TBA

Maria Reboredo Prado
Stratosphere-Troposphere Interactions: Understanding how the Upper Atmosphere Shapes the Weather and Climate We See.
It is well known that the stratosphere – the second layer of the atmosphere – can exert a powerful influence on weather and climate at the surface. This influence is particularly important in winter, when the strength of the stratospheric polar vortex — a belt of fast-moving winds encircling the pole — can vary dramatically. If the impacts of these variations on the lower atmosphere were better understood and more accurately represented in forecast models, they could provide early signals of winter weather patterns, improving predictions on subseasonal to seasonal timescales. Yet, the mechanisms by which changes high in the atmosphere produce a response near the surface remain poorly understood. 
In this talk, I will use an idealised atmospheric model to test how much of this downward effect can be explained by large-scale balanced dynamics. The model allows individual processes – such as atmospheric cooling, surface friction, and boundary effects – to be switched on or off, making it possible to assess their relative roles in shaping the surface response. A key improvement on previous theoretical models is that the displacement of the tropopause — the boundary between the troposphere and stratosphere – emerges naturally as part of the flow’s response to forcing. Overall, this framework provides a controlled setting for identifying the dynamical mechanisms that transmit stratospheric disturbances to the surface.

Orson Hart
Inertialess instability of viscosity-stratified Couette flow
In this talk, we discuss the stability of viscosity-stratified Couette flow. By neglecting inertia, we isolate the destabilising effect of viscosity stratification on a fluid configuration consisting of three layers of immiscible, incompressible fluid. We show how the linear stability analysis can be simplified by considering symmetric flow configurations and, by considering disturbances of arbitrary wavelength, we identify a new instability mechanism that is only induced by finite-wavelength disturbances.

Vedanta Thapar

Embedding complex networks with the random walk first return time distribution

We consider the problem of network embedding, specifically we propose the first return time distribution (FRTD) of a random walk as an interpretable and mathematically grounded node embedding. The FRTD assigns a probability mass function to each node, allowing us to define a distance between any pair of nodes using standard metrics for discrete distributions. We present several arguments to motivate the FRTD embedding. First, we show that FRTDs are strictly more informative than eigenvalue spectra, yet insufficient for complete graph identification, thus placing FRTD equivalence between cospectrality and isomorphism. Second, we argue that FRTD equivalence between nodes captures structural similarity. Third, we empirically demonstrate that the FRTD embedding outperforms manually designed graph metrics in network alignment tasks. Finally, we show that random networks that approximately match the FRTD of a desired target also preserve other salient features. Together these results demonstrate the FRTD as a simple and mathematically principled embedding for complex networks.

Chun Lam Li

Neural network augmentation of the Maxey-Riley equation for Particle-Laden Flows
Fluid-particle interactions in low-Reynolds-number confined flows govern many biological and engineering processes, including microthrombi transport in cerebral microvessels and particle separation in microfluidic devices. Fully resolved direct numerical simulations (DNS) are accurate but costly for small particle sizes and large numbers of particles, limiting the simulation and analysis of particle-laden flows. We develop a machine learning (ML) model based upon the Maxey-Riley (M-R) equation to provide fast predictions of particle motion. A key feature is that the ML model is physics-based; neural networks learn corrections to an M-R based model to improve its predictions beyond the conditions for which it was derived. We consider a single spherical particle moving between two parallel plates, with plane Poiseuille flow as the undisturbed flow. The problem is parametrized by the flow Reynolds number, particle-to-fluid density ratio, confinement ratio (particle diameter to channel height), and initial wall-normal position. The model is trained on particle velocities from DNS sampled at discrete time points, and evaluated on trajectories that were not used for training. The ML model improves prediction accuracy of particle trajectories over the uncorrected M-R baseline across the tested physical parameters, at a far lower computational cost than DNS.

work with Justin Sirignano¹, and Sarah L. Waters¹
1. Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK

Underneath large glaciers and ice sheets, water flows through a permeable network of cavities and channels, held open by melting the ice above balancing the downwards flow of ice. Dissipation within the water flow is a significant enough source of heat that instabilities can develop if the flow rate is high enough, eroding large channels that rapidly drain water from the glacier bed. I will present a model for the system, and discuss the linear problem, observational evidence for the stability criterion, and the non-linear interactions that rapidly become the dominant control on channel spacing. Recently, there has been some discussion of slowing glaciers down by pumping water out from under them - I will consider the viability of this strategy in view of the results in this talk.