arXiv subjects

Giulio Foggi Rota

Publications and source records attributed to Giulio Foggi Rota.

16 recordsLinked to original sources

arXiv2026

Free surfaces in turbulence - A unified framework from water surfaces to elastic solids

What do the ocean surface and a swaying flag have in common? Both are deformable surfaces exhibiting chaotic motion when exposed to turbulent flows. Whether such motion is primarily driven by flow turbulence or by nonlinear dynamics intrinsic to the surface remains debated. Surface waves can interact nonlinearly and transfer energy across scales through the cascade of wave turbulence, a behaviour observed at interfaces between otherwise quiescent fluids and in controlled laboratory experiments. They can as well induce turbulent motions in the neighbouring fluids (wave-induced-turbulence), provided the local Reynolds number is large enough. Realistic environments, however, are more complex and typically involve the simultaneous presence of wave turbulence and wave-induced-turbulence with turbulence-induced-waves, the dynamic relevance of which remains unclear. Here we develop a theoretical framework describing the response of a deformable surface to pressure fluctuations generated by a turbulent flow, and validate it using numerical simulations of the air-water interface in quasi-realistic conditions, complemented by simulations of a deformable rubber layer. Our linear theory, which excludes nonlinear wave-wave interactions, predicts distinct dynamical regimes depending on whether intrinsic surface dynamics emerge or whether the interface is enslaved by flow turbulence. Remarkably, although our fully resolved and nonlinear simulations do not inhibit the onset of wave turbulence, interface spectra measured in the configurations studied here are controlled at leading order by turbulent pressure forcing and linear surface response, in strong agreement with our theoretical assumptions. Our predictions appear compatible with aerial surveys of the ocean surface, highlighting the need for further measurements to distinguish among wave turbulence and turbulence-induced-waves.

physics.flu-dyn↗

arXiv2026

Elastic turbulence in straight confined geometries

Elastic turbulence (ET) in straight geometries has been extensively studied in idealised configurations such as periodic shear and planar channel flow, yet experiments are typically restricted to confined systems like ducts and pipes. While chaotic elastic fluctuations are observed in ducts, their onset in pipes is debated due to geometric constraints. Here we report sustained chaotic dynamics in both geometries and show they correspond to the same ET state identified in idealised setups. Our results establish ET as a geometry-independent attractor and point to a distinct transition mechanism in pipes.

physics.flu-dyn↗

arXiv2026

Coexisting chaos and order in micro-textured elastic flows

Viscoelastic fluid flows over micro-textured surfaces - densely covered by slender protrusions like cilia lining the body airways or villi covering the intestinal epithelium - underpin essential biological processes including transport, mixing, and absorption. Despite their ubiquity, the dynamics generated by the interplay between fluid elasticity and these complex geometries remain largely unexplored. Here we combine fully resolved numerical simulations with microfluidic experiments to reveal the flow dynamics established above dense arrays of microscopic pillars (canopies) immersed in the low-Reynolds-number flow of a viscoelastic liquid. We observe that the flow above the canopy tips spontaneously develops elastic turbulence. Remarkably, the chaotic state coexists with elastic waves emerging from the coupling between fluid elasticity and the heterogeneous shear induced by the canopy geometry. These ordered fluid motions persist across a broad range of flow conditions and canopy configurations. Our results demonstrate that coherent wave propagation and elastic turbulence are complementary manifestations of viscoelastic fluid flow. Beyond their fundamental significance, these mechanisms have broad implications for transport in biological and engineered environments, and reveal how structured geometries can harness the spontaneous dynamics of viscoelastic liquids to manipulate complex flows.

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arXiv2026

Energy transfer and scale organisation in dense canopy turbulence

This study identifies the scale-dependent processes that sustain turbulence in dense submerged canopy flows. Using a scale-resolved energy budget, we determine where in space and at which scales production, pressure-strain redistribution, and inter-scale transfer predominantly occur, and how they link the canopy layer to the overlying shear flow. We show that energy production is localised at the interfacial shear layer, over a narrow range of streamwise and spanwise scales, while fluctuations within the canopy are primarily maintained through inter-scale transfer and pressure-strain redistribution. The dynamically active scales in the canopy are largely imposed by outer-layer structures, with their organisation and coherence mediated by these inherited motions. Energy exchange across the canopy interface is asymmetric but not unidirectional: although the dominant transfer is from the outer layer towards the canopy, intermittent reverse interactions occur at all scales. The most intense cross-interface exchanges are associated with finer-scale motions rather than large-scale structures, indicating that extreme interfacial energy fluxes are governed predominantly by small-scale dynamics. The flexibility of the canopy weakens the coherence of outer-layer structures and reduces the efficiency of inter-layer energy transfer, thereby altering both the organisation and scale of the fluctuations within the canopy. These results clarify how turbulence in dense canopies is organised and sustained, providing a unified energetic interpretation that links coherent structures to scale-dependent mechanisms.

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arXiv2026

Waves dictate the yo-yoing decay of a viscoelastic mixing layer

We find that waves develop in a time-decaying mixing layer of viscoelastic fluid, leading the mean-flow to yo-yo. This is in sharp contrast with Newtonian fluids, where laminar mixing layers evolve monotonically. We combine direct numerical simulations with a theoretical analysis of the energy budget for the flow to uncover the underlying physical mechanism. The yo-yoing of the mean-flow is shown to be driven by the elastic polymers injecting energy into the fluid and, in turn, being rotated by the large-scale mean shear. We then provide the mathematical model of the problem and solve it analytically, finding wave solutions with non-linear dispersion predicting the period of the yo-yoing and the parameter range where it occurs. As decaying mixing layers are one of the simplest and canonical examples of unsteady flows, the phenomenon identified here explains the anomalies recently observed in experiments of unsteady viscoelastic flows in complex geometries.

physics.flu-dyn↗

arXiv2026

Beyond Stokes drift -- Lagrangian transport in evolving gravity waves

Finite-amplitude gravity waves at the air-water interface induce net fluid and particle transport, known as Stokes drift. While this mechanism is well understood for steady waves, transport under unsteady, evolving conditions remains poorly characterized. Here, we investigate Lagrangian transport in freely decaying waves using high-resolution two-phase simulations and a perturbative analytical model. Wave decay modifies the classical Lagrangian drift by introducing both first- and second-order corrections in the wave amplitude expansion, and generates a net vertical transport, governed by the balance between inertia and viscosity. These effects alter particle trajectories and enhance anisotropic mixing, with implications for interpreting field observations and modelling surface transport processes.

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arXiv2026

The broken link between space and time in elastic turbulence

Elastic turbulence (ET), observed in flows of sufficiently elastic polymer solution at small inertia, is characterized by chaotic motions and power-law scaling of energy spectrum ($E$) in both wavenumber ($k$) and frequency ($ω$): $E(k) \sim k^{-α}$ and $E(ω) \sim ω^{-β}$. Experiments of ET have obtained a vast range of values for the exponent $β$. In inertial turbulence, Taylor's frozen-flow hypothesis implies $α= β$, i.e., spatial and temporal scales are linearly related to each other. In contrast, from high-resolution simulation in three different setups, a tri-periodic box, a channel, and a planar jet, we show that in ET $α\approx 4$ while $β$ varies significantly. Our analysis shows that in general Taylor's hypothesis does not hold in ET as there is no universal relation, linear or otherwise, between space and time. We thus clear the confusion of the different scaling exponents found in ET, and focus the attention of future research on understanding $α$. Our analysis also implies that waves-like dynamics with a linear dispersion relation (e.g., Alfvén waves) can not play a role in determining the scaling behavior of ET. The techniques introduced here can be useful for studying smooth chaotic flows in general, e.g., active turbulence.

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arXiv2025

Effect of submerged vegetation on water surface geometry and air-water momentum transfer

Understanding how submerged vegetation modifies the water surface is crucial for modeling momentum exchange between shallow waters and the atmosphere. In particular, quantifying its impact on the equivalent aerodynamic roughness of the water surface is essential for improved boundary-layer parameterization in oceanic and atmospheric models. In this Letter, we present fully resolved multiphase simulations of gravity-driven flow over a fully submerged vegetated bed, capturing the coupled dynamics of air, water, and individual plant stems, under quasi-realistic conditions (the air/water viscosity ratio is real, while the density ratio is reduced tenfold). Our results show that vegetation submerged for four times its height regularizes the water surface suppressing strong deformations and homogenizing streamwise-propagating wave fronts along the transversal direction. Despite these alterations, the equivalent roughness perceived by the overlying air flow remains unchanged. These findings clarify vegetation-surface interactions and provide quantitative insights for nature-based wave mitigation strategies and atmospheric boundary-layer modeling.

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arXiv2025

Filament inclination effect on turbulent canopy flows

Inspired by the spontaneous behaviour observed in filamentous layers -- where the balance between flow-induced drag and structural elasticity dictates the filaments' equilibrium streamlined posture -- we perform a series of large-eddy simulations to investigate how filament inclination affects turbulent shear flows developing both above and within a canopy of filaments. We examine six distinct filament inclination angles ranging from 0°to 90°. The in-plane solid fraction and filament length are chosen to achieve a fully dense canopy at zero inclination, and these parameters remain constant throughout our study. By setting a nominal bulk Reynolds number of 6000, we provide a detailed statistical characterisation of the turbulent flow. Our findings illustrate distinct changes in the flow regime with varying filament inclination. At lower angles, the canopy remains dense and significantly influences the flow, conforming to a classical canopy-flow regime. However, as the inclination approaches 90°, the intra-canopy region progressively becomes shielded from the outer flow. Remarkably, at 90°inclination, the flow drag reduces significantly, and the total drag becomes lower than that typically seen in an open, filament-free flow. We document this transition from a canopy-dominated regime to a scenario where the canopy becomes largely sheltered from the outer turbulent flow, highlighting key alterations in intra-canopy dynamics as filament inclination increases. Our observations are substantiated by an analysis of the velocity spectra, providing deeper insight into the interactions between the canopy and the developing turbulent boundary layer.

physics.flu-dyn↗

arXiv2025

Edge-effects in the turbulent flow over flexible aquatic vegetation

Riparian vegetation along riverbanks and seagrass along coastlines interact with water currents, significantly altering their flow. To characterise the turbulent fluid motion along the streamwise--edge of a region covered by submerged vegetation (canopy), we perform direct numerical simulations of a half--channel partially obstructed by flexible stems, vertically clamped to the bottom wall. An intense streamwise vortex forms along the canopy edge, drawing high--momentum fluid into the side of the canopy and ejecting low--momentum fluid from the canopy tip, in an upwelling close to the canopy edge. This mechanism has a profound impact on the mean flow and on the exchange of momentum between the fluid and the structure, which we thoroughly characterise. The signature of the canopy--edge vortex is also found in the dynamical response of the stems, assessed for two different values of their flexibility. Varying the flexibility of the stems, we observe how different turbulent structures over the canopy are affected, while the canopy--edge vortex does not exhibit major modifications. Our results provide a better understanding of the flow in fluvial and coastal environments, informing engineering solutions aimed at containing the water flow and protecting banks and coasts from erosion.

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arXiv2024

Reconfiguration and dynamics of clamped fibers under finite-amplitude surface gravity waves

We investigate the behaviour of a flexible stem completely submerged under a surface gravity wave of finite amplitude using fully resolved direct numerical simulations. By varying the rigidity of the stem over ten orders of magnitude, we explore its motion in the drag-dominated regime with realistic air and water properties. Our findings reveal two distinct structural responses of the stem depending on the ratio between its natural frequency (f_nat) and the wave frequency (f_wave). For f_nat/f_wave >> 1, the stem maintains on average a straight configuration and exhibits streamwise oscillations in phase-opposition with the wave, moving symmetrically with respect to the vertical direction. Conversely, for f_nat/f_wave << 1, the stem reconfigures under the influence of the Stokes drift, bending forward and breaking the symmetry, and exhibits oscillations that are more coherent with the surrounding flow field. Resonance is observed when f_nat is approximatively f_wave. These results provide new insights into the dynamics of slender vegetation and man-made structures in wave fields, offering valuable implications for marine biology and engineering.

physics.flu-dyn↗

arXiv2024

A unified view of elastic and elasto-inertial turbulence in channel flows at low and moderate Reynolds numbers

The chaotic flow of elastic fluids at low Reynolds number (Re) is typically distinguished into elasto-inertial and elastic turbulence (EIT/ET). However, the clear separation among these two turbulent regimes in parallel flows with a gradual Re decrease remains elusive. Here, spanning Re over four orders of magnitude, we investigate the statistical and structural nature of the flows computed by fully resolved 3D numerical simulations, revealing that as inertia becomes sub-dominant all flows share similar dynamical properties. Supported by the results, we thus propose a unified view of fully developed ET and EIT in parallel flows.

physics.flu-dyn↗

arXiv2024

Dynamics and fluid-structure interaction in turbulent flows within and above flexible canopies

Flexible canopy flows are often encountered in natural scenarios, e.g., when crops sway in the wind or when submerged kelp forests are agitated by marine currents. Here, we provide a detailed characterisation of the turbulent flow developed above and between the flexible filaments of a fully submerged dense canopy and we describe their dynamical response to the turbulent forcing. We investigate a wide range of flexibilities, encompassing the case in which the filaments are completely rigid and standing upright as well as that where they are fully compliant to the flow and deflected in the streamwise direction. We are thus able to isolate the effect of the canopy flexibility on the drag and on the inner-outer flow interactions, as well as the two flapping regimes of the filaments already identified for a single fiber. Furthermore, we offer a detailed description of the Reynolds stresses throughout the wall-normal direction resorting to the Lumley triangle formalism, and we show the multi-layer nature of turbulence inside and above the canopy. The relevance of our investigation is thus twofold: the fundamental physical understanding developed here paves the way towards the investigation of more complex and realistic scenarios, while we also provide a thorough characterisation of the turbulent state that can prove useful in the development of accurate turbulence models for RANS and LES.

physics.flu-dyn↗

arXiv2023

Forced and natural dynamics of a clamped flexible fiber in wall turbulence

We characterize the dynamical behavior of a clamped flexible fiber immersed in wall turbulence over a wide range of natural frequencies by means of direct numerical simulations. Only two flapping states are possible: one where the fiber oscillates at the characteristic frequency of the largest turbulent eddies and another where the natural structural response dominates. The former is obtained in the more flexible cases, while the latter in the more rigid ones. We observe here for the first time that in the turbulence dominated regime the fiber always sways at a frequency proportional to the largest scale of the flow, regardless of its structural parameters. The hindrance of the clamp to the wall prevents the synchronization of the fiber with turbulent eddies of comparable size.

physics.flu-dyn↗

arXiv2023

On-off pumping for drag reduction in a turbulent channel flow

We show that the energy required by a turbulent flow to displace a given amount of fluid through a straight duct in a given time interval can be reduced by modulating in time the pumping power. The control strategy is hybrid: it is passive, as it requires neither a control system nor control energy, but it manipulates how pumping energy is delivered to the system (as in active techniques) to increase the pumping efficiency. Our control employs a temporally periodic pumping pattern, where a short and intense acceleration (in which the pumping system is on) followed by a longer deceleration (in which the pumping system is off) makes the flow alternately visit a quasi-laminar and a turbulent state. The computational study is for a plane channel flow, and employs direct numerical simulations, which present specific computational challenges, for example the highly varying instantaneous value of the Reynolds number, and the importance of discretisation effects. Particular care is devoted to a meaningful definition of drag reduction in the present context. The ability of the forcing to yield significant savings is demonstrated. Since only a small portion of the parameter space is investigated, the best performance of the control technique remains to be assessed.

physics.flu-dyn↗

arXiv2023

Saving Energy in Turbulent Flows with Unsteady Pumping

Viscous dissipation causes significant energy losses in fluid flows; in ducts, laminar flows provide the minimum resistance to the motion, whereas turbulent currents substantially increase the friction at the wall and the energy requirement for pumping. Great effort is currently being devoted to find new ways of reducing the energy losses induced by turbulence. Here we propose a simple and novel drag-reduction technique which achieves substantial energy savings in internal flows, even after the energy cost of the control is accounted for. Our approach consists in driving the flow with a pulsed pumping, unlike the common practice of a constant pumping. We alternate "pump on" phases where the flow accelerates, and "pump off" phases where the flow decays freely. The flow cyclically enters a quasi-laminar state during the acceleration, and transitions to a more classic turbulent state during the deceleration. Our numerical results demonstrate that important net energy savings can be achieved by simply modulating the power injection in the system over time. The physical understanding we have achieved can help the industry in reducing the waste of energy, making it cheaper and preserving the environment by reducing harmful emissions.

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