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SUMMARY:Post-doc talks - Post-doc talks\, DAMTP
DTSTART:20250221T140000Z
DTEND:20250221T170000Z
UID:TALK227206@talks.cam.ac.uk
CONTACT:Professor Grae Worster
DESCRIPTION:*Dario Klingenberg:  Using nonlinear optimisation to investiga
 te shear turbulence*\n\nMuch research has focused on understanding how flo
 ws transition to turbulence. However\, an equally important question is ho
 w\, once established\, turbulence is sustained. \nInterestingly\, the same
  methods used for the transition problem are also useful in the turbulent 
 setting\, despite the stark differences between the two.\nIn this work\, I
  will use nonlinear optimisation to find the initial perturbation that\, o
 ver a given time horizon\, experiences the highest energy growth in channe
 l flow with a friction Reynolds number of 180.\nAlthough the precise form 
 of the initial condition depends on this time horizon\, and also the initi
 al energy available to it\, it turns out that over a wide range in this pa
 rameter space\, optimals with very similar dynamics arise.\nInterestingly\
 , many important aspects of these dynamics are consistent with observation
 s made in real turbulence.\nBased on these results\, it is argued that non
 linear optimals are a conceptually simple and valuable concept to investig
 ate turbulence.\n\n\n*Philipp Vieweg: Large-scale flow structures and thei
 r induced mixing in horizontally extended forced stratified shear flows*\n
 \nCovering about 70% of Earth's surface\, the oceans represent the biggest
  heat sink in climate and weather models. However\, our understanding of t
 he oceans' inherent turbulent processes is still far from complete. Here\,
  we study an idealised or simplified configuration that is stably stratifi
 ed and continuously forced. The basic configuration has been introduced by
  Smith et al. (Journal of Fluid Mechanics 910\, A42 (2021)) for small nume
 rical domains and may be susceptible to Kelvin-Helmholtz instabilities. We
  extend these results to horizontally extended domains by conducting direc
 t numerical simulations using the GPU-accelerated open-source spectral ele
 ment solver NekRS.\n\nOn the one hand\, we analyse the formation and conve
 rgence of large-scale flow structures in extended domains. Due to the anis
 otropic nature of the flow\, this involves separate treatments of the stre
 am-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 flu
 id.\n\nBased on these structural and statistical analyses of stratified tu
 rbulent flows\, this research contributes to advancing our current underst
 anding of oceanic flows and allowing for improved predictions using global
  simulations that involve turbulence modelling.\n\n\n*James Shemilt: Visco
 plastic dynamics of mucus transport during coughing*\n\nCoughing is a mech
 anism by which excess mucus is cleared from the lungs’ airways. In obstr
 uctive lung diseases such as cystic fibrosis\, the rheology of mucus chang
 es\, including its yield stress increasing\, and coughing can become a cen
 tral 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 tra
 velling-wave solutions\, are used to quantify how the liquid’s yield str
 ess alters the dynamics. Criteria are determined for finite-time blow-up o
 f solutions\, where the liquid layer reaches the upper wall of the channel
 . I will also discuss how these theoretical results compare with experimen
 ts in which viscoplastic liquid layers are exposed to high-speed air flow.
 \n\n\n*Fabio Pino: Stability and Dynamics of Evaporating/Condensing Liquid
  Film Flows*\n\nPulsating heat pipes (PHPs) have emerged as an effective h
 eat transfer device for small-scale electronics. Their enhanced thermal pe
 rformance relies on the periodic evaporation and condensation of a liquid 
 film lining the pipe walls. However\, an incomplete understanding of the p
 hase change mechanism limits its broader application.\n\nThis research add
 resses this gap by investigating the linear and nonlinear stability of a 3
 D evaporating/condensing liquid film over an inclined plate. To reduce the
  complexity of the governing equations\, we will develop a liquid film int
 egral boundary layer model. This model will capture key liquid film dynami
 cs\, including phase change\, inertia\, and thermo-capillarity. The integr
 al model's validation will involve comparing the linear stability properti
 es with the solution to the linearised full governing equations and assess
 ing nonlinear dynamics against COMSOL simulations of the governing equatio
 ns.\n\nBased on the integral model\, the continuation and bifurcation anal
 ysis of steady-state solutions will reveal how the liquid film's behaviour
  develops as the evaporation rate or the Reynolds number varies. This anal
 ysis will identify key transitions and stability shifts affecting system p
 erformance. In addition\, we will investigate the transient behaviour of d
 isturbances via a nonlinear\, nonmodal stability analysis. This approach w
 ill uncover nonlinear mechanisms that drive instabilities\, such as the im
 pact of temperature variations on the solid substrate during the evaporati
 on or condensation phase.\n\nThe findings of this research will provide de
 eper insight into liquid film dynamics and develop a predictive reduced-or
 der model for PHP systems. Additionally\, these will be critical for desig
 ning optimal control laws based on liquid film stability properties\, enha
 ncing the evaporation/condensation mechanism\, and guiding the design of m
 ore stable and efficient PHP configurations.\n\n\n*Gergely Buza: Rigorizat
 ion of model reduction in fluid dynamics*\n\nThe emergence of data-driven 
 methods has fueled a newfound interest in the utilization of nonlinear too
 ls from dynamical systems theory. In fluid dynamics\, prominent examples a
 re Koopman eigenfunctions (through dynamic mode decomposition) and spectra
 l 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 iss
 ue that has remained mostly untouched\, and it is perhaps the most pressin
 g 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 asses
 sment. 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.\n
LOCATION:MR2
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