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Stuart B. Dalziel

Publications and source records attributed to Stuart B. Dalziel.

At least 19 recordsLinked to original sources

Emergent Transfer of a Physics Foundation Model from Simulation to Laboratory Turbulence

Whether physics foundation models can be usefully deployed on laboratory experiments remains an open question for scientific machine learning (ML). We test this question on the Rayleigh-Taylor instability (RTI), a ubiquitous and demanding fluid instability seen from tabletop flows to supernova explosions, in which small perturbations at a density interface grow into chaotic, multiscale mixing as a lighter fluid accelerates into a heavier one. Standard ML models struggle with RTI, and despite over a century of theoretical, numerical, and experimental work, it carries an unresolved discrepancy between simulation and experiment: the late-time mixing growth rate, $α$, measured in most laboratory experiments ($\sim$ 0.06-0.07), is roughly three times the value from idealized direct numerical simulations (DNS, $\sim$ 0.02). The gap's origin remains debated. These properties make RTI a stringent test for a question that matters well beyond RTI: can foundation models trained only on simulations generalise to sparse, messy, and noisy laboratory settings? We finetune Walrus, a foundation model for continuum dynamics, on three or fewer DNS realizations and recover key RTI physics over long rollouts. Applied zero-shot to sliding-barrier laboratory data, the finetuned model leaves the DNS-like regime and enters the observed growth band, having never seen a single experimental sample. These results provide independent, data-driven evidence that initial conditions play a crucial role in the longstanding sim-experiment gap in $α$. The model also generalises zero-shot to stable stratification, a buoyancy regime absent from training, correctly slowing mixing-layer growth. Together, our results show that foundation models can generalise well beyond their training data, predicting laboratory behavior and unseen physical regimes, opening new ways to probe longstanding simulation-experiment gaps.

physics.flu-dyn

Transport and removal of a passive tracer in porous media employing surface washing

This experimental study investigates the dynamics of surface washing to remove a passive tracer from a porous plate by a gravity-driven liquid film across its surface. A disodium fluorescein tracer is introduced at the surface of a water-saturated porous plate and allowed to diffuse into the plate for a number of hours before a film of water solution flows over its surface to extract and transport the tracer away. The removal rate of the tracer is monitored quantitatively by using fluorescence measurements to determine the concentration in the effluent from the washing process. These measurements are supplemented by dye-attenuation imaging, which provides mainly qualitative insights about the tracer's concentration distribution on the porous plate surface. Our findings reveal a three-stage mass-transport process consisting of an initial period of rapid removal of the tracer found within the surface roughness, followed by a period of slower removal, which appears to be limited by vertical diffusion, and a third stage of accelerated advection-dominated removal when the tracer-rich region that was transported downstream during the second stage reaches the downstream boundary of the porous plate. A parametric study explores the influence of the characteristics of the washing film, the permeability of the porous plate, the amount and initial spatial extent of the tracer on the porous plate and the tracer's diffusive penetration depth on the mass removal rates. Our insights offer practical guidance for optimising surface washing protocols for porous systems in industrial and environmental applications.

physics.flu-dyn

The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning

Machine learning based surrogate models offer researchers powerful tools for accelerating simulation-based workflows. However, as standard datasets in this space often cover small classes of physical behavior, it can be difficult to evaluate the efficacy of new approaches. To address this gap, we introduce the Well: a large-scale collection of datasets containing numerical simulations of a wide variety of spatiotemporal physical systems. The Well draws from domain experts and numerical software developers to provide 15TB of data across 16 datasets covering diverse domains such as biological systems, fluid dynamics, acoustic scattering, as well as magneto-hydrodynamic simulations of extra-galactic fluids or supernova explosions. These datasets can be used individually or as part of a broader benchmark suite. To facilitate usage of the Well, we provide a unified PyTorch interface for training and evaluating models. We demonstrate the function of this library by introducing example baselines that highlight the new challenges posed by the complex dynamics of the Well. The code and data is available at https://github.com/PolymathicAI/the_well.

cs.LG

Pattern Formation in Crumpled Hydrogel upon Rapid Dehydration with Acetone

From microactuators to biological tissues, non-porous materials with the ability to strongly expand when in contact with a solvent are ubiquitous. Consequently, the swelling of polymer systems such as hydrogel has received recently much research attention. However, the related dehydration of these systems has received much less attention. Here, we present experiments investigating the rapid dehydration of a swollen hydrogel sheet whose surface exhibits a transient crumpling instability characterised by line segments of cusps patterning the surface of the gel into an array of bumps. We perform this dehydration through immersion in acetone, which is highly miscible in water, but poorly miscible in the hydrogel. We report the onset of a fascinating pattern formation where regions of the hydrogel sheet turn turbid. We find that the emerging pattern is independent of the overall extent of the hydrated swollen surface. The pattern wavelength only depends on the duration of hydration before immersion in acetone, growing temporally with a power law behaviour. We conclude through drawing comparisons between features of this dehydration induced pattern and the original crumpling instability in the water swollen hydrogel sheet.

cond-mat.soft

Dye Attenuation Without Dye: Quantifying Concentration Fields with Short-wave Infrared Imaging

Dye attenuation, or photometric imaging, is an optical technique commonly used in fluid dynamics to measure tracer concentration fields and fluid thicknesses under the assumption that the motion of the dye is representative of the fluid motion and that its presence does not affect the behaviour of the system. However, in some systems, particularly living biological systems or those with strong chemical interactions and reactions, the addition of dye may non-trivially influence the system and may not follow the fluid containing it. To overcome this, we demonstrate how short-wave infrared imaging can be used to measure concentration and height profiles of water and other liquids without the introduction of dye for heights down to 0.2mm with spatial and temporal resolutions of the order of 50 microns per pixel and 120 fps respectively. We showcase the utility of this technique by demonstrating its ability to accurately track the temporal evolution of the total water content of two model systems, namely a water drop spreading on a glass slide and spreading within a hydrogel sheet, validating both against an analytical mass balance. Finally, we discuss how the spectral resolution of the present setup could be increased to the point that concentrations within a multi-component system containing more than one type of liquid could be quantified.

physics.flu-dyn

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

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

Bouncing behaviour of a particle settling through a density transition layer

The present work focuses on a specific bouncing behaviour as a particle settling through a three-layer stratified fluid in the absence of neutral buoyant position, which was firstly discovered by Abaid, N., Adalsteinsson D., Agyapong A. & McLaughlin, R.M. (2004) in salinity-induced stratification. Both experiments and numerical simulations are carried out. In our experiments, illuminated by a laser sheet on the central plane of the particle, its bouncing behaviour is well captured. We find that the bouncing process starts after the wake detaches from the particle. The PIV results show that an upward jet is generated at the central axis behind the particle after the wake breaks. By conducting a force decomposition procedure, we quantify the enhanced drag caused by the buoyancy of the wake ($F_{sb}$) and the flow structure ($F_{sj}$). It is noted that $F_{sb}$ contributes primarily to the enhanced drag at the early stage, which becomes less dominant after the detachment of the wake. In contrast, $F_{sj}$ plays a pivotal role in reversing the particle's motion. We conjecture that the jet flow is a necessary condition for the occurrence of bouncing motion. Then, we examine the minimal velocities (negative values when bounce occurs) of the particle by varying the lower Reynolds number $Re_l$, the Froude number $Fr$ and the upper Reynolds number $Re_u$ within the ranges $1 \leq Re_l\leq 125$, $115 \leq Re_u\leq 356$ and $2 \leq Fr\leq 7$. We find that the bouncing behaviour is primarily determined by $Re_l$. In our experiments, the bouncing motion is found to occur below a critical lower Reynolds number around $Re^ \ast _{l}=30$. In the numerical simulations, the highest value for this critical number is $Re^ \ast _{l}=46.2$, limited in the currently studied parametric ranges.

physics.flu-dyn

The long view of triadic resonance instability in finite-width internal gravity wave beams

This paper presents our investigation into the modification of a finite-width internal gravity wave beam arising from triadic resonance instability. We present both experimental and weakly non-linear modelling to examine this instability mechanism, in which a primary wave beam generates two secondary wave beams of lower frequencies and shorter length scales. Through a versatile experimental set-up, we examine how this instability develops over hundreds of buoyancy periods. Unlike predictions from previous zero-dimensional weakly non-linear theory, we find that the approach to a saturated equilibrium state for the triadic interactions is not monotonic; rather, the amplitudes and structures of the constituent beams continue to modulate without ever reaching a steady equilibrium. To understand this behaviour we develop a weakly non-linear approach to account for the spatio-temporal evolution of the amplitudes and structures of the beams over slow time-scales and long distances, and explore the consequences using a numerical scheme. Through this approach, we establish that the evolution of the instability is remarkably sensitive to the spatio-temporal triadic configuration for the system and how part of the observed modulations can be attributed to a competition between the linear growth rate of the secondary wave beams and the finite residence time of the triadic perturbations within the underlying primary beam.

physics.flu-dyn

Droplet absorption and spreading into thin layers of polymer hydrogels

From biological tissues to layers of paint, macroscopic non-porous materials with the capacity to swell when brought in contact with an appropriate solvent are ubiquitous. Here, we study experimentally and theoretically one of the conceptually simplest of such systems, the swelling of a thin hydrogel layer by a single water drop. Using a bespoke experimental setup, we observe fast absorption leading to a radially spreading axisymmetric blister. Employing a linear poroelastic framework and thin-layer scalings, we develop a non-linear one-dimensional diffusion equation for the evolution of the blister height profile, which agrees well with experimental observations.

cond-mat.soft

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

Three-dimensional advective--diffusive boundary layers in open channels with parallel and inclined walls

We study the steady laminar advective transport of a diffusive passive scalar released at the base of narrow three-dimensional longitudinal open channels with non-absorbing side walls and rectangular or truncated-wedge-shaped cross-sections. The scalar field in the advective--diffusive boundary layer at the base of the channels is fundamentally three-dimensional in the general case, owing to a three-dimensional velocity field and differing boundary conditions at the side walls. We utilise three-dimensional numerical simulations and asymptotic analysis to understand how this inherent three-dimensionality influences the advective-diffusive transport as described by the normalised average flux, the Sherwood $Sh$ or Nusselt numbers for mass or heat transfer, respectively. We show that $Sh$ is well approximated by an appropriately formulated two-dimensional calculation, even when the boundary layer structure is itself far from two-dimensional. This important result can significantly simplify the modelling of many laminar advection--diffusion scalar transfer problems: the cleaning or decontamination of confined channels, or transport processes in chemical or biological microfluidic devices.

physics.flu-dyn

A versatile scanning method for volumetric measurements of velocity and density fields

Understanding turbulence in a stratified environment requires a detailed picture of both the velocity field and the density field. Experimentally, this represents a significant measurement challenge, especially when full three-dimensional data is needed to accurately characterise the turbulent fields. This paper presents a new approach to obtaining such data through well-resolved, near-instantaneous volume-spanning measurements. This is accomplished by rapidly scanning the volume with a light sheet so that, at each scan location, planar two-dimensional measurements of three velocity components via stereo particle image velocimetry (PIV) and simultaneous density information via planar laser induced fluorescence (PLIF) can be made. Ultimately, this rapid scanning technique permits the measurement of all three components of velocity in a volume as well as simultaneously capturing the three-dimensional density field. The scanning of the light sheet is accomplished by mounting the optics producing the light sheet on a linear traverse that is capable of rapidly scanning the volume in a continuous manner. The key and novel aspect enabling high scan rates is the addition of two mirrors on galvanometers to make small adjustments to the position of the light sheet and ensure a precise overlap between pairs of image frames. This new technique means the light sheet does not have to be excessively thick, the scanning speed too slow, or that inappropriately small interframe times have to be used, while ensuring overlapping particle patterns between pairs of images that are required by the PIV algorithm. The technique is illustrated with some preliminary results from the buoyancy-driven exchange flow through an inclined duct connecting two reservoirs containing different density fluids.

physics.flu-dyn

Nonlinear waves in stratified Taylor--Couette flow. Part 1. Layer formation

This paper is the first part of a two-fold study of mixing, i.e. the formation of layers and upwelling of buoyancy, in axially stratified Taylor--Couette flow, with fixed outer cylinder. Using linear analysis and direct numerical simulation, we show the critical role played by non-axisymmetric instability modes, despite the fact that the flow is centrifugally unstable in the sense of Rayleigh's criterion. Interactions between helical modes of opposite handedness leads to the formation of nonlinear coherent structures: (mixed)-ribbons and (mixed)-cross-spirals. These give birth to complex density interface patterns, seemingly appearing and disappearing periodically as the coherent structure slowly rotates around the annulus. These coherent structures seem to be responsible for the formation of layers reported in a recent experiment by Oglethorpe et al. (2013). We distinguish `dynamic layering', instantaneous, localized and caused by the vortical motions, from `static layering' corresponding to the formation of a `staircase profile' in the adiabatically sorted background density. The latter only occurs at large enough Schmidt number, revealing the significant impact of the Schmidt number in the layering process.

physics.flu-dyn

Nonlinear waves in stratified Taylor--Couette flow. Part 2. Buoyancy flux

This paper is the second part of a two-fold study of mixing, i.e. the formation of layers and upwelling of buoyancy, in axially stratified Taylor--Couette flow, with fixed outer cylinder. In a first paper, we showed that the dynamics of the flow was dominated by coherent structures made of a superposition of nonlinear waves. (Mixed)-ribbons and (mixed)-cross-spirals are generated by interactions between a pair of linearly unstable helical modes of opposite `handedness', and appear to be responsible for the formation of well-mixed layers and sharp density interfaces. In this paper, we show that these structures are also fully accountable for the upwards buoyancy flux in the simulations. The mechanism by which this occurs is a positive coupling between the density and vertical velocity components of the most energetic waves. This coupling is primarily caused by diffusion of density at low Schmidt number Sc, but can also be a nonlinear effect at larger Sc. Turbulence was found to contribute negatively to the buoyancy flux at Sc=1,10,16, which lead to the conclusion that mass upwelling is a consequence of chaotic advection, even at large Reynolds number. Artificially isolating the coherent structure therefore leads to excellent estimates of the flux Richardson numbers Ri_f from the DNS. We also used the theoretical framework of Winters et al. (1995) to analyse the energetics of mixing in an open control volume, shedding light on the influence of end effects in the potential energy budget. The potential connection with the buoyancy flux measurements made in the recent experiment of Oglethorpe et al. (2013) is also discussed.

physics.flu-dyn

Convective mass transfer from a submerged drop in a thin falling film

We study the fluid mechanics of removing a passive tracer contained in small, viscous drops attached to a flat inclined substrate using thin gravity-driven film flows. A convective mass transfer establishes across the drop-film interface and the tracer in the drop diffuses into the film flow. The Peclet number for the tracer in the film is large. The Peclet number Pe_d in the drop varies from 0.01 to 1. The characteristic transport time in the drop is much larger than in the film. We model the mass transfer of the tracer from the drop bulk into the film using an empirical model based on Newton's law of cooling. This model is supported by a theoretical model solving the quasi-steady 2D advection-diffusion equation in the film coupled with a time-dependent 1D diffusion equation in the drop. We find excellent agreement between our experimental data and the 2 models, which predict an exponential decrease in time of the tracer concentration in the drop. The results are valid for all drop and film Peclet numbers studied. The transport characteristic time is related to the drop diffusion time scale, as diffusion within the drop is the limiting process. Our theoretical model predicts the well-known relationship between the Sherwood and Reynolds numbers in the case of a well-mixed drop Sh~Re_L^{1/3}=γL^2/ν_f, based on the drop length L, film shear rate γand film kinematic viscosity ν_f. We show that this relationship is mathematically equivalent to a more physically intuitive relationship Sh~Re_δ, based on the diffusive boundary layer thickness δ. The model also predicts a correction in the case of a non-uniform drop concentration, which depends on Re_δ, the Schmidt number, the drop aspect ratio and the diffusivity ratio. This prediction is in agreement with experiments at low Pe_d. It also agrees as Pe_d approaches 1, although the influence of Re_δincreases.

physics.flu-dyn

Rayleigh-Taylor instability between two stable stratifications

These fluid dynamics video sequences show two Rayleigh-Taylor instability experiments. The first video sequence shows an experiment where two layers of uniform density are arranged such that the density of the upper layer is greater than the density of the lower. The unstable interface between the two layers is initially supported by a stainless steel barrier. With the removal of the barrier, Rayleigh-Taylor instability results in the creation of a mixing region, which grows with time. This growth accelerates until the mixing region fills the entire tank. The second sequence shows Rayleigh-Taylor instability when it is confined between two stable stratifications. Although initially the growth of the mixing region accelerates, the stable stratification slows the growth of the instability and brings it to a halt before it can fill the tank. The stratifications are constructed of fresh and salt water and both experiments have the same Atwood number. Visualisation of the upper surface of the mixing layer was achieved by the use of fluorescent dye in the lower layer.

physics.flu-dyn

Bursting water balloons

The impact and rupture of water-filled balloons upon a flat, rigid surface is studied experimentally, for which three distinct stages of the flow are observed. Due to the impact, waves are formed on the balloon's surface for which the restoring force is tension in the latex. Immediately following rupture of the membrane, a shear instability created by the retraction of the balloon is observed. At later times, a larger-scale growth of the interfacial amplitude is observed, that may be regarded as a manifestation of a phenomenon known as the Richtmyer-Meshkov instability. This flow is closely related to the classical understanding of the Richtmyer-Meshkov instability for when there exists a density difference between the fluids inside and outside the balloon. Further, it is shown experimentally that this growth of the interface may also occur when there is no density difference across the balloon, a situation that does not arise for the standard Richtmyer-Meshkov instability.

physics.flu-dyn