arXiv subjects

Marc Avila

Publications and source records attributed to Marc Avila.

At least 19 recordsLinked to original sources

arXiv2026

A causal model of drop breakup in turbulence

Fragmentation of drops and bubbles in turbulence controls interfacial area generation, mixing, and transport in environmental and engineering flows. Reduced-order models of breakup are highly sought after, but the bidirectional, nonlinear coupling between the interfacial and hydrodynamic stresses is an obstacle to their development. By leveraging a decomposition of the flow into outer and inner regions introduced by Vela-Martín & Avila (2021), we demonstrate that at low Weber numbers breakup is caused by outer eddies that produce extreme events of interfacial stretching. Capillary forces oppose stretching and transfer the interfacial energy back to the velocity field by generating inner eddies as the drop relaxes. Hence, for breakup to occur, outer stretching events must inject energy faster than the interface can convert it into inner eddies. Numerical simulations initialized with ellipsoidal drops reveal that the energy transfer to the inner eddies is governed by the capillary time, whereas the outer forcing acts on the eddy-turnover time scale. Building on these observations and the governing equations, we derive a simple model for the breakup rate. Although the underlying assumptions are strictly valid only in the limit of large surface tension, the resulting equation quantitatively captures both drop and bubble breakup rates over a wide range of Weber numbers using only a single fitting parameter. Our results establish a direct causal link between turbulent intermittency and the memoryless nature of breakup, and suggest a universal mechanism governing drop and bubble breakup at low Weber numbers.

physics.flu-dyn↗

arXiv2026

Stages of turbulence generation and decay in a T-shaped mixer

The T-shaped mixer is widely used in fundamental studies of chemical engineering. Its transitional regime is well understood, whereas the turbulent dynamics has received scarce attention so far. Here we perform direct numerical simulations of the turbulent regime for Reynolds numbers up to $Re=2000$ at Schmidt number $Sc=1$. Our analysis reveals two distinct stages along the mixing channel prior to relaxation toward duct flow. Near the junction, a jet-like flow forms and exhibits the approximately self-similar behaviour of transitional planar jets. Subsequently, a decay region characterised by power-law decay of turbulent kinetic energy, dissipation and scalar variance emerges. For the velocity field, the observed exponents are consistent with those of decaying turbulence in bounded domains, whereas the scalar-variance exponent is consistent with that of unbounded turbulence. We argue that this apparent discrepancy is a consequence of the mixing process progressing from the center of the channel toward the side walls in the decay region, while turbulence already fills the channel cross-section entirely at the end of the jet region.The time-averaged mixing state presents error-function profiles of the scalar in the transverse direction, similar to the laminar cases, and is quantified here through a stream-wise evolving effective diffusion coefficient.

physics.flu-dyn↗

arXiv2026

Scaling of the minimal energy for turbulence transition in pipe flow

Predicting the transition of turbulence in pipe flow remains a fundamental problem in fluid dynamics. We use a variational approach to compute nonlinear optimal perturbations to the laminar flow at Reynolds number $Re\leq 5000$. As $Re$ increases, optimal perturbations remain structurally similar, but increasingly localize while their thickness scales as $δ_r \propto Re^{-1/3}$. They grow via the Orr mechanism, followed by a phase of strong nonlinear interaction of oblique waves and a lift-up phase. The energy gain during the Orr phase increases linearly with $Re$ and is independent of the initial perturbation energy, $E_0$. The energy gain during the oblique and lift-up phases is governed by nonlinearities and scales as $\propto Re^2$. We find that regardless of the Reynolds number, transition occurs if the energy of the perturbation exceeds a constant threshold. As a result, the minimum perturbation energy required to cause transition in pipe flow scales as $\mathcal{O}(Re^{-3})$.

physics.flu-dyn↗

arXiv2025

Experimental study of turbulent mixing in a T-shaped mixer

One of the most widespread canonical devices for fluid mixing is the T-shaped mixer, in which two opposing miscible liquid streams meet at a junction and then mix along a main channel. Laminar steady and time-periodic flows in T-shaped mixers have been thoroughly studied, but turbulent flows have received much less scrutiny despite their prevalence in applications. We here introduce a novel experimental setup with a hydraulic diameter of four centimetres that enables the optical study of turbulent mixing at small scales. Using this setup, we perform two-dimensional particle image velocimetry and planar laser-induced fluorescence measurements. First, we successfully replicate characteristic flow regimes observed in micro-scale T-shaped mixers at low Reynolds numbers. We then focus on the turbulent regime and characterize the turbulent kinetic energy and dissipation along the mixing channel. Further, we measure the scalar concentration variance and its corresponding probability density function and spectra. The latter exhibits an incipient Batchelor scaling. We estimate the mechanical-to-scalar timescale ratio and examine the link between the turbulent velocity and scalar fields. The measurement data are compared with model predictions and correlations used in engineering practice, and with our own direct numerical simulations performed with a spectral-element code.

physics.flu-dyn↗

arXiv2025

Nonlinear optimal perturbation growth in pulsatile pipe flow

Pulsatile fluid flows through straight pipes undergo a sudden transition to turbulence that is extremely difficult to predict. The difficulty stems here from the linear Floquet stability of the laminar flow up to large Reynolds numbers, well above experimental observations of turbulent flow. This makes the instability problem fully nonlinear and thus dependent on the shape and amplitude of the flow perturbation, in addition to the Reynolds and Womersley numbers and the pulsation amplitude. This problem can be tackled by optimizing over the space of all admissible perturbations to the laminar flow. In this paper, we present an adjoint optimization code, based on a GPU implementation of the pseudo-spectral Navier-Stokes solver nsPipe, which incorporates an automatic, optimal check-pointing strategy. We leverage this code to show that the flow is susceptible to two distinct instability routes: One in the deceleration phase, where the flow is prone to oblique instabilities, and another during the acceleration phase with similar mechanisms as in steady pipe flow. Instability is energetically more likely in the deceleration phase. Specifically, localised oblique perturbations can optimally exploit nonlinear effects to gain over nine orders of magnitude in energy at a peak Reynolds number of $Re_{\max}\approx 4000$. These oblique perturbations saturate into regular flow patterns that decay in the acceleration phase or break down to turbulence depending on the flow parameters. In the acceleration phase, optimal perturbations are substantially less amplified, but generally trigger turbulence if their amplitude is sufficiently large.

physics.flu-dyn↗

arXiv2025

Bayesian minimisation of energy consumption in turbulent pipe flow via unsteady driving

Turbulence accounts for most of the energy losses associated with the pumping of fluids in pipes. Pulsatile drivings can reduce the drag and energy consumption required to supply a desired mass flux, when compared to steady driving. However, not all pulsation waveforms yield reductions. Here, we compute drag- and energy-optimal driving waveforms using direct numerical simulations and a gradient-free black-box optimisation framework. Specifically, we show that Bayesian optimisation is vastly superior to ordinary gradient-based methods in terms of computational efficiency and robustness, due to its ability to deal with noisy objective functions, as they naturally arise from the finite-time averaging of turbulent flows. We identify optimal waveforms for three Reynolds numbers and two Womersley numbers. At a Reynolds number of 8600 and a Womersley number of 10, optimal waveforms reduce total energy consumption by 22 % and drag by 37 %. These reductions are rooted in the suppression of turbulence prior to the acceleration phase, the resulting delay in turbulence onset, and the radial localization of turbulent kinetic energy and production toward the pipe centre. Our results pinpoint that the predominant, steady operation mode of pumping fluids through pipes is far from optimal.

physics.flu-dyn↗

arXiv2025

Effect of filter kernel on scale-energetics of near-wall turbulent structures

Inter-scale energy fluxes, $Π^λ$, are widely used as a diagnostic tool to analyse energy transfer across length scales, $λ$, in turbulence data. Here, we investigate how the choice of filter kernel (sharp spectral, Gaussian, box) affects the computed energy fluxes at constant filter width. We apply spatial filtering to a turbulent pipe flow simulation dataset and assess the effect on the local structure of $Π$. While the mean energy flux profile at each wall-normal distance is qualitatively robust across kernels, we observe significant differences in the intensity and spatial distribution of localised $Π$ events. Correlations between typical flow structures in the buffer layer (streaks, vortices, and Q-events) and regions of forward/backward transfer in the instantaneous $Π$ field differ markedly between kernel types. Cross-correlations appear strongly upstream--downstream symmetric when using the sharp spectral kernel, but asymmetric for the Gaussian and box kernels. For the Gaussian and box kernels $Π$ events tend to localise along the inclined meander of streaks, while they are centred on top of the streaks for the sharp spectral kernel. Moreover, using the sharp spectral kernel, we observe a coincidence of backward scatter and fluid transport away from the wall ($Q_1$), which does not appear with the Gaussian and box kernels. All kernels, however, predict backward scatter directly downstream of $Q_1$ events. The results suggest that interpretations of inter-scale energy flux based on sharp spectral scale separation should be treated with caution, since such kernels act non-local in physical space, whereas $Π$ events are inherently localised. Our python post-processing tool eFlux for scale separation and energy flux analysis in pipe flows is freely available and readily adaptable to other flow configurations and filter widths.

physics.flu-dyn↗

arXiv2025

Probabilistic thresholds of turbulence decay in transitional shear flows

Linearly stable shear flows first transition to turbulence in the form of localised patches. At low Reynolds numbers, these turbulent patches tend to suddenly decay, following a memoryless process typical of rare events. How far in advance their decay can be forecasted is still unknown. We perform massive ensembles of simulations of pipe flow and a reduced order model of shear flows (Moehlis et al. 2004) and determine the first moment in time at which decay becomes fully predictable, subject to a given magnitude of the uncertainty on the flow state. By extensively sampling the chaotic sets, we find that, as one goes back in time from the point of inevitable decay, predictability degrades at greatly varying speeds. However, a well-defined (average) rate of predictability loss can be computed. This rate is independent of the uncertainty and also of the type of rare event, i.e. it applies to decay and to other extreme events. We leverage our databases to define thresholds that approximately separate phase-space regions of distinct decay predictability. Our study has implications for the development of predictive models, in particular it sets their theoretical limits. It also opens avenues to study the causes of extreme events in turbulent flows: a state which is predictable to produce an extreme event, it is causal to it from a probabilistic perspective.

physics.flu-dyn↗

arXiv2025

Turbulent puffs in transitional pulsatile pipe flow at moderate pulsation amplitudes

We show that, in the transitional regime of pulsatile pipe flow, at moderate-to-high amplitudes 0.5 < A < 1, the first long-lived turbulent structures are localized and take the form of the puffs and slugs observed in statistically steady pipe flow. We perform direct numerical simulations at many pulsation frequencies, amplitudes and Re, and observe different dynamics of puffs and slugs. At certain flow parameters we find, using a causal analysis, that puffs actively make use of linear instabilities in the laminar Sexl-Womersley profile to survive the pulsation. Using all these lessons learned, we extend a low order model by Barkley et al., Nature (2015), to reproduce these dynamics. We find a good agreement between the extended model and our numerical results in a broad parametric space of pulsation amplitudes 0.5 < A < 1, frequencies Wo > 5 and 2100 < Re < 3000. With the help of our numerical results, causal analysis and model, we determine that turbulence production has two sources at these flow parameters: the mean shear as in statistically steady pipe flow, and the instabilities of the instantaneous pulsatile mean profile.

physics.flu-dyn↗

arXiv2024

Taylor rolls on tour: Slow drift of turbulent large-scale structures in flows with continuous symmetries

In Rayleigh-Benard convection and Taylor-Couette flow cellular patterns emerge at the onset of instability and persist as large-scale coherent structures in the turbulent regime. Their long-term dynamics has been thoroughly characterised and modelled for the case of turbulent convection, whereas turbulent Taylor rolls have received much less attention. Here we present direct numerical simulations of axisymmetric Taylor-Couette flow and show a discontinuous phase-transition to spatio-temporal chaos as the system size increases. Beyond this transition, Taylor rolls suddenly undergo erratic drifts evolving on a very slow time scale. We estimate an effective diffusion coefficient for the drift and compare the dynamics to analogous motions in Rayleigh-Benard convection and Poiseuille flow, suggesting that this spontaneous diffusive displacement of large coherent structures is common among different types of wall-bounded turbulent flows.

physics.flu-dyn↗

arXiv2023

Towards indirect assessment of surface anomalies on wind turbine rotor blades

We present results from novel field, lab and computer studies, that pave the way towards non-invasive classification of localised surface defects on running wind turbine rotors using infrared thermography (IRT). In particular, we first parametrise the problem from a fluid dynamical point of view using the roughness Reynolds number ($Re_k$) and demonstrate how the parameter regime relevant for modern wind turbines translate to parameter values that are currently feasible in typical wind tunnel and computer experiments. Second, we discuss preparatory wind tunnel and field measurements, that demonstrate a promising degree of sensitivity of the recorded IRT data w.r.t. the key control parameter ($Re_k$), which is a minimum requirement for the proposed classification technique to work. Third, we introduce and validate a local domain ansatz for future computer experiments, that enables well-resolved Navier-Stokes simulations for the target parameter regime at reasonable computational costs.

physics.flu-dyn↗

arXiv2023

Routes to turbulence in Taylor-Couette flow

Fluid flows between rotating concentric cylinders exhibit two distinct routes to turbulence. In flows dominated by inner-cylinder rotation, a sequence of linear instabilities leads to temporally chaotic dynamics as the rotation speed is increased. The resulting flow patterns occupy the whole system and sequentially lose spatial symmetry and coherence in the transition process. In flows dominated by outer-cylinder rotation, the transition is abrupt and leads directly to turbulent flow regions that compete with laminar ones. We here review the main features of these two routes to turbulence. Bifurcation theory rationalises the origin of temporal chaos in both cases. However, the catastrophic transition of flows dominated by outer-cylinder rotation can only be understood by accounting for the spatial proliferation of turbulent regions with a statistical approach. We stress the role of the rotation number (the ratio of Coriolis to inertial forces) and show that it determines the lower border for the existence of intermittent laminar-turbulent patterns.

physics.flu-dyn↗

arXiv2022

Measurement error of tracer-based velocimetry in single-phase turbulent flows with inhomogeneous refractive indices

Inhomogeneous refractive index fields lead to errors in optical flow velocity measurements. Former respective studies are mostly in quasi two-dimensional flows, and attribute the measurement errors to spatial gradients in the refractive index field, while less attention has been paid to flows with three-dimensional refractive index fields which usually change in space and in time. In this study, ray tracing simulations were carried out in a three-dimensional flow, which is from a direct numerical simulation of single-phase turbulent mixing of two fluids. Given the data of the numerical simulation as reference, the ray tracing simulation is used to quantify the measurement errors of the flow velocity and flow acceleration for tracer-based velocimetry, i.e. particle tracking velocimetry in this study. The errors of both flow velocity and flow acceleration are attributed to the spatial and the spatio-temporal gradients of the refractive indices, respectively, which are closely inherited from flow characteristics. While the dominant type of error depends on the studied flow, the main measurement error for the considered turbulent mixing flow is caused by the random error. When the maximum spatial difference of the refractive indices is about 10 to the power of -6, the relative random measurement error is about 1 % in velocity and about 200 % in acceleration, respectively. When the maximum index difference is about 0.01 (water), the relative random measurement errors of velocity and acceleration are 2000 % and 100,000%, respectively, for the flow considered in this study.

physics.flu-dyn↗

arXiv2021

A single-camera synthetic Schlieren method for the measurement of free liquid surfaces

A single-camera synthetic Schlieren method is introduced to measure the height of a dynamic free liquid surface in a container with a flat bottom. Markers placed on the bottom, seen through the free surface, are virtually displaced due to light refraction at the surface. According to Snell's law, the marker displacements depend on the refractive indices of the transparent liquid and the air, and on the surface height and its spatial gradients. We solve the resulting governing nonlinear equation with the Newton-Raphson method to obtain the surface height. Our method does not require a reference surface height, which allows the measurement of surfaces topography in situations where the liquid depth is unknown. We demonstrate the accuracy of the method by performing experiments of surface ripples and dam-break flows and discuss the measurement uncertainty, errors and limitations.

physics.flu-dyn↗

arXiv2021

Deformation of drops by outer eddies in turbulence

Drop deformation in fluid flows is investigated here as an exchange between the kinetic energy of the fluid and the surface energy of the drop. We show analytically that this energetic exchange is controlled only by the stretching (or compression) of the drop surface by the rate-of-strain tensor. This mechanism is analogous to the stretching of the vorticity field in turbulence. Leveraging the non-local nature of turbulence dynamics, we introduce a new decomposition that isolates the energetic exchange due to local drop-induced surface effects, from the non-local action of turbulent fluctuations. We perform direct numerical simulations of single inertial drops in isotropic turbulence and show that an important contribution to the increments of the surface energy arises from the non-local stretching of the fluid-fluid interface by eddies far from the drop surface (outer eddies). We report that this mechanism is dominant and independent of surface dynamics in a range of Weber numbers in which drop breakup occurs. These findings shed new light on drop deformation and breakup in turbulent flows, and open the venue for the improvement and simplification of breakup models.

physics.flu-dyn↗

arXiv2021

Direct numerical simulation of two-phase pipe flow: influence of the domain length on the flow regime

We perform direct numerical simulations of a kerosene-water mixture in pipe flow under realistic experimental conditions by solving the Cahn-Hilliard-Navier-Stokes equations. We compute the linear stability of core-annular flow of kerosene and water in a vertical pipe and find that it is highly unstable. By performing DNS initialized with a slightly perturbed core-annular flow, we show that the system transitions to turbulence and finally relaxes into a turbulent slug flow regime provided that the pipe is sufficiently long. This configuration presents mild turbulence and large scale three-dimensional recirculation patterns inside the slugs. Our work highlights the need for applying nonlinear-dynamics approaches and carefully selecting the domain length to investigate the patterns observed in two-phase pipe flows and demonstrates the capabilities of phase field methods to reliably simulate experimental conditions.

physics.flu-dyn↗

arXiv2021

Statistical Analysis of Thermal Conductivity Experimentally Measured in Ethylene Glycol - Based Nanofluids

We collected literature data of thermal conductivity experimentally measured in ethylene glycol-based nanofluids and investigated the influence of concentration, temperature and nanoparticle size. We implemented statistical linear regression analysis of all data points and examined four separate nanoparticle materials - alumina, titania, copper oxide and carbon-nanotubes. We found that the statistical correlations are in good agreement with Maxwell's effective medium theory, despite large scatter in the data. The thermal conductivity increases linearly with concentration, and in the case of carbon-nanotubes with temperature, whereas the nanoparticle size shows significant influence for alumina and titania. The large scatter in the experimental data is one of the main problems. We suggest that there is a need for careful, detailed characterizations and measurements to quantify the potential of nanofluids.

cond-mat.soft↗

arXiv2021

Effects of Pore-scale on the Macroscopic Properties of Natural Convection in Porous Media

Natural convection in porous media is a fundamental process for the long-term storage of CO2 in deep saline aquifers. Typically, details of mass transfer in porous media are inferred from the numerical solution of the volume-averaged Darcy-Oberbeck-Boussinesq (DOB) equations, even though these equations do not account for the microscopic properties of a porous medium. According to the DOB equations, natural convection in a porous medium is uniquely determined by the Rayleigh number. However, in contrast with experiments, DOB simulations yield a linear scaling of the Sherwood number with the Rayleigh number (Ra) for high values of Ra (Ra>>1,300). Here, we perform Direct Numerical Simulations (DNS), fully resolving the flow field within the pores. We show that the boundary layer thickness is determined by the pore size instead of the Rayleigh number, as previously assumed. The mega- and proto- plume sizes increase with the pore size. Our DNS results exhibit a nonlinear scaling of the Sherwood number at high porosity, and for the same Rayleigh number, higher Sherwood numbers are predicted by DNS at lower porosities. It can be concluded that the scaling of the Sherwood number depends on the porosity and the pore-scale parameters, which is consistent with experimental studies.

physics.flu-dyn↗