Idealised mathematical models for geophysical flows

Liste des Contributions

1. Introduction

29/06/2026 09:45

2. Stable regime singularity for the Muskat problem

Andrej Zlatos (UCSD)

29/06/2026 10:00

The Muskat problem on the half-plane models motion of an interface between two fluids of distinct densities in a porous medium that sits atop an impermeable layer, such as oil and water in an aquifer above bedrock. We develop a local well-posedness theory for this model in the stable regime (lighter fluid above the heavier one) that includes considerably more general fluid interface...

3. A model for breaking of surface waves

Maria Kazakova (LAMA, USMB)

29/06/2026 10:50

A shallow water model for the propagation and breaking of surface waves is proposed in the form of a hyperbolic system of conservation laws, with dispersive effects introduced through a relaxation term and a localized dissipative term. The latter is activated in regions where a new breaking criterion is satisfied. The objective is to obtain a simple mathematical and numerical structure while...

4. A Great Red Spot: Models vs Observations

Philip Marcus (California at Berkeley, University of)

29/06/2026 11:20

Co-authors: Aidi Zhang, Sungkyu Kim, Imke de Pater, Mike Wong, Anton Ermakov, Chris Moeckel, Daniele Durantej
Abstract: With sufficient resolution, a range of numerically-computed 3D vortices can quantitatively reproduce the observed velocity field of Jupiter’s Great Red Spot (GRS) at its cloud-tops. Due to the range of these solutions’ properties below the visible cloud tops, no particular...

5. On local energy conservation

Helena Nussenzveig Lopes (Universidade Federal do Rio de Janeiro)

29/06/2026 13:30

Co-authors: Tobias Barker, Milton Lopes Filho
Abstract: Anomalous dissipation, i.e. the non-vanishing of the dissipation term in the limit of zero viscosity, is a cornerstone of turbulence theory. In the case of periodic, two-dimensional, incompressible fluid flow there has been a lot of recent work in which anomalous dissipation is ruled out if the vorticity, which is the curl of velocity,...

6. Progress towards the inviscid dynamo

Andy Jackson

29/06/2026 14:20

Co-authors: Longhui Yuan, Philippe Marti and Jiawen Luo
Abstract: Earth’s magnetic field is believed to be generated in the metallic outer core through a process known as geodynamo. Direct numerical simulation (DNS) of geodynamo has successfully reproduced many features of the Earth’s field. Still, even the state-of-the-art simulations have a much higher viscosity than the Earth’s outer core....

7. Short presentations Posters

29/06/2026 15:40

8. Poster session

29/06/2026 16:40

9. Ocean Transit Times

Paola Cessi (Scripps Institution of Oceanography, University of California, San DIego)

30/06/2026 09:30

Abstract: Lagrangian transit times on basin to planetary scales are controlled by the interplay of multiscale processes. The primary advective timescale is set by throughflow currents, such as interhemispheric western boundary currents. Dispersion by mesoscale eddies introduces fluctuations that erase memory and enhance dispersion, widening the transit-time distribution. The tortuous paths of...

10. Reduced models for bubbly flows

David Gerard-Varet (Université Paris Cité et IMJ-PRG)

30/06/2026 10:50

One main issue in the analysis or simulation of immiscible two phase flows is the description of the moving interface between the two phases, especially when this interface has several connected components. In the case of bubbly liquids, in which the gas bubbles do not deviate much from simple geometries (spheres, ellipsoids), one may try to reduce the complexity of the model by imposing...

11. Solutions near monotone vortices

Ángel Castro (Instituto de Ciencias Matemáticas)

30/06/2026 11:20

Abstract: In this talk we will consider the existence of rotating solutions arbitrarily close (in some topology) to radial monotone decreasing vorticity for 2D Euler. In a paper by Bedrossian, Coti-Zelati and Vicol was shown that radial monotone decreasing vorticities are stable at the linear level, thus, our result shows that this phenomenon can break even for small perturbation. The problem...

12. Stratified turbulence

Pascale Garaud (UC Santa Cruz)

30/06/2026 13:30

Co-authors: Greg Chini, Colm-cille Caulfield, Kasturi Shah, Laura Cope, Dante Buhl, Daniel Klos
Abstract: In this talk I will describe recent results using asymptotic analysis to create a simple reduced model for strongly stratified turbulence (driven by horizontal body forces) across parameter space, together with Direct Numerical Simulations that validate the model. More specifically, the...

28. 3D-2D asymptotics for the rotating MHD

Frédéric Charve (UPEC)

30/06/2026 14:00

Co-authors: Van-Sang Ngo
Abstract: In this joint work with Van-Sang Ngo, we consider the 3D-rotating magnetohydrodynamic (MHD) system.

We begin this talk by providing a few examples of penalized geophysical models similar to the incompressible Navier-Stokes system, and which converge (when the small penalization parameter goes to zero) towards a limit system that can be easily seen to be...

13. The deep-seated solar dynamo

Toby Wood (Newcastle University)

30/06/2026 14:30

Co-authors: Devika Tharakkal, Craig Duguid, Paul Bushby
Abstract: Since the advent of helioseismology, the strong rotational shear in the solar "tachocline" has been recognised as a likely site for toroidal field generation in the Sun. But the generation of poloidal field, which is essential to close the "dynamo loop", has generally been attributed to the overlying convection zone, and...

14. Linear Stability of small BGK waves

Benoit Pausader (Brown University)

30/06/2026 15:30

Co-authors: Dongfen Bian, Emmanuel Grenier, Wenrui Huang
Abstract: We consider the Vlasov-Poisson system in a 1d periodic setting, and consider the stability of steady states. The simplest family corresponds to homogeneous steady states, and a lot of literature has been devoted to their study. When a Penrose-type criterion is satisfied, following works of Mouhot-Villani and later works,...

15. QG convection on the f-plane

Benjamin Miquel (CNRS, Ecole Centrale Lyon)

30/06/2026 16:20

Co-authors: A. Ellison, M. Calkins, K. Julien, E. Knobloch
Abstract: Planetary cores and the subsurface oceans of icy moons are stirred by quasi-geostrophic turbulent convection. The transport (of heat, momentum, etc.) by the flow vary regionally with the colatitude, which coincides with the tilt angle between gravity and rotation. Here, we analyse rapidly rotating Rayleigh-Benard convection...

16. Couette flow and rotation/stratification

Klaus Widmayer

30/06/2026 16:50

Abstract: As is well known, perturbations of Couette flow in the 3d Navier-Stokes equations experience phase mixing, which stabilizes fluid motion. In the presence of suitable rotational forces or stratification, additionally dispersive internal gravity or inertial waves arise. These two mechanisms are of fundamentally different nature and relevant in complementary dynamical regimes. We will...

29. New frontiers of mathematics: doing numerics in the age of AI

Javier Gomez-Serrano (Brown University)

01/07/2026 09:30

In this talk I will discuss recent results in Mathematics+AI. I will describe several concrete instances in which AI systems have contributed to genuine mathematical and scientific results, ranging from the discovery of new objects to the optimization of the numerical kernels that underpin modern computation. A recurring theme is that these tools do not replace mathematical reasoning but...

31. Data-driven reduced order models

Taraneh Sayadi (Conservatoire National Arts et Métiers)

01/07/2026 10:50

Reduced-order models offer computationally efficient approximations of
complex systems, enabling multi-query tasks in design and optimisation with
low cost and sufficient accuracy. Data-driven strategies are particularly
appealing when underlying models are inaccessible or too expensive to
evaluate, and recent advances in AI-based architectures have naturally
entered this space. However,...

30. Data-driven dynamo equations

Anna Guseva (Polytechnic University of Catalonia)

01/07/2026 11:40

Co-authors: C. Skene, S. Tobias
Abstract: Many low-mass stars like the Sun host periodic, oscillatory magnetic fields that lead to variable levels of stellar activity and variations of space weather, affecting habitability and detection of exoplanets. Due to the intrinsic difficulties of modelling stellar magnetohydrodynamics at all scales, realistic numerical simulations of this process are...

32. The elephant in the room: Probabilistic Machine Learning into physical models

Matthew Juniper (University of Cambridge)

01/07/2026 13:30

John von Neumann is often quoted as saying "with four parameters I can fit an elephant, and with five I can make him wiggle his trunk." The implication seems to be that physical models should contain only a handful of parameters. A century later, however, we seem happy to use physics-agnostic neural networks containing millions of parameters. What would von Neumann say? How should physical...

33. Generative modeling of QG solutions

Louis Thiry (Sorbonne Universite)

01/07/2026 14:20

Co-authors: Petar Samardzic
Abstract: In this talk, we'll introduce denoising diffusion models, a class of generative models that rely on additive Gaussian white noise denoising. We'll explain the link with particule based method of the heat equation in high-dimension. We'll apply these techniques to numerical of multi-layer QG equation in a double-gyre setting, which is an idealized model of...

34. Post-Geostrophy: Numerics, Computation, AI

Peter Korn (Max Planck Institute for Meteorology)

01/07/2026 15:20

Ocean climate modelling can now resolve geostrophic turbulence rather than merely parametrize it. With this step the ocean has taken the stage as a genuinely turbulent fluid - a remarkable achievement that also marks the end of the "geostrophic era." That ending is equally a beginning, and one that falls in line with the technological shift toward GPU and AI computing. This talk describes new...

35. Thoughts on Machine Learning

Rupert Klein (Freie Universität Berlin)

01/07/2026 16:10

Abstract: Techniques of machine learning (ML) find a rapidly increasing range of applications touching upon many aspects of everyday life. They are also used with enthusiasm to close gaps in our scientific knowledge by data-based modeling. I have followed these developments with interest, concern, and mounting disappointment. When these technologies take over decisive functionality in...

17. Intermittency & dissipation in turbulence

Theodore Drivas (Stony Brook University)

02/07/2026 09:30

Co-authors: Luigi De Rosa
Abstract: Intermittency is a remarkable and robust feature of three-dimensional turbulence for which we still lack explanation from first principles. It will be shown how a dissipation with a non-trivial lower-dimensional part induces a quantitative intermittent regularity on the weak solution.

19. Exact solutions to Euler's equations

Nick Pizzo (University of Rhode Island)

02/07/2026 10:50

Co-authors: Rick Salmon
Abstract: Exact solutions to the two dimensional Euler's equations, on Euclidean and non-Euclidean surfaces, are presented in Lagrangian coordinates. These solutions arise due to a particle relabeling invariance, a subset of which, associated with particle label rotations, are shown to transform time independent solutions to time dependent solutions by these...

21. Simple model for the strength of the ACC

David Marshall (University of Oxford)

02/07/2026 11:20

Co-authors: Xiaoming Zhai (University of East Anglia), James Maddison (University of Edinburgh), Julian Mak (Hong Kong University of Science and Technology)
Abstract: The volume transport of the Antarctic Circumpolar Current (ACC) is described in textbooks as set by wind and buoyancy forcing. However, eddy-permitting numerical ocean models indicate minimal sensitivity of ACC transport to the...

23. How to determine the speed and amplitude of the leading edge of a dispersive shock wave

Sergey Gavrilyuk (Aix-Marseille University)

02/07/2026 13:30

Abstract: The objective of my talk is to describe the solitary wave of largest amplitude in the dispersive shock appearing in the solution of Riemann problem for dispersive equations describing non-linear long dispersive waves, in particular, the Benjamin-Bona-Mahony equation and Serre-Green-Naghdi equations. Such a large-amplitude solitary wave is the leading wave of the corresponding...

24. Water-waves problem with contact angles

Mei Ming (Yunnan University, China)

02/07/2026 14:20

Abstract: We will talk about a weighted a priori energy estimate for the two dimensional water-waves problem with contact points in the absence of gravity and surface tension and some related topics. When the surface graph function and its time derivative have some decay near the contact points, we show that there is corresponding decay for the velocity, the pressure and other quantities in a...

25. Wave resonances in bounded domains

Paul Milewski (Penn State University)

02/07/2026 15:20

Co-authors: Matthew Durey
Abstract: Nonlinear surface gravity waves sloshing in a container of rectangular cross-section can behave very differently than those with other cross sections. Wave resonance is a mechanism by which energy is continuously exchanged between a small number of wave modes and is common to many nonlinear dispersive wave systems. They have been studied extensively over...

26. Metriplectic ocean thermodynamics

Francisco Beron-Vera (University of Miami)

02/07/2026 16:10

Abstract: We present a metriplectic formulation of a reduced model for the upper ocean. The model is valid at low frequencies, includes a single layer with lateral inhomogeneity and uniform stratification, and is thermodynamically consistent - that is, it conserves energy while producing entropy. The evolution of any functional of the model variables (horizontal velocity, layer thickness, and...

27. Boundary layer around a rotating cylindre

Slim Ibrahim (University of Victoria, Department of Mathematics and Statistics)

02/07/2026 16:40

Co-authors: Yasunori Maekawa
Abstract: In this talk, I will first review the boundary layer problem and flow separation in a viscous incompressible fluid past a rigid cylindrical obstacle undergoing constant, but fast rotation (compared to a uniform background flow). Then, I will show how to solve the boundary layer equations, give a solvability criterion for the matched asymptotic expansion,...

18. Boundary conditions and non kinematic free boundaries for wave-structure interactions

David Lannes (Institut de Mathématiques de Bordeaux)

03/07/2026 09:30

The description of waves, through the water waves equations or simpler asymptotic models (such as the nonlinear shallow water equations or the Boussinesq system) is well understood in a domain without boundaries. In the case of wave-structure interactions, such as the dynamics of the shoreline or of floating objects, the free surface has a boundary formed by the contact line between the...

20. Scaling Trends in Rotating Convection

Paula Wulff (University of California, Los Angeles)

03/07/2026 10:50

Co-authors: Jewel Abbate, Hao Cao, Jonathan Aurnou
Abstract: Asymptotic analysis of rotating convective turbulence, as exists in planets and stars, yields two sets of scaling predictions for the limits of slowly rotating and rapidly rotating systems. These all hinge on the value of the convective Rossby number, Ro_c (e.g. Julien et al. 2012; Aurnou et al. 2020).
Here, we test these...

22. Polar Vortex Crystals

William Young (University of California, San Diego)

03/07/2026 11:20

Co-authors: Lia Siegelman
Abstract: Vortex crystals are quasiregular arrays of like-signed vortices in solid-body rotation embedded within a uniform background of weaker vorticity. Vortex crystals are observed at the poles of Jupiter and in laboratory experiments with magnetized electron plasmas in axisymmetric geometries. We computationally test the hypothesis that these organized...

36. Talk