Post-doc talks

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• Post-doc talks, DAMTP
• Friday 21 February 2025, 14:00-17:00
• MR2.

If you have a question about this talk, please contact Professor Grae Worster.

Dario Klingenberg: Using nonlinear optimisation to investigate shear turbulence

Much research has focused on understanding how flows transition to turbulence. However, an equally important question is how, once established, turbulence is sustained. Interestingly, the same methods used for the transition problem are also useful in the turbulent setting, despite the stark differences between the two. In this work, I will use nonlinear optimisation to find the initial perturbation that, over a given time horizon, experiences the highest energy growth in channel flow with a friction Reynolds number of 180. Although the precise form of the initial condition depends on this time horizon, and also the initial energy available to it, it turns out that over a wide range in this parameter space, optimals with very similar dynamics arise. Interestingly, many important aspects of these dynamics are consistent with observations made in real turbulence. Based on these results, it is argued that nonlinear optimals are a conceptually simple and valuable concept to investigate turbulence.

Philipp Vieweg: Large-scale flow structures and their induced mixing in horizontally extended forced stratified shear flows

Covering about 70% of Earth’s surface, the oceans represent the biggest heat sink in climate and weather models. However, our understanding of the oceans’ inherent turbulent processes is still far from complete. Here, we study an idealised or simplified configuration that is stably stratified and continuously forced. The basic configuration has been introduced by Smith et al. (Journal of Fluid Mechanics 910, A42 (2021)) for small numerical domains and may be susceptible to Kelvin-Helmholtz instabilities. We extend these results to horizontally extended domains by conducting direct numerical simulations using the GPU -accelerated open-source spectral element solver NekRS.

On the one hand, we analyse the formation and convergence of large-scale flow structures in extended domains. Due to the anisotropic nature of the flow, this involves separate treatments of the stream-wise and span-wise direction. On the other hand, we analyse the impact of these flow structures on their induced mixing of the two layers of fluid.

Based on these structural and statistical analyses of stratified turbulent flows, this research contributes to advancing our current understanding of oceanic flows and allowing for improved predictions using global simulations that involve turbulence modelling.

James Shemilt: Viscoplastic dynamics of mucus transport during coughing

Coughing is a mechanism by which excess mucus is cleared from the lungs’ airways. In obstructive lung diseases such as cystic fibrosis, the rheology of mucus changes, including its yield stress increasing, and coughing can become a central mechanism for mucus clearance. I will present thin-film modelling of a viscoplastic liquid layer driven by high-speed confined air flow, which is a model for mucus transport during a cough that accounts for the yield stress of mucus. Numerical solutions of the thin-film equations, and travelling-wave solutions, are used to quantify how the liquid’s yield stress alters the dynamics. Criteria are determined for finite-time blow-up of solutions, where the liquid layer reaches the upper wall of the channel. I will also discuss how these theoretical results compare with experiments in which viscoplastic liquid layers are exposed to high-speed air flow.

Fabio Pino: Stability and Dynamics of Evaporating/Condensing Liquid Film Flows

Pulsating heat pipes (PHPs) have emerged as an effective heat transfer device for small-scale electronics. Their enhanced thermal performance relies on the periodic evaporation and condensation of a liquid film lining the pipe walls. However, an incomplete understanding of the phase change mechanism limits its broader application.

This research addresses this gap by investigating the linear and nonlinear stability of a 3D evaporating/condensing liquid film over an inclined plate. To reduce the complexity of the governing equations, we will develop a liquid film integral boundary layer model. This model will capture key liquid film dynamics, including phase change, inertia, and thermo-capillarity. The integral model’s validation will involve comparing the linear stability properties with the solution to the linearised full governing equations and assessing nonlinear dynamics against COMSOL simulations of the governing equations.

Based on the integral model, the continuation and bifurcation analysis of steady-state solutions will reveal how the liquid film’s behaviour develops as the evaporation rate or the Reynolds number varies. This analysis will identify key transitions and stability shifts affecting system performance. In addition, we will investigate the transient behaviour of disturbances via a nonlinear, nonmodal stability analysis. This approach will uncover nonlinear mechanisms that drive instabilities, such as the impact of temperature variations on the solid substrate during the evaporation or condensation phase.

The findings of this research will provide deeper insight into liquid film dynamics and develop a predictive reduced-order model for PHP systems. Additionally, these will be critical for designing optimal control laws based on liquid film stability properties, enhancing the evaporation/condensation mechanism, and guiding the design of more stable and efficient PHP configurations.

Gergely Buza: Rigorization of model reduction in fluid dynamics

The emergence of data-driven methods has fueled a newfound interest in the utilization of nonlinear tools from dynamical systems theory. In fluid dynamics, prominent examples are Koopman eigenfunctions (through dynamic mode decomposition) and spectral submanifolds. Due to their immense popularity, both of these techniques have been studied extensively, to the point that most aspects regarding their implementation are now fully fleshed out. However, there is one issue that has remained mostly untouched, and it is perhaps the most pressing one — the mathematical foundation of these tools. While the theory is well understood in the case of finite-dimensional systems, fluid dynamics is inherently infinite-dimensional, which calls for a more careful assessment. The talk will provide existence and uniqueness results for spectral submanifolds, smooth invariant foliations and Koopman eigenfunctions in the full, infinite-dimensional phase space of the Navier-Stokes system, alongside avenues to make the approximation procedure rigorous.

This talk is part of the Fluid Mechanics (DAMTP) series.

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