the break-even distance can be as low as approximately $K=\frac{\nu}{U_e^2}\frac{dU_e}{dx},$2 for short devices, though it rises to about $K=\frac{\nu}{U_e^2}\frac{dU_e}{dx},$3 for the strongest relaminarizer (Kühnen et al., 2018).

Transient wall forcing can act through the same mechanism. In a moving-wall experiment, a pipe segment is briefly translated in the streamwise direction. The wall motion does not annihilate turbulence immediately; it first produces a flatter, plug-like profile with severely reduced lift-up potential. At $K=\frac{\nu}{U_e^2}\frac{dU_e}{dx},$4, the measured transient growth drops by about a factor of 20, and the remaining fluctuations then decay exponentially after the wall stops (Scarselli et al., 2018). The minimum shift length required for relaminarization increases linearly with Reynolds number, and at higher Reynolds number the allowable wall-speed range narrows to values close to $K=\frac{\nu}{U_e^2}\frac{dU_e}{dx},$5 (Scarselli et al., 2018). Streamwise traveling-wave wall transpiration generalizes the same idea. DNS shows that downstream traveling waves can trigger relaminarization up to $K=\frac{\nu}{U_e^2}\frac{dU_e}{dx},$6, with the favorable net-energy regime collapsing to

$K=\frac{\nu}{U_e^2}\frac{dU_e}{dx},$7

essentially independent of Reynolds number (Bauer et al., 3 Sep 2025).

Other wall-based controls act through more specific near-wall mechanisms. Streamwise-varying wall rotation in a pipe creates an annular Spatial Stokes Layer. Relaminarization requires both sufficiently large layer thickness and sufficiently large velocity amplitude, and the proposed mechanism is continuous absorption of energy from wall-normal stress so that the turbulence self-sustaining process cannot be maintained; in the relaminarized cases, the laminar state is reported to be stable even to extremely large perturbations (Liu et al., 2021). In plane channel flow at $K=\frac{\nu}{U_e^2}\frac{dU_e}{dx},$8, globally stabilizing linear feedback control based on wall-normal velocity can relaminarize the full nonlinear discretized system; only scales larger than the mean streak spacing need active control, the forcing concentrates near $K=\frac{\nu}{U_e^2}\frac{dU_e}{dx},$9, and once the laminar state is reached the required control effort becomes minimal (Sharma et al., 2013).

Relaminarization also appears in transitional localized structures. Highly resolved DNS of pipe puffs at $\Delta_p=\frac{\nu}{\rho u_\tau^3}\frac{dP}{dx},$0, 1900, and 1920 verifies exponential decay of the total energy of streamwise velocity fluctuations and weak Reynolds-number dependence of the decay rate; at the trailing edge, the cross-sectional streamline topology contains saddle-node pairs whose separation follows a square-root-in-time law as they collide and vanish (Khan et al., 16 Sep 2025). In square-duct flow at $\Delta_p=\frac{\nu}{\rho u_\tau^3}\frac{dP}{dx},$1, a perturbation with $\Delta_p=\frac{\nu}{\rho u_\tau^3}\frac{dP}{dx},$2 shows growth followed by rapid relaminarization, whereas $\Delta_p=\frac{\nu}{\rho u_\tau^3}\frac{dP}{dx},$3 produces a long turbulent transient; near that boundary the dynamics alternates between edge-like states with two pairs of large vortices near opposing walls (Biau et al., 2010).

Passive geometric relaminarization extends these ideas beyond straight pipes. In a $\Delta_p=\frac{\nu}{\rho u_\tau^3}\frac{dP}{dx},$4 bend, a local increase in curvature combined with ovalization of the cross-section relaminarizes the flow at $\Delta_p=\frac{\nu}{\rho u_\tau^3}\frac{dP}{dx},$5 and $\Delta_p=\frac{\nu}{\rho u_\tau^3}\frac{dP}{dx},$6, reduces pressure loss by 53% relative to the baseline bend and by 36% relative to an equal-length straight turbulent pipe, and acts by suppressing streamwise Reynolds-stress production while simultaneously weakening the Dean-vortex secondary flow (Bagheri et al., 21 Nov 2025).

4. Magnetic, stratified, viscoelastic, thermal, and homogeneous-flow relaminarization

In low-magnetic-Reynolds-number magnetohydrodynamic pipe flow, relaminarization under a static transverse magnetic field is interpreted as magnetic destruction of the near-wall turbulence regeneration cycle. The proposed control parameter is

$\Delta_p=\frac{\nu}{\rho u_\tau^3}\frac{dP}{dx},$7

rather than $\Delta_p=\frac{\nu}{\rho u_\tau^3}\frac{dP}{dx},$8, because the decisive competition is between magnetic damping and wall-scaled near-wall coherent structures. An empirical estimate from available experiments gives an approximate criterion $\Delta_p=\frac{\nu}{\rho u_\tau^3}\frac{dP}{dx},$9 for the targeted inflow configuration (Moriconi, 2019).

In spanwise-stratified plane Couette flow, relaminarization is tied to a scale interaction. Stratification imposes a buoyancy-controlled vertical/spanwise scale

$\Lambda$0

while the near-wall streak spacing remains

$\Lambda$1

As stratification strengthens, the buoyancy scale shrinks until it intersects the streak spacing; at that point the stratified large-scale roll structure disrupts the SSP/VWI mechanism and sustained turbulence fails (Lucas et al., 2018).

Viscoelastic systems exhibit two distinct relaminarization scenarios. In elastic turbulence at vanishing inertia, a viscoelastic channel flow past an obstacle first develops elastic instability and elastic turbulence, then at sufficiently high elasticity enters drag reduction and can fully re-laminarize, identified by $\Lambda$2. The proposed mechanism is that elastic-wave frequency rises with $\Lambda$3, wave attenuation increases, wall-normal vorticity amplification weakens, and the fluctuating state collapses (Kumar et al., 2022). In viscoelastic channel drag-reducing turbulence, the issue is competition between two self-sustaining processes. At low Reynolds number, increasing elasticity can suppress inertial turbulence before an EIT-related self-sustaining process has formed, so the flow passes through a laminar regime; at moderate Reynolds number, the EIT-related process can appear early enough to avoid relaminarization and carry the flow directly toward MDR and EIT (Wen-Hua et al., 2021).

Thermal turbulence can also relaminarize under imposed wall shear. In wall-sheared Rayleigh–Bénard convection at $\Lambda$4 and $\Lambda$5, increasing $\Lambda$6 can suppress broadband turbulence, reduce plume area, drive volume-averaged TKE to zero, and replace the turbulent plume field with steady or quasi-periodic coherent channels (Xu et al., 2023). The proposed mechanism is reduction of buoyancy production $\Lambda$7 because detached plumes are swept away by the imposed wall shear. Strikingly, the laminarized state can transport heat more efficiently than the turbulent state because the coherent convection channels are stronger and more stable (Xu et al., 2023).

Homogeneous systems display related but differently organized collapses. Forced isotropic turbulence at low-to-moderate Reynolds number can undergo sudden transitions from chaotic multiscale dynamics to a simple large-scale state; survival probabilities are exponential and characteristic lifetimes increase superexponentially with Reynolds number, supporting a chaotic-saddle interpretation (Linkmann et al., 2015). In compressed turbulent plasma, relaminarization is modeled as a viscosity-growth-driven crossover from turbulent to viscous self-similar decay. In the two-equation M2 model, rapid relaminarization is associated with

$\Lambda$8

while the laboratory-frame condition for sudden viscous dissipation is

$\Lambda$9

which gives $H=\delta^\ast/\theta$0 for Saffman turbulence $H=\delta^\ast/\theta$1 (Thévenin et al., 2022).

5. Diagnostics, modeling frameworks, and dynamical-systems interpretations

No universal relaminarization diagnostic exists. The accelerated-boundary-layer literature repeatedly uses $H=\delta^\ast/\theta$2, $H=\delta^\ast/\theta$3, $H=\delta^\ast/\theta$4, $H=\delta^\ast/\theta$5, and $H=\delta^\ast/\theta$6, but explicitly states that onset is diffuse and not sharply localized (Ranjan et al., 2017). Bump-flow DNS and flapping-foil LES/DNS reinforce that conclusion: log-law departure, intermittency, suppression of Reynolds shear stress, and wall-scaled production collapse can appear without a clean crossing of any single classical threshold (Balin et al., 2020, Zurman-Nasution et al., 13 Aug 2025).

A second family of diagnostics is based on disturbance amplification. In pipe relaminarization by steady profile modification, moving walls, or shaped honeycombs, the recurring interpretation is that the altered mean profile reduces transient growth and therefore weakens lift-up and the near-wall regeneration cycle (Kühnen et al., 2018, Scarselli et al., 2018, Kühnen et al., 2018). In streamwise-varying wall rotation, the key diagnostic is an energy pathway: the Spatial Stokes Layer continuously absorbs energy from wall-normal stress, preventing self-sustainment (Liu et al., 2021).

A third family is dynamical-systems-based. Puff decay in pipe flow is described globally by exponential fluctuation-energy decay and locally by a time-evolving saddle-node bifurcation at the trailing interface (Khan et al., 16 Sep 2025). Forced isotropic turbulence shows exponential survival probabilities and finite lifetimes consistent with escape from a chaotic saddle (Linkmann et al., 2015). Near-threshold square-duct flow displays edge-like states and escape toward the laminar fixed point along an unstable manifold (Biau et al., 2010). These perspectives do not replace budget or profile analysis; they identify relaminarization as a state-space escape process whose observable manifestation is loss of the sustaining cycle.

6. Retransition, performance tradeoffs, and unresolved issues

Relaminarization is often temporary, local, or incomplete rather than terminal. In the Gaussian-bump boundary layer, strong favorable pressure gradient produces genuine relaminarization symptoms but not a fully quasi-laminar state; when favorable pressure gradient relaxes near the crest, partial retransition begins and forms a new internal layer (Balin et al., 2020). In the optimized curved bend, turbulence collapses only within the modified geometry and reappears when the pipe returns to a straight circular section, with faster recovery at $H=\delta^\ast/\theta$7 than at $H=\delta^\ast/\theta$8 (Bagheri et al., 21 Nov 2025). In an accelerating riblet-covered boundary layer, the overlying TBL relaminarizes much like the smooth-wall case, but retransition begins earlier and more violently because spanwise Kelvin–Helmholtz rollers develop near the riblet crest and interact with residual streaks (Savino et al., 23 Apr 2026).

Drag reduction and relaminarization are not equivalent. Upstream traveling transpiration waves can produce sublaminar drag through a pumping effect while destabilizing rather than relaminarizing the flow (Bauer et al., 3 Sep 2025). Riblets that are drag reducing in zero-pressure-gradient flow can become drag increasing during relaminarization because viscous shear concentrates near the crest, while the overlying boundary layer remains governed by the total shear stress at the groove opening rather than by the total wall drag (Savino et al., 23 Apr 2026). Wall-sheared thermal convection demonstrates the opposite paradox: the laminarized state can carry more heat than the turbulent state because transport reorganizes into stable convection channels (Xu et al., 2023).

Practical implementation remains system-dependent. Shaped honeycombs are highly sensitive to manufacturing defects; even a single partially blocked cell can prevent relaminarization, and the best-performing geometries incur longer break-even distances (Kühnen et al., 2018). Passive curved-pipe relaminarization has been demonstrated only over a limited operating range and does not yet provide a full Reynolds-number or disturbance-sensitivity map (Bagheri et al., 21 Nov 2025). Elastic-turbulence relaminarization and compressed-plasma models likewise identify compelling mechanisms without establishing universal operating envelopes (Kumar et al., 2022, Thévenin et al., 2022). The combined evidence suggests that relaminarization is best understood not as a single threshold phenomenon, but as a family of route-specific collapses of turbulence sustainment, each controlled by the geometry, forcing, constitutive physics, and relevant instability or regeneration mechanisms of the underlying flow.