arXiv subjects

Adrien Lefauve

Publications and source records attributed to Adrien Lefauve.

18 recordsLinked to original sources

arXiv2026

Sidewall effects on the onset of interfacial Holmboe waves in stratified exchange flows at high Schmidt number

Predicting the onset of interfacial instabilities is central to understanding turbulent mixing in natural and engineered stratified shear flows. Here, we study the onset of travelling Holmboe waves in confined exchange flows along a slope. Earlier stratified inclined duct experiments have mapped this transition, and stability analyses based on measured or prescribed profiles have explained their emergence. However, a predictive criterion linking forcing, geometry, base flow, and wave onset was still lacking. We closed this gap with a long-duct, sharp-interface asymptotic theory for the three-dimensional laminar exchange flow, including the effects of sidewall friction. The resulting analytical solution naturally identifies a confinement-adjusted Froude number, $Fr^*$, which unifies the effects of forcing and confinement into a single measure of the effective laminar exchange flow. Using this solution to parameterise sidewall drag in a practical width-averaged model, we perform linear stability analyses and numerical simulations at high Schmidt number. Together, linear stability analysis, direct numerical simulations, and existing experiments across a range of duct widths show that wave onset is accurately predicted by an approximately constant critical value of $Fr^*$. Deviations arise only in very narrow ducts, where sidewalls influence instability not only by modifying the laminar exchange flow but also by directly damping perturbations and delaying wave onset. These findings provide a predictive criterion for wave onset, reconcile long-standing discrepancies among experimental configurations, and establish lateral confinement as a fundamental control on the transition from laminar exchange to wave-driven mixing in stratified shear flows.

physics.flu-dyn↗

arXiv2026

Early onset of secondary shear instability in Kelvin-Helmholtz braids at high Reynolds number

We study the onset of two-dimensional secondary shear instability (SSI) in the braid regions connecting primary Kelvin-Helmholtz billows in stratified shear flows. While strain induced by the billows stabilises the braids, it also compresses their tilted isopycnals, enhancing baroclinic shear that enables rapid perturbation growth. By modifying the classical analysis of Corcos & Sherman (J. Fluid Mech. 73, 241-264, 1976) in braid-aligned coordinates and adding an additional stability criterion based on the ratio of strain rate to shear, we develop an inviscid, time-dependent model for the braid and the onset of SSI. We show that the criterion for instability can be achieved significantly earlier than the saturation of the primary billow at sufficiently high initial Richardson number Ri, as increased stratification slows billow growth while accelerating baroclinic shear production in the braid. Two-dimensional direct numerical simulations up to Reynolds numbers Re=10^7 quantify the role of viscosity. At high Re, we find that SSI indeed develops early in the braid, as predicted by the inviscid model, while the primary billow is still growing and before viscosity slows braid thinning. These results provide a mechanistic explanation for field observations of braid-dominated mixing and suggest that, at geophysically relevant Ri and Re, SSI can control the three-dimensional turbulent transition and ensuing diapycnal mixing by preceding and pre-empting both vortex pairing instabilities and secondary convective instabilities in the billow core.

physics.flu-dyn↗

arXiv2025

Transition to the ultimate regime of turbulent convection in stratified inclined duct flow

The stratified inclined duct (SID) flow provides a canonical model for sustained, buoyancy-driven exchange between two reservoirs of different density, and emerges as a new paradigm in geophysical fluid dynamics. Yet, the flow dynamics remain unclear in the highly turbulent regime; laboratory experiments can access this regime but they lack resolution, while direct numerical simulations (DNS) at realistically high Prandtl number $\mathrm{Pr}=7$ (for heat in water) have not achieved sufficiently high Reynolds numbers $\mathrm{Re}$. We conduct three-dimensional DNS up to $\mathrm{Re}= 8000$ and observe the transition to the so-called ultimate regime of turbulent convection as evidenced by the Nusselt number scaling $\mathrm{Nu} \sim \mathrm{Ra}^{1/2}$, i.e., considerably enhanced transport. At the transition the shear Reynolds number, a key parameter characterizing boundary layer (BL) dynamics, exceeds the threshold range of 420 for turbulent kinetic BLs with the emergence of logarithmic velocity profiles. The nature of the transition towards ultimate SID flow is of non-normal-nonlinear nature, i.e., subcritical and hysteretic, as typical for the transition to fully turbulent shear flows. Our work connects SID flow with the broader class of wall-bounded turbulent convection flows and gives insight into mixing in the vigorously turbulent regimes in oceanography and industry.

physics.flu-dyn↗

arXiv2024

Routes to stratified turbulence and temporal intermittency revealed by a cluster-based network model of experimental data

Modelling fluid turbulence using a `skeleton' of coherent structures has traditionally progressed by focusing on a few canonical laboratory experiments such as pipe flow and Taylor-Couette flow. We here consider the stratified inclined duct, a sustained shear flow whose density stratification allows for the exploration of a wealth of new coherent and intermittent states at significantly higher Reynolds numbers than in unstratified flows. We automatically identify the underlying turbulent skeleton of this experiment with a data-driven method combining dimensionality reduction and unsupervised clustering of shadowgraph visualisations. We demonstrate the existence of multiple types of turbulence across parameter space and intermittent cycling between them, revealing distinct transition pathways. With a cluster-based network model of intermittency we uncover patterns in the transition probabilities and residence times under increasing levels of turbulent dissipation. Our method and results pave the way for new reduced-order models of multi-physics turbulence.

physics.flu-dyn↗

arXiv2024

Boiling stratified flow: a laboratory analogy for atmospheric moist convection

We present a novel laboratory experiment, boiling stratified flow, as an analogy for atmospheric moist convection. A layer of diluted syrup is placed below freshwater in a beaker and heated from below. The vertical temperature profile in the experiment is analogous to the vapor mixing ratio in the atmosphere while the vertical profile of freshwater concentration in the experiment is analogous to the potential temperature profile in the atmosphere. Boiling starts when the bottom of the syrup layer reaches the boiling point, producing bubbles and vortex rings that stir the two-layer density interface and bring colder fresh water into the syrup layer. When the syrup layer at the beginning of the experiment is sufficiently thin and diluted, the vortex rings entrain more cold water than needed to remove superheating in the syrup layer, ending the boiling. When the syrup layer is deep and concentrated, the boiling is steady since the entrained colder water instantaneously removes the superheating in the bottom syrup layer. A theory is derived to predict the entrainment rate and the transition between the intermittent and steady boiling regimes, validated by experimental data. We suggest that these dynamics may share similarities with the mixing and lifecycle of cumulus convection.

physics.flu-dyn↗

arXiv2023

Physics-informed neural network to augment experimental data: an application to stratified flows

We develop a physics-informed neural network (PINN) to significantly augment state-of-the-art experimental data and apply it to stratified flows. The PINN is a fully-connected deep neural network fed with time-resolved, three-component velocity fields and density fields measured simultaneously in three dimensions at $Re = O(10^3)$ in a stratified inclined duct experiment. The PINN enforces incompressibility, the governing equations for momentum and buoyancy, and the boundary conditions by automatic differentiation. The physics-constrained, augmented data are output at an increased spatio-temporal resolution and demonstrate five key results: (i) the elimination of measurement noise; (ii) the correction of distortion caused by the scanning measurement technique; (iii) the identification of weak but dynamically important three-dimensional vortices; (iv) the revision of turbulent energy budgets and mixing efficiency; and (v) the prediction of the latent pressure field and its role in the observed Holmboe wave dynamics. These results mark a significant step forward in furthering the reach of experiments, especially in the context of turbulence, where accurately computing three-dimensional gradients and resolving small scales remain enduring challenges.

physics.flu-dyn↗

arXiv2023

Geometry of stratified turbulent mixing: local alignment of the density gradient with rotation, shear and viscous dissipation

We introduce a geometric analysis of turbulent mixing in density-stratified flows based on the alignment of the density gradient in two orthogonal bases that are locally constructed from the velocity gradient tensor. The first basis connects diapycnal mixing to rotation and shearing motions, building on the recent 'rortex-shear decomposition' in stratified shear layers (Jiang et al., J. Fluid Mech. 947, A30, 2022), while the second basis connects mixing to the principal axes of the viscous dissipation tensor. Applying this framework to datasets taken in the stratified inclined duct laboratory experiment reveals that density gradients in locations of high shear tend to align preferentially (i) along the direction of minimum dissipation and (ii) normal to the plane spanned by the rotex and shear vectors. The analysis of the local alignment across increasingly turbulent flows offers new insights into the intricate relationship between the density gradient and dissipation, and thus diapycnal mixing.

physics.flu-dyn↗

arXiv2023

Long-wave instabilities of sloping stratified exchange flows

We investigate the linear instability of two-layer stratified shear flows in a sloping two-dimensional channel, subject to non-zero longitudinal gravitational forces. We reveal three previously unknown instabilities, distinct from the well-known Kelvin-Helmholtz Instability (KHI) and Holmboe Wave Instability (HWI), in that they have longer wavelengths (of the order of 10 to $10^3$ shear-layer depths) and often slower growth rates. Importantly, they can grow in background flows with gradient Richardson number $\gg 1$, which offers a new mechanism to sustain turbulence and mixing in strongly stratified flows. These instabilities are shown to be generic and relatively insensitive to Reynolds number $\mathrm{Re}$, Prandtl number $\mathrm{Pr}$, base flow profile, and boundary conditions. The nonlinear evolution of these instabilities is investigated through a forced direct numerical simulation, in which the background momentum and density are sustained. The growth of long unstable waves in background flows initially stable to short wave instabilities causes a decrease in the local gradient Richardson number. This leads to local nonlinear processes that result in small-scale overturns resembling Kelvin-Helmholtz billows. Our results establish a new energy exchange pathway, where the mean kinetic energy of a strongly stratified flow is extracted by primary unstable long waves and secondary short waves, and subsequently dissipated into internal energy.

physics.flu-dyn↗

arXiv2023

Data-driven classification of sheared stratified turbulence from experimental shadowgraphs

We propose a dimensionality reduction and unsupervised clustering method for the automatic classification and reduced-order modeling of density-stratified turbulence in laboratory experiments. We apply this method to 113 long shadowgraph movies collected in a `Stratified Inclined Duct' (SID) experiment, where turbulence is generated by instabilities arising from a sheared buoyancy-driven counterflow at Reynolds numbers $Re \approx 300-5000$, tilt angles $θ=1^\circ-6^\circ$ and Prandtl number $Pr \approx$ 700. The method automatically detects edges representative of discrete density interfaces, extracts a low-dimensional vector of statistics representative of their morphology, projects these statistics onto a two-dimensional phase space of principal coordinates, and applies the OPTICS clustering algorithm. Five clusters are detected and interpreted physically based on their typical interface morphology and an examination of representative frames, revealing distinct types of turbulence and mixing: laminarizing, braided, overturning, granular and unstructured, as well as some intermediate types. The ratio of time spent in each cluster varies gradually across the $(Re,θ)$ space. At intermediate values of $Re\,θ$, intermittent turbulence cycles between clusters in phase space and reveals at least two distinct routes to stratified turbulence. These insights demonstrate the potential of this method to reveal the underlying physics of complex turbulent systems from large experimental datasets.

physics.flu-dyn↗

arXiv2023

Routes to stratified turbulence revealed by unsupervised classification of experimental data

Modeling fluid turbulence using a 'skeleton' of coherent structures has traditionally progressed by focusing on a few canonical experiments, such as pipe flow and Taylor-Couette flow. We here consider an alternative canonical experiment, the stratified inclined duct, a sustained shear flow whose density stratification allows for the exploration of a wealth of new coherent and intermittent states at significantly higher Reynolds numbers than in unstratified flows. We automatically identify the underlying turbulent skeleton of this experiment with a novel data-driven method combining dimensionality reduction and unsupervised clustering of shadowgraph visualizations. We demonstrate the existence of multiple types of energetic turbulence across parameter space, as well as intermittent turbulence that cycles between these types, revealing distinct transition pathways. Our method and results pave the way for new reduced-order models of multi-physics turbulence.

physics.flu-dyn↗

arXiv2023

Stratified inclined duct: two-layer hydraulics and instabilities

The stratified inclined duct (SID) sustains an exchange flow in a long, gently sloping duct as a model for continuously-forced density-stratified flows such as those found in estuaries. Experiments have shown that the emergence of interfacial waves and their transition to turbulence as the tilt angle is increased appears linked to a threshold in the exchange flow rate given by inviscid two-layer hydraulics. We uncover these hydraulic mechanisms with (i) recent direct numerical simulations (DNS) providing full flow data in the key flow regimes (Zhu & Atoufi et al., arXiv:2301.09773, 2023), (ii) averaging these DNS into two layers, (iii) an inviscid two-layer shallow water and instability theory to diagnose interfacial wave behaviour and provide physical insight. The laminar flow is subcritical and stable throughout the duct and hydraulically controlled at the ends of the duct. As the tilt is increased, the flow becomes everywhere supercritical and unstable to long waves. An internal undular jump featuring stationary waves first appears near the centre of the duct, then leads to larger-amplitude travelling waves, and to stronger jumps, wave breaking and intermittent turbulence at the largest tilt angle. Long waves described by the (nonlinear) shallow water equation are locally interpreted as linear waves on a two-layer parallel base flow described by the Taylor-Goldstein equation. This link helps us interpret long-wave instability and contrast it to short-wave (e.g. Kelvin-Helmholtz) instability. Our results suggest a transition to turbulence in SID through long-wave instability relying on vertical confinement by the top and bottom walls.

physics.flu-dyn↗

arXiv2023

Stratified inclined duct: direct numerical simulations

The stratified inclined duct (SID) experiment consists of a zero-net-volume exchange flow in a long tilted rectangular duct, which allows the study of realistic stratified shear flows with sustained internal forcing. We present the first three-dimensional direct numerical simulations (DNS) of SID to explore the transitions between increasingly turbulent flow regimes first described by Meyer \& Linden (\textit{J. Fluid Mech.} \textbf{753}, 242-253, 2014). We develop a numerical set-up that faithfully reproduces the experiments and sustains the flow for arbitrarily long times at minimal computational cost. We recover the four qualitative flow regimes found experimentally in the same regions of parameter space: laminar flow, waves, intermittent turbulence, and fully-developed turbulence. We find good qualitative and quantitative agreement between DNS and experiments and highlight the added value of DNS to complement experimental diagnostics and increase our understanding of the transition to turbulence, both temporally (laminar/turbulent cycles) and parametrically (as the tilt angle of the duct and the Reynolds number are increased). These results demonstrate that numerical studies of SID -- and deeper integration between simulations and experiments -- have the potential to lead to a better understanding of stratified turbulence in environmental flows.

physics.flu-dyn↗

arXiv2022

The evolution of coherent vortical structures in increasingly turbulent stratified shear layers

We study the morphology of Eulerian vortical structures and their interaction with density interfaces in increasingly turbulent stably-stratified shear layers. We analyse the three-dimensional, simultaneous velocity and density fields obtained in the stratified inclined duct laboratory experiment. We track, across 15 datasets, the evolution of coherent structures from pre-turbulent Holmboe waves, through intermittent turbulence, to full turbulence and mixing. We use the Rortex--Shear decomposition of the vorticity field into a pure rotational part (the rortex vector), and a non-rotational part (the shear vector). We describe the morphology of ubiquitous hairpin-like vortical structures (revealed by the rortex), similar to those commonly observed in boundary-layer turbulence. These are born as relatively weak vortices around the strong three-dimensional shearing structures of confined Holmboe waves, and gradually strengthen and deform under increasing turbulence, transforming into pairs of upward- and downward-pointing hairpins propagating in opposite directions on the top and bottom edge of the shear layer. Each hairpin's pair of legs are counter-rotating and entrain fluid laterally and vertically, and their arched-up `heads', which are transverse vortices, entrain fluid vertically. We then elucidate how this large-scale vortex morphology stirs and mixes the density field. Essentially, vortices located at the sharp density interface on either edge of the mixing layer (mostly hairpin heads) engulf blobs of unmixed fluid into the mixing layer, while vortices inside the mixing layer (mostly hairpin legs) further stir it, generating strong, small-scale shear, enhancing mixing. These findings provide new insights into the role of turbulent coherent structures in shear-driven stratified mixing.

physics.flu-dyn↗

arXiv2021

The effects of spanwise confinement on stratified shear instabilities

We consider the influence of transverse confinement on the instability properties of velocity and density distributions reminiscent of those pertaining to exchange flows in stratified inclined ducts, such as the recent experiment of Lefauve et al. (J. Fluid Mech. 848, 508-544, 2018). Using a normal mode streamwise and temporal expansion for flows in ducts with various aspect ratios $B$ and non-trivial transverse velocity profiles, we calculate two-dimensional (2D) dispersion relations with associated eigenfunctions varying in the 'crosswise' direction, in which the density varies, and the spanwise direction, both normal to the duct walls and to the flow direction. We also compare these 2D dispersion relations to the so-called one-dimensional (1D) dispersion relation obtained for spanwise invariant perturbations, for different aspect ratios $B$ and bulk Richardson numbers $Ri_b$. In this limited parameter space, the presence of lateral walls has a stabilizing effect. Furthermore, accounting for spanwise-varying perturbations results in a plethora of unstable modes, the number of which increases as the aspect ratio is increased. These modes present an odd-even regularity in their spatial structures, which is rationalized by comparison to the so-called one-dimensional oblique (1D-O) dispersion relation obtained for oblique waves. Finally, we show that in most cases, the most unstable 2D mode is the one that oscillates the least in the spanwise direction, as a consequence of viscous damping. However, in a limited region of the parameter space and in the absence of stratification, we show that a secondary mode with a more complex `twisted' structure dominated by crosswise vorticity becomes more unstable than the least oscillating Kelvin-Helmholtz mode associated with spanwise vorticity.

physics.flu-dyn↗

arXiv2021

Experimental properties of continuously-forced, shear-driven, stratified turbulence. Part 1. Mean flows, self-organisation, turbulent fractions

We study the experimental properties of exchange flows in a stratified inclined duct (SID), which are simultaneously turbulent, strongly stratified by a mean vertical density gradient, driven by a mean vertical shear, and continuously forced by gravity. We focus on the core shear layer away from the duct walls, where these flows are excellent experimentally-realisable approximations of canonical hyperbolic-tangent stratified shear layers, whose forcing allows mean and turbulent properties to reach quasi steady states. We analyse state-of-the-art data sets of the time-resolved density and velocity in three-dimensional sub-volumes of the duct in 16 experiments covering a range of flow regimes (Holmboe waves, intermittent turbulence, full turbulence). In this Part 1 we first reveal the permissible regions in the multi-dimensional parameter space (Reynolds number, bulk Richardson number, velocity-to-density layer thickness ratio), and their link to experimentally-controllable parameters. Reynolds-averaged balances then reveal the subtle momentum forcing and dissipation mechanisms in each layer, the broadening or sharpening of the density interface, and the importance of the streamwise non-periodicity of these flows. Mean flows suggest a tendency towards self-similarity of the velocity and density profiles with increasing turbulence, and gradient Richardson number statistics support prior internal mixing theories of equilibrium Richardson number, marginal stability and self-organised criticality. Turbulent volume fractions based on enstrophy and overturn thresholds quantify the nature of turbulence between different regimes, while highlighting the challenges of obtaining representative statistics in spatio-temporally intermittent flows. These insights may stimulate and assist the development of numerical simulations with a higher degree of experimental realism.

physics.flu-dyn↗

arXiv2021

Experimental properties of continuously-forced, shear-driven, stratified turbulence. Part 2. Energetics, anisotropy, parameterisation

In this Part 2 we study further experimental properties of two-layer exchange flows in a stratified inclined duct (SID), which are turbulent, strongly-stratified, shear-driven, and continuously-forced. We analyse the same state-of-the-art data sets using the same core shear layer methodology as in Part 1, but we focus here on turbulent energetics and mixing statistics. The detailed analysis of kinetic and scalar energy budgets reveals the specificity and scalings of SID turbulence, while energy spectra provide insight into the current strengths and limitations of our experimental data. The anisotropy of the flow at different scales characterises the turbulent kinetic energy production and dissipation mechanisms of Holmboe waves and turbulence. We then assess standard mixing parameterisations models relying on uniform eddy diffusivities, mixing lengths, flux parameters, buoyancy Reynolds numbers or turbulent Froude numbers, and we compare representative values with the stratified mixing literature. The dependence of these measures of mixing on controllable flow parameters is also elucidated, providing asymptotic estimates that may be extrapolated to more strongly turbulent flows, quantified by the product of the tilt angle of the duct and the Reynolds number. These insights may serve as benchmark for the future generation of experimental data with superior spatio-temporal resolution required to probe increasingly vigorous turbulence.

physics.flu-dyn↗

arXiv2019

Buoyancy-driven exchange flows in inclined ducts

Buoyancy-driven exchange flows arise in the natural and built environment wherever bodies of fluids at different densities are connected by a narrow constriction. In this paper we study these flows in the laboratory using the canonical stratified inclined duct experiment, which sustains an exchange flow in an inclined duct of rectangular cross-section over long time periods (Meyer & Linden, J. Fluid Mech., vol. 753, 2014). We study the behaviour of these sustained stratified shear flows by focusing on three dependent variables of particular interest: the qualitative flow regime (laminar, wavy, intermittently turbulent, or fully turbulent), the mass flux (net transport of buoyancy between reservoirs), and the interfacial thickness (thickness of the layer of intermediate density between the two counter-flowing layers). Dimensional analysis reveals five non-dimensional independent input parameters: the duct aspect ratios in the longitudinal direction $A$ and spanwise direction $B$, the tilt angle $θ$, the Reynolds number $Re$ (based on the initial buoyancy difference driving the flow), and the Prandtl number $Pr$ (we consider both salt and temperature stratifications). After reviewing the literature and open questions on the scaling of regimes, mass flux, and interfacial thickness with $A,B,θ,Re,Pr$, we present the first extensive, unified set of experimental data where we varied systematically all five input parameters and measured all three output variables with the same methodology. Our results in the $(θ,Re)$ plane for five sets of $(A,B,Pr)$ reveal a variety of scaling laws, and a non-trivial dependence of all three variables on all five parameters, in addition to a sixth elusive parameter. We further develop three classes of candidate models to explain the observed scaling laws: ...

physics.flu-dyn↗

arXiv2013

Globally aligned states and hydrodynamic traffic jams in confined active suspensions

Strongly confined active liquids are subject to unique hydrodynamic interactions due to momentum screening and lubricated friction by the confining walls. Using numerical simulations, we demonstrate that 2D dilute suspensions of fore-aft asymmetric polar swimmers in a Hele-Shaw geometry can exhibit a rich variety of novel phase behaviors depending on particle shape, including: coherent polarized density waves with global alignment, stationary asters, persistent counter-rotating vortices, density shocks and rarefaction waves. We also explain these phenomena using a linear stability analysis and a nonlinear traffic flow model, both derived from a mean-field kinetic theory.

cond-mat.soft↗