arXiv subjects

Neil J. Balmforth

Publications and source records attributed to Neil J. Balmforth.

6 recordsLinked to original sources

arXiv2026

A transition to elasto-viscoplastic turbulence in inertialess channel flow?

We conduct 2D numerical simulations employing a widely used constitutive law for elasto-viscoplastic fluids to show that linear instability leads to spatio-temporal complexity in inertialess channel flow. Fluctuations in the final state are pronounced near and between the yield surfaces that border an unyielded plug spanning the centre of the channel. The instability and transition arise for Weissenberg numbers of order unity and higher.

physics.flu-dyn↗

arXiv2026

Start-up and inertialess instability of elasto-viscoplastic channel flow

An exploration is presented of the start-up and linear stability of pressure-driven channel flow of an elasto-viscoplastic fluid described by Saramito's constitutive law. Streamwise uniform base states are non-unique, depending on the initial stress configuration, and develop discontinuities in the normal stresses and shear rate at the yield surfaces over infinite times. Such stress discontinuities can be eliminated by introducing a sufficient extensional pre-stress; true plugs bordered by stress jumps then become replaced by marginally yielded, plug-like flow, or pseudo-plugs. To examine the stability of all of these state, the linear initial-value problem is solved along with the evolving base states. Because this analysis is performed for finite times, the base states remain continuous and there is no need to perturb any stress discontinuities. Armed with the insights provided, stability is then analyzed as a normal-mode problem for the final states, building in perturbations to the stress discontinuities via certain jump conditions across any yield surfaces. Regardless of whether the base flows contain true plugs or pseudo-plugs, the base states are found to be linearly unstable at zero Reynolds number. The most unstable perturbations possess the highest streamwise wavenumbers and become spatially localized to the regions where stresses lie close to the yield stress.

physics.flu-dyn↗

arXiv2025

Rayleigh-Plateau instability of an elasto-viscoplastic filament

A slender-thread model is used to explore the Rayleigh-Plateau instability of a filament of elasto-viscoplastic fluid. Without elasticity, a finite yield stress suppresses any linear instability for a filament of constant radius. Including sub-yield elastic deformation permits an elastic Rayleigh-Plateau instability above a critical Deborah number. If stresses over the thinner sections of the thread breach the yield threshold, viscoplastic deformations then drive the filament towards pinch-off. The thread consequently evolves to a beads-on-a-string structure. The elasto-plastic anatomy of the beads is explored and categorized.

physics.flu-dyn↗

arXiv2025

Dynamics of levitation during rolling over a thin viscous film

A mathematical model is derived for the dynamics of a cylinder, or wheel, rolling over a thin viscous film. The model combines the Reynolds lubrication equation for the fluid with an equation of motion for the wheel. Two asymptotic limits are studied in detail to interrogate the dynamics of levitation: an infinitely wide wheel and a relatively narrow one. In both cases the front and back of the fluid-filled gap are either straight or nearly so. To bridge the gap between these two asymptotic limits, wheels of finite width are considered, introducing a further simplying approximation: although the front and back are no longer expected to remain straight for a finite width, the footprint of the fluid-filled gap is still taken to be rectangular, with boundary conditions imposed at the front and back in a wheel-averaged sense. The Reynolds equation can then be solved by separation of variables. For wider wheels, with a large amount of incoming flux or a relatively heavy loading of the wheel, the system is prone to flooding by back flow with fluid unable to pass underneath. Otherwise steady planing states are achieved. Both lift-off and touch-down are explored for a wheel rolling over a film of finite length. Theoretical predictions are compared with a set of experimental data.

physics.flu-dyn↗

arXiv2025

Air-driven dynamics of viscoplastic liquid layers

Airway clearance by coughing is a key mechanism for mucus transport, particularly in obstructive lung diseases associated with altered mucus rheology. We investigate the dynamics of a viscoplastic liquid film driven by flow in a turbulent air layer, which is a model for air-driven mucus transport that incorporates yield-stress effects. Our theoretical analysis is based on a long-wave model for the liquid film flow, and we complement this with experiments, in which layers of Newtonian and yield-stress liquids are exposed to air flow in a rectangular duct. We demonstrate how perturbations to the layer depth can lead to localised yielding and wave generation. Rapid wave growth occurs when the fluid ahead of the oncoming wave is unyielded, so that as the wave propagates, it consumes this static fluid while depositing a much thinner film behind. This mechanism causes dramatic "blow-out" events in experiments, where liquid hits the roof of the tank. By contrast, in Newtonian thin films, multiple surface waves typically form, and blow-out only occurs in experiments when a Newtonian film is sufficiently thick.

physics.flu-dyn↗

arXiv2019

Nonlinear dynamics of forced baroclinic critical layers

In this paper, we study the forcing of baroclinic critical levels, which arise in stratified fluids with horizontal shear flow along the surfaces where the phase speed of a wave relative to the mean flow matches a natural internal wavespeed. Linear theory predicts the baroclinic critical layer dynamics is similar to that of a classical critical layer, characterized by the secular growth of flow perturbations over a region of decreasing width. By using matched asymptotic expansions, we construct a nonlinear baroclinic critical layer theory to study how the flow perturbation evolves once they enter the nonlinear regime. A key feature of the theory is that, because the location of the baroclinic critical layer is determined by the streamwise wavenumber, the nonlinear dynamics filters out harmonics and the modification to the mean flow controls the evolution. At late times, we show that the vorticity begins to focus into yet smaller regions whose width decreases exponentially with time, and that the addition of dissipative effects can arrest this focussing to create a drifting coherent structure. Jet-like defects in the mean horizontal velocity are the main outcome of the critical-layer dynamics.

physics.flu-dyn↗