Vortices and vorticity in geophysical flows

Liste des Contributions

2. Introduction

20/04/2026 09:45

1. Clay Lectures -- Incompressible fluids with inflow/outflow

Anna Mazzucato (Penn State University)

20/04/2026 10:00

This lecture is organised in partnership with the Clay Mathematics Institute.
I will discuss recent results concerning the well-posedness of the Euler equations with inflow/outflow (injection/suction) at permeable boundary and the vanishing viscosity limit for both Navier-Stokes and the Boussinesq system.

3. Maths-vives Chair -- Superrotation in Planetary Atmospheres

Geoffrey Vallis (University of Exeter)

20/04/2026 11:00

Jets and Superrotation are ubiquitous features in some, but not all, planetary atmospheres. In particular superrotation occurs in slowly rotating terrestrial atmospheres (like Venus), in rapidly rotating gas giants (like Jupiter) and in some exoplanets. In this talk I'll discuss the various mechanisms giving rise to superrotation and their connection to potential vorticity.

4. 2D flows with random initial vorticity

Prof. Milton da Costa Lopes Filho (Universidade Federal do Rio de Janeiro)

20/04/2026 13:30

We consider a random initial vorticity $\omega_0(x) = \sum_{n\in \mathbb{Z}^2} a_n \phi(x-n)$, where $\phi$ is bounded and compactly supported and $\{a_n\}$ are independent, uniformly bounded, mean $0$, variance $1$ random variables (in other words, $\omega_0$ is an array of randomly weighted vortex blobs). We prove global well-posedness of weak solutions to the Euler equations in...

5. Kelvin waves along a free-surface vortex

Jason Barckicke (Université Paris Cité)

20/04/2026 14:30

Many flows feature a strong vorticity: tornadoes, hurricanes, aircraft wakes ... Vortices also play a key role in the energy cascade of classical and quantum turbulence. Kelvin waves are elementary perturbations of such vortices - helical waves propagating along the vortex line.
Many theoretical works have predicted their behaviour but no experimental confirmation has been reported so...

6. poster presentation 2min each

20/04/2026 15:30

7. Poster session

20/04/2026 16:30

8. Triple-deck theory for tropical cyclones

Rupert Klein (Freie Universität Berlin)

21/04/2026 09:30

Multiscale interactions including boundary layer effects and moist convection are generally thought to be essential for the acceleration of tropical cyclones. Here we present an asymptotic analysis involving a triple-deck matched asymptotic expansion in the vertical and meanfield arguments for multiscale convection in an axisymmetric vortex. The resulting theory suggests transparent...

9. Quantitative stability of the Rossby—Haurwitz waves of degree two for the Euler equations on the sphere

Luca Melzi (Imperial College London)

21/04/2026 11:00

The motion of an incompressible, ideal fluid is described by the Euler equations. Choosing the unit sphere $\mathbb{S}^2$ embedded in $\mathbb{R}^3$ as the domain of interest, the Euler equations represent a suitable model for stratospheric flows. Among such flows, of particular importance in atmospheric dynamics are the Rossby—Haurwitz waves, that are observed in the stratosphere of the Earth...

10. Eye of the cyclone:an experimental study

Brichet Lyse (Irphé)

21/04/2026 11:30

One of the most characteristic flow in the atmosphere is the eye of tropical cyclones. Yet, its dynamic formation process is still poorly understood. This study focuses on a small number of parameters to improve our fundamental understanding of these dynamics. We have set up an experimental model in air to analyze the conditions for the formation of the eye of a cyclone in dry rotating...

11. Quantitative classification of potential Navier-Stokes singularities beyond the blow-up time

Tobias Barker

21/04/2026 13:30

It remains an open problem whether or not solutions to the 3D Navier-Stokes equations with smooth data remain smooth for all time.
All previously known regularity criteria are formulated in times of a blow-up time (where the solution loses smoothness), which make it practically impossible to use such necessary conditions to test the viability of certain numerically computed...

12. Vorticity generation in water waves

Alan Riquier (École Normale Supérieure - PSL)

21/04/2026 14:30

We propose to discuss the relevance of the irrotationality assumption commonly made to obtain reduced water waves models (Shallow Water/Saint-Venant, Korteweg-de Vries, Green-Naghdi, etc.). To do so, we investigate the asymptotic behaviour of two boundary layers associated with oceanic flows: one appearing in the vicinity of the free surface and the other lying at the bottom boundary. This is...

13. Physics of Tropical Cyclones

Kerry Emanuel (MIT)

21/04/2026 15:30

Outside the immediate subdiscipline of tropical cyclone physics, it is widely held that these vortices are a mode of organization of deep, moist convection. In this lecture, I will dispel that idea and show that TC-like vortices arise from thermodynamic disequilibrium between a fluid and a solid or liquid surface, a disequilibrium that arises from the discontinuity in radiative emissivities...

14. Filamentation near monotone zonal caps

Emeric Roulley (SISSA)

21/04/2026 16:30

We study the Euler equations on the rotating unit sphere, focusing on the dynamics of vortex caps, i.e. piecewise constant absolute vorticity. Leveraging the area stability of monotone, longitude-independent profiles, we demonstrate that certain ill-prepared initial data within the vortex cap class exhibit an instability characterized by the growth of the interface perimeter. These...

15. The Fluid Dynamics of Tornadoes

Richard Rotunno (NSF National Center for Atmospheric Research)

22/04/2026 09:30

Observations, laboratory experiments and numerical simulations provide the basis for the theoretical fluid dynamics of the tornado. Tornado fluid dynamics is best understood in terms of the dynamics of several subproblems: the two-cell vortex, the boundary-layer beneath a potential vortex, the formation of an end-wall vortex and its vortex breakdown. Vortex breakdown involves further...

17. Coupled Atmosphere-Ocean Models

Matthias Hieber (MFO Oberwolfach, TU Darmstadt, Allemagne)

22/04/2026 11:00

In this talk we discuss coupled atmosphere-ocean models described by compressible/incompressible primitive equations subject to either deterministic nonlinear winddriven boundary conditions or stochastic boundary conditions on the interface.

18. QG dynamics of the LANS-alpha model

Beth Wingate (University of Exeter)

22/04/2026 13:30

The Lagrangian-Averaged Navier-Stokes-$\alpha$ (LANS-$\alpha$) model, a fluid dynamics model based on energy-conserving modifications to nonlinear advection, can produce more energetic simulations than standard models, leading to improved fidelity (e.g., in ocean models). However, comprehensive understanding of the mechanism driving this energetic enhancement has proven elusive. To address...

16. Vortex dynamics for the lake equations

Lars Eric Hientzsch (Karlsruhe Institute for Technology (KIT))

22/04/2026 14:30

The lake equations arise as a 2D geophysical model describing the vertically averaged evolution of an incompressible inviscid 3D fluid in a domain with spatially varying topography.
We rigorously derive the asymptotic dynamics of point vortices. Specifically, we show that initially sharply concentrated vorticity remains concentrated in a suitable sense. The vortices' trajectories are proven...

19. Surface Waves and Vortex Interaction

Delia Ionescu-Kruse ("Simion Stoilow" Institute of Mathematics of the Romanian Academy (IMAR))

22/04/2026 15:30

The interaction between free-surface waves and localized vorticity structures is a fundamental problem in fluid dynamics, with relevance to geophysical flows. We study this problem by using the general framework for 2D water waves with arbitrary vorticity developed by Ionescu-Kruse and Ivanov (JDE, 2023). In the small-amplitude long-wave Boussinesq and KdV regimes, we derive coupled evolution...

20. Mixing with random cellular flows

Victor Navarro-Fernandez (Imperial College London)

22/04/2026 16:00

We study a passive scalar equation on the two-dimensional torus, where the advecting velocity field is given by a cellular flow with a randomly moving center. We prove that the passive scalar undergoes mixing at a deterministic exponential rate, independent of any underlying diffusivity. Furthermore, we show that the velocity field enhances dissipation and we establish sharp decay rates that,...

30. Boundary layers of Navier-Stokes system

Dongfen Bian (Beijing Institute of Techonology)

22/04/2026 16:30

The question of the stability of the boundary layers which appear as the viscosity of the fluid goes to zero is a classical question in Fluid Mechanics. In this talk I will discuss recent mathematical results on this question and in particular show that any shear layer is linearly and nonlinearly unstable provided the viscosity is small enough, and that the classical Prandtl boundary layers...

23. Vorticity dynamics of coastal fronts

Edward Johnson (University College London)

23/04/2026 09:30

This talk examines how free, long waves propagate along a potential vorticity front beside a vertical coast, using a 1.5-layer quasi-geostrophic model with piecewise-constant potential vorticity. The coastal boundary drives flow via image vorticity and a Kelvin wave, which can either reinforce or oppose Rossby wave dynamics at the front. Front behavior depends on the relative strengths of...

28. The vanishing limit of a rigid body

Jiao He (LMO)

23/04/2026 11:00

We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space R3 . When the small rigid body shrinks to a point in the sense that its density is constant, we prove that the solution of the fluid-rigid body system converges to a solution of the Navier–Stokes equations in the full space.Based on some $L^p$-$L^q$ estimates of the fluid–structure...

25. GFD on a fast rotating surface

Bin Cheng (University of Surrey, UK)

23/04/2026 11:30

We consider the rotating shallow water equations with small (planetary) Rossby and Froude numbers on a surface of revolution with variable Coriolis parameter having opposite signs at the poles. The large variation of the linear operator in the PDE is a possible mechanism of short-time instability as the small parameters tend to zero. However, we prove that such instability does not happen in...

26. Desingularisation of Vortex Sheets

David Meyer (ICMAT)

23/04/2026 13:30

We show how to regularize vortex sheets by means of smooth, compactly supported vorticities that asymptotically evolve according to the Birkhoff--Rott vortex sheet dynamics. More precisely, consider a vortex sheet initial datum $\omega^0_{\mathrm{sing}}$, which is a signed Radon measure supported on a closed curve. We construct a family of initial vorticities~$\omega^0_\epsilon\in...

34. A Lagrangian Vor-Div SWE Solver

Anthony Chen (University of Michigan)

23/04/2026 14:00

In this work, I present a semi-Lagrangian solver for the spherical Shallow Water Equations, written in vorticity-divergence form. The solver makes use of a Biot-Savart law to compute the velocity, and is discretized on a tensor product Chebyshev grid on the cubed sphere. I also discuss some advantages and difficulties associated with using a semi-Lagrangian discretization, as well as the...

27. Leapfrogging of Vortex Rings

Martin Donati (CNRS, LMA Poitiers)

23/04/2026 14:30

In this talk, we discuss recent developments concerning the motion of concentrated vortex rings. In particular, we outline the proof that, in the appropriate asymptotic regime, two concentrated coaxial vortex rings separated by a small distance exhibit the so-called leapfrogging motion. This highly singular regime lies beyond the scope of the standard tools of vorticity confinement. We...

24. On the stabilizing effect of rotation for 3D fluids

Haram Ko (Brown University)

23/04/2026 15:30

It is well known to geophysicists that the rotation of the background can bring about different phenomena not observed in steady fluids. In this talk, I will explain from a mathematical point of view what the rotation introduces in 3D Euler/Navier-Stokes equation, and talk about recent results of how the rotation can enhance the stability (a) in incompressible fluid with high Reynolds number...

29. Instability of dusty rotating vortices

Henrik Latter (DAMTP, University of Cambridge)

23/04/2026 16:00

We explore the various instabilities that potentially assail vortex cores in the presence of rotation and/or radially drifting solids. We first revisit the classical elliptical instability of rotating purely hydrodynamic vortices, showing that, in certain natural limits, the problem is governed by the ‘inverted Matthieu equation’, which provides a novel and remarkably simple way to...

35. Cumulus Cloud Tilt and Ellipticity

Dario Falcone (University of California, Davis)

23/04/2026 16:30

Developing a tractable understanding of the interaction between cumulus clouds’ ellipticity and tilt from shear flows is crucial to expanding theories associated with squall line development and tradewind cumuli climatological feedbacks. Here, we focus on the dynamic interplay between cloud-scale flows and shear flows. To perform this investigation, we implement a Kinematic Representation of...

21. Dynamics of aerosol-filled vortices

Kasturi Shah

23/04/2026 17:00

Long-lived, self-lofting, diabatically-driven anticyclones co-located with aerosols and trace gases have been detected in the stratosphere following strong wildfire events. An important unresolved dynamical question is the apparent single-signed vorticity anomaly. The expected vorticity structure from localised heating is an anticyclone-above-cyclone dipole and recent idealised dynamical...

32. Geometry and vortex motion

Andrew Gilbert (University of Exeter)

24/04/2026 09:30

A geometrical viewpoint of inviscid incompressible fluid dynamics highlights vorticity as the key field which generates the velocity field and is in turn transported, stretched and rotated, that is Lie-dragged, in the fluid flow. In this setting it is most natural to consider the velocity as a vector field, the momentum as a one-form (or co-vector) field, and the vorticity as a two-form field,...

33. A point vortex in a half-plane

Thierry Gallay (Institut Fourier, Université Grenoble Alpes)

24/04/2026 11:00

As a model for vortex-wall interactions, we consider the two-dimensional incompressible Navier-Stokes equations in a half-plane with no-slip boundary condition and point vortices as initial data. We concentrate on the paradigmatic example of a single vortex in an otherwise stagnant fluid, which is already quite challenging from the mathematical point of view. As a warm-up, we prove that this...

22. Long talk

31. Talk