arXiv subjects

Miles M. P. Couchman

Publications and source records attributed to Miles M. P. Couchman.

9 recordsLinked to original sources

arXiv2026

Instability and breaking of internal waves in a horizontal shear layer

The behaviour of internal waves propagating in a background shear flow is studied in the case where the direction of shear is orthogonal to gravity. Ray-tracing theory is used to predict properties of the wave state at locations where instability occurs. Local wave energy growth is found to result from two distinct mechanisms: an increase in wave steepness due to refraction by the shear, or an increase in streamwise velocity perturbations due to wave advection of the background flow. Based on the initial conditions, a dimensionless perturbation energy ratio $F$ is constructed to predict the relative importance of these two mechanisms in facilitating wave-breaking. When $F$ is small and waves become locally steep, perturbation kinetic and potential energy remain approximately equipartitioned and subsequent instabilities are expected to develop due to a combination of shear and convection. On the other hand, as $F$ increases, kinetic energy dominates and wave advection of momentum may instead cause breaking to become increasingly driven by enhanced vertical shear. To test these predictions, fully nonlinear direct numerical simulations are conducted, spanning a range of wave-breaking dynamics. Good qualitative agreement with the theory is found despite substantial departures from the underlying assumptions. Wave breaking leads to significant turbulent dissipation, which in some cases greatly exceeds the initial wave energy. Momentum and energy transfers between the wave, background flow and turbulence are found to be sensitive to the dynamics of breaking, as are the mixing properties.

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

Inertial enhancement of the polymer diffusive instability

Beneitez et al. (Phys. Rev. Fluids, 8, L101901, 2023) have recently discovered a new linear "polymer diffusive instability" (PDI) in inertialess rectilinear viscoelastic shear flow using the FENE-P model when polymer stress diffusion is present. Here, we examine the impact of inertia on the PDI for both plane Couette (PCF) and plane Poiseuille (PPF) flows under varying Weissenberg number $W$, polymer stress diffusivity $\varepsilon$, solvent-to-total viscosity ratio $β$, and Reynolds number $Re$, considering the FENE-P and simpler Oldroyd-B constitutive relations. Both the prevalence of the instability in parameter space and the associated growth rates are found to significantly increase with $Re$. For instance, as $Re$ increases with $β$ fixed, the instability emerges at progressively lower values of $W$ and $\varepsilon$ than in the inertialess limit, and the associated growth rates increase linearly with $Re$ when all other parameters are fixed. For finite $Re$, it is also demonstrated that the Schmidt number $Sc=1/(\varepsilon Re)$ collapses curves of neutral stability obtained across various $Re$ and $\varepsilon$. The observed strengthening of PDI with inertia and the fact that stress diffusion is always present in time-stepping algorithms, either implicitly as part of the scheme or explicitly as a stabiliser, implies that the instability is likely operative in computational work using the popular Oldroyd-B and FENE-P constitutive models. The fundamental question now is whether PDI is physical and observable in experiments, or is instead an artifact of the constitutive models that must be suppressed.

physics.flu-dyn↗

arXiv2023

Prandtl number effects on extreme mixing events in forced stratified turbulence

Relatively strongly stratified turbulent flows tend to self-organise into a 'layered anisotropic stratified turbulence' (LAST) regime, characterised by relatively deep and well-mixed density 'layers' separated by relatively thin 'interfaces' of enhanced density gradient. Understanding the associated mixing dynamics is a central problem in geophysical fluid dynamics. It is challenging to study 'LAST' mixing, as it is associated with Reynolds numbers $Re := UL/ν\gg 1$ and Froude numbers $Fr :=(2πU)/(L N) \ll 1$, ($U$ and $L$ being characteristic velocity and length scales, $ν$ being the kinematic viscosity and $N$ the buoyancy frequency). Since a sufficiently large dynamic range (largely) unaffected by stratification and viscosity is required, it is also necessary for the buoyancy Reynolds number $Re_{b} := ε/(νN^{2}) \gg 1$ where $ε$ is the (appropriately volume-averaged) turbulent kinetic energy dissipation rate. This requirement is exacerbated for oceanically relevant flows, as the Prandtl number $Pr := ν/κ= \mathcal{O}(10)$ in thermally-stratified water (where $κ$ is the thermal diffusivity), thus leading (potentially) to even finer density field structures. We report here on four forced fully resolved direct numerical simulations of stratified turbulence at various Froude ($Fr=0.5, 2$) and Prandtl numbers ($Pr=1, 7$) forced so that $Re_{b}=50$, with resolutions up to $30240 \times 30240 \times 3780$. We find that, as $Pr$ increases, emergent 'interfaces' become finer and their contribution to bulk mixing characteristics decreases at the expense of the small-scale density structures populating the well-mixed 'layers'. However, extreme mixing events (as quantified by significantly elevated local destruction rates of buoyancy variance $χ_0$) are always preferentially found in the (statically stable) interfaces, irrespective of the value of $Pr$.

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

Mixing across stable density interfaces in forced stratified turbulence

Understanding how turbulence enhances irreversible scalar mixing in density-stratified fluids is a central problem in geophysical fluid dynamics. While isotropic overturning regions are commonly the focus of mixing analyses, we here investigate whether significant mixing may arise in anisotropic statically-stable regions of the flow. Focusing on a single forced direct numerical simulation of stratified turbulence, we analyze spatial correlations between the vertical density gradient $\partialρ/\partial z$ and the dissipation rates of kinetic energy $ε$ and scalar variance $χ$, the latter quantifying scalar mixing. The domain is characterized by relatively well-mixed density layers separated by sharp stable interfaces that are correlated with high vertical shear. While static instability is most prevalent within the mixed layers, much of the scalar mixing is localized to the intervening interfaces, a phenomenon not apparent if considering local static instability or $ε$ alone. While the majority of the domain is characterized by the canonical flux coefficient $Γ\equivχ/ε=0.2$, often assumed in ocean mixing parameterizations, extreme values of $χ$ within the statically-stable interfaces, associated with elevated $Γ$, strongly skew the bulk statistics. Our findings suggest that current parameterizations of turbulent mixing may be biased by undersampling, such that the most common, but not necessarily the most significant, mixing events are overweighted. Having focused here on a single simulation of stratified turbulence, it is hoped that our results motivate a broader investigation into the role played by stable density interfaces in mixing, across a wider range of parameters and forcing schemes representative of ocean turbulence.

physics.flu-dyn↗

arXiv2020

Collective vibrations of confined levitating droplets

We report a new type of fluid-based driven dissipative oscillator system consisting of a lattice of millimetric fluid droplets bouncing on a vertically vibrating liquid bath and bound within an annular ring. We characterize the system behavior as it is energized through a progressive increase in the bath's vibrational acceleration. Depending on the number of drops, the onset of motion of the lattice may take the form of either out-of-phase oscillations or a striking solitary wave-like instability. Theoretical modeling demonstrates that these behaviors may be attributed to different bifurcations at the onset of instability. The results presented here demonstrate the potential and utility of the walking droplet system as a platform for investigating wave-mediated, inertial, non-equilibrium particle dynamics at the macroscale.

cond-mat.soft↗

arXiv2016

Capillary levelling of free-standing liquid nanofilms

We report on the capillary-driven levelling of a topographical perturbation at the surface of a free-standing liquid nanofilm. The width of a stepped surface profile is found to evolve as the square root of time. The hydrodynamic model is in excellent agreement with the experimental data. In addition to exhibiting an analogy with diffusive processes, this novel system serves as a precise nanoprobe for the rheology of liquids at interfaces in a configuration that avoids substrate effects.

cond-mat.soft↗