arXiv subjects

Rich Kerswell

Publications and source records attributed to Rich Kerswell.

9 recordsLinked to original sources

arXiv2025

Stable stratification enhances transient growth in streaky shear flows

Recent work has found that the well-known `lift-up' mechanism is not important for, and may even inhibit, the transient growth possible on streaky wall-bounded shear flows which is believed an important process in the near-wall cycle for turbulent flows. Moreover, artificially removing the wall-normal velocity has been found to unleash 3 orders of magnitude more perturbation energy growth in an unbounded streaky flow model. Motivated by this, we examine the effect of introducing stable stratification which naturally suppresses wall-normal velocities (the `vertical' shear case) and find it permits the hugely enhanced linear energy growth predicted by simply removing the wall-normal velocity. Alternatively, imposing stable stratification such that the spanwise velocities are suppressed (`horizontal shear') not surprisingly inhibits transient growth by weakening the active `push over' mechanism. A formula for the critical stratification strength to completely suppress the preferred growth mechanism is determined which proves a useful predictor for what is seen in the full numerical solutions of the model. Implications for a stratified near-wall cycle are briefly discussed.

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arXiv2025

A Physics-Augmented GraphGPS Framework for the Reconstruction of 3D Riemann Problems from Sparse Data

In compressible fluid flow, reconstructing shocks, discontinuities, rarefactions, and their interactions from sparse measurements is an important inverse problem with practical applications. Moreover, physics-informed machine learning has recently become an increasingly popular approach for performing reconstructions tasks. In this work we explore a machine learning recipe, known as GraphGPS, for reconstructing canonical compressible flows known as 3D Riemann problems from sparse observations, in a physics-informed manner. The GraphGPS framework combines the benefits of positional encodings, local message-passing of graphs, and global contextual awareness, and we explore the latter two components through an ablation study. Furthermore, we modify the aggregation step of message-passing such that it is aware of shocks and discontinuities, resulting in sharper reconstructions of these features. Additionally, we modify message-passing such that information flows strictly from known nodes only, which results in computational savings, better training convergence, and no degradation of reconstruction accuracy. We also show that the GraphGPS framework outperforms numerous machine learning benchmarks.

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arXiv2024

Revisiting 2D Viscoelastic Kolmogorov Flow: A Centre-mode-driven transition

We revisit viscoelastic Kolmogorov flow to show that the elastic linear instability of an Oldroyd-B fluid at vanishing Reynolds numbers ($Re$) found by Boffetta et al. (J. Fluid Mech. 523, 161-170, 2005) is the same `centre-mode' instability found at much higher $Re$ by Garg et al. (Phys. Rev. Lett. 121, 024502, 2018) in a pipe and Khalid et al. (J. Fluid Mech. 915, A43, 2021) in a channel. In contrast to these wall-bounded flows, the centre-mode instability exists even when the solvent viscosity vanishes (e.g. it exists in the upper-convective Maxwell limit with $Re=0$). Floquet analysis reveals that the preferred centre-mode instability almost always has a wavelength twice that of the forcing. All elastic instabilities give rise to familiar `arrowheads' (Page et al. Phys. Rev. Lett. 125, 154501, 2020) which in sufficiently large domains and at sufficient Weissenberg number ($W$) interact chaotically in 2D to give elastic turbulence via a bursting scenario. Finally, it is found that the $k^{-4}$ scaling of the kinetic energy spectrum seen in this 2D elastic turbulence is already contained within the component arrowhead structures.

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arXiv2024

Weakening the effect of boundaries: `diffusion-free' boundary conditions as a `do least harm' alternative to Neumann

In this note, we discuss a poorly known alternative boundary condition to the usual Neumann or `stress-free' boundary condition typically used to weaken boundary layers when diffusion is present but very small. These `diffusion-free' boundary conditions were first developed (as far as the authors know) in 1995 (Sureshkumar & Beris, J. Non-Newtonian Fluid Mech., vol 60, 53-80, 1995) in viscoelastic flow modelling but are worthy of general consideration in other research areas. To illustrate their use, we solve two simple ODE problems and then treat a PDE problem - the inertial wave eigenvalue problem in a rotating cylinder, sphere and spherical shell for small but non-zero Ekman number $E$. Where inviscid inertial waves exist (cylinder and sphere), the viscous flows in the Ekman boundary layer are $O(E^{1/2})$ weaker than for the corresponding stress-free layer and fully $O(E)$ weaker than in a non-slip layer. These diffusion-free boundary conditions can also be used with hyperdiffusion and provide a systematic way to generate as many further boundary conditions as required. The weakening effect of this boundary condition could allow precious numerical resources to focus on other areas of the flow and thereby make smaller, more realistic values of diffusion accessible to simulations.

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arXiv2023

Asymptotics of the centre mode instability in viscoelastic channel flow: with and without inertia

Motivated by the recent numerical results of Khalid et al., Phys. Rev. Lett., 127, 134502 (2021), we consider the large-Weissenberg-number ($W$) asymptotics of the centre mode instability in inertialess viscoelastic channel flow. The instability is of the critical layer type in the distinguished ultra-dilute limit where $W(1-β)=O(1)$ as $W \rightarrow \infty$ ($β$ is the ratio of solvent-to-total viscosity). In contrast to centre modes in the Orr-Sommerfeld equation, $1-c=O(1)$ as $W \rightarrow \infty$ where $c$ is the phase speed normalised by the centreline speed as a central `outer' region is always needed to adjust the non-zero cross-stream velocity at the critical layer down to zero at the centreline. The critical layer acts as a pair of intense `bellows' which blows the flow streamlines apart locally and then sucks them back together again. This compression/rarefaction amplifies the streamwise-normal polymer stress which in turn drives the streamwise flow through local polymer stresses at the critical layer. The streamwise flow energises the cross-stream flow via continuity which in turn intensifies the critical layer to close the cycle. We also treat the large-Reynolds-number ($Re$) asymptotic structure of the upper (where $1-c=O(Re^{-2/3})$) and lower branches of the $Re$-$W$ neutral curve confirming the inferred scalings from previous numerical computations. Finally, we argue that the viscoelastic centre mode instability was actually first found in viscoelastic Kolmogorov flow by Boffetta et al., J. Fluid Mech., 523, 161-170 (2005).

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arXiv2023

The polymer diffusive instability in highly concentrated polymeric fluids

The extrusion of polymer melts is known to be susceptible to `melt fracture' instabilities, which can deform the extrudate, or cause it to break entirely. Motivated by this, we consider the impact that the recently discovered polymer diffusive instability (PDI) can have on polymer melts and other concentrated polymeric fluids using the Oldroyd-B model with the effects of polymer stress diffusion included. Analytic progress can be made in the concentrated limit (when the solvent-to-total-viscosity ratio $β\rightarrow 0$), illustrating the boundary layer structure of PDI, and allowing the prediction of its eigenvalues for both plane Couette and channel flow. We draw connections between PDI and the polymer melt `sharkskin' instability, both of which are short wavelength instabilities localised to the extrudate surface. Inertia is shown to have a destabilising effect, reducing the smallest Weissenberg number ($W$) where PDI exists in a concentrated fluid from $W\sim 8$ in inertialess flows, to $W \sim 2$ when inertia is significant.

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arXiv2016

Sustaining processes from recurrent flows in body-forced turbulence

By extracting unstable invariant solutions directly from body-forced three-dimensional turbulence, we study the dynamical processes at play when the forcing is large scale and either unidirectional in the momentum or the vorticity equations. In the former case, the dynamical processes familiar from recent work on linearly-stable shear flows - variously called the Self-Sustaining Process (Waleffe 1997) or Vortex-Wave Interaction (Hall & Smith 1991; Hall & Sherwin 2010) - are important even when the base flow is linearly unstable. In the latter case, where the forcing drives Taylor-Green vortices, a number of mechanisms are observed from the various types of periodic orbits isolated. In particular, two different transient growth mechanisms are discussed to explain the more complex states found.

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arXiv2015

Recurrent flow analysis in spatiotemporally chaotic 2-dimensional Kolmogorov flow

Motivated by recent success in the dynamical systems approach to transitional flow, we study the efficiency and effectiveness of extracting simple invariant sets (recurrent flows) directly from chaotic/turbulent flows and the potential of these sets for providing predictions of certain statistics of the flow. Two-dimensional Kolmogorov flow (the 2D Navier-Stokes equations with a sinusoidal body force) is studied both over a square [0, 2π]2 torus and a rectangular torus extended in the forcing direction. In the former case, an order of magnitude more recurrent flows are found than previously (Chandler & Kerswell 2013) and shown to give improved predictions for the dissipation and energy pdfs of the chaos via periodic orbit theory. Over the extended torus at low forcing amplitudes, some extracted states mimick the statistics of the spatially-localised chaos present surprisingly well recalling the striking finding of Kawahara & Kida (2001) in low-Reynolds-number plane Couette flow. At higher forcing amplitudes, however, success is limited highlighting the increased dimensionality of the chaos and the need for larger data sets. Algorithmic developments to improve the extraction procedure are discussed.

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arXiv2007

Asymmetric, helical and mirror-symmetric travelling waves in pipe flow

New families of three-dimensional nonlinear travelling waves are discovered in pipe flow. In contrast to known waves (Faisst & Eckhardt Phys. Rev. Lett. 91, 224502 (2003), Wedin & Kerswell, J. Fluid Mech. 508, 333 (2004)), they possess no rotational symmetry and exist at much lower Reynolds numbers. Particularly striking is an `asymmetric mode' which has one slow streak sandwiched between two fast streaks located preferentially to one side of the pipe. This family originates in a pitchfork bifurcation from a mirror-symmetric travelling wave which can be traced down to a Reynolds number of 773. Helical and non-helical rotating waves are also found emphasizing the richness of phase space even at these very low Reynolds numbers. The delay in Reynolds number from when the laminar state ceases to be a global attractor to turbulent transition is then even larger than previously thought.

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