Instabilities and transitions in geophysical flows

Liste des Contributions

1. Introduction

18/05/2026 09:45

34. A primer on ocean mesoscale eddy parameterizations for numerical models

Stephen Griffies (Princeton University)

18/05/2026 10:00

Abstract: This talk summarizes some ongoing math/physics/numerics questions related to tracer mixing and stirring as realized in ocean models, moving from the small-scale turbulence to the large-scale mesoscale eddy stirring. The presentation will be pedagogical in style, and it touches only a few topics with an aim to engage both students and researchers.

3. Coexisting fluxes in rotating turbulence

Anna Frishman

18/05/2026 10:50

Co-author: Sebastien Gome
Abstract: Turbulence is characterized by energy fluxes, whose direction is determined by conservation laws.
In 3D rotating turbulence, however, energy is observed to flow simultaneously toward large-scale two-dimensional structures and toward small-scale three-dimensional waves. Using a mean–wave kinetic theory, we derive analytical expressions for these competing...

4. Stable Implosions

Vlad Vicol (New York University)

18/05/2026 11:20

Co-authors: J. Chen (U Chicago) and S. Shkoller (UC Davis).
Abstract: We exhibit a new class of self-similar implosion solutions for the full compressible Euler equations. For any value of the adiabatic exponent, we construct a sequence of implosion profiles that are smooth before collapse and have an explicit similarity exponent. The first profile in this sequence (the ''ground state'')...

5. Horizontal/vertical convective stability

Stefan Llewellyn Smith (University of California, San Diego)

18/05/2026 13:30

Co-authors: Michael Le Bars, Clement Audefroy
Abstract: Motivated by planetary science, we examine the stability of flows with both buoyancy gradients on horizontal boundaries and vertical buoyancy fluxes entering the domain, hence combining aspects of horizontal convection (HC) and Rayleigh–Bénard (RB) convection. Exact steady states exist in the form of shear flows. Unlike the case of RB...

6. Nonuniqueness in fluid models

Julien Guillod

18/05/2026 14:20

Co-authors: Dallas Albritton, Mikhail Korobkov, Xiao Ren, and Vladimír Šverák
Abstract: It is well known in physics literature, despite almost no mathematical results, that the steady states of fluid model equations are not unique and appear through bifurcations when the Reynolds number increases. After presenting this, the same methodology will be used for time-dependent problems to obtain...

7. poster presentation 2min each

18/05/2026 15:20

8. Poster session

18/05/2026 16:20

9. Ideal Magnetic Reconnection

Peter Constantin (Princeton University)

19/05/2026 09:30

Co-author: Zhongtian Hu
Abstract: Magnetic fields do not change topology during smooth dynamics of ideal MHD. But topology change does occur in nature. Magnetic resistivity and near singularities have been suggested as a possible explanation.
In this talk I will focus on a different explanation, also suggested in the physics literature: reconnection due to magneto-hydrodynamic inertia. I...

10. Boundary layers and inviscid limits

Jincheng Yang (Johns Hopkins University)

19/05/2026 10:50

Co-author: Alexis Vasseur
Abstract: I will discuss several recent results on vanishing-viscosity limits for incompressible Navier-Stokes flows near boundaries. I will begin with boundary vorticity estimates and their application to weak inviscid limits near plug flow in a periodic tunnel, giving short-time control of deviations from the shear profile. I will then present unconditional $L^2$...

11. Arnold's Geometry on Finite Meshes

Peter Korn (Max Planck Institute for Meteorology)

19/05/2026 11:20

Abstract: Arnold identified ideal fluid motion with geodesics on the group of volume-preserving diffeomorphisms, whose curvature controls hydrodynamic stability. We develop this programme on finite meshes, establishing an approximate finite-dimensional Lie algebra supported by a discrete de Rham complex. This yields well-posed discrete Euler equations that converge to the continuum Euler...

23. Bifurcations of shear flows

Emmanuel Grenier (Beijing Institute of Technology)

19/05/2026 13:30

Abstract: Generic shear flows are unstable for the incompressible Navier-Stokes equation as the viscosity goes to 0 between the so-called lower and upper marginal stability curves. The aim of this talk is to discuss recent results on the bifurcation which occurs near the upper marginal stability curve.

13. Diffusive instabilities in seawater

Remi Tailleux (University of Reading, Department of Meteorology)

19/05/2026 14:20

Abstract: In two-component seawater, the thermobaric and cabbeling nonlinearities of the equation of state, combined with the disparate molecular diffusivities of salt and heat, give rise to a diverse range of diffusive instabilities. Beyond standard salt finger and diffusive convection instabilities, these include instabilities associated with densification upon mixing. Unlike conventional...

14. Rotating fingering convection

Celine Guervilly (Newcastle University)

19/05/2026 15:20

Co-authors: Martin Gray, Graeme Sarson
Abstract: We study double-diffusive convection in the case of an unstable compositional gradient in the presence of a stabilising temperature gradient. Experimental and analytical studies (Hage and Tilgner 2010; Schmitt 2011) have shown that narrow salt fingers (usually encountered in thermohaline convection in “bottom-heavy” layers) can be preferred...

15. Asymptotics of inviscid stratified flows

Lucas Ertzbischoff (Université Paris Dauphine-PSL)

19/05/2026 16:10

Abstract: I will talk about recent mathematical progress on asymptotic regimes for inviscid stratified fluid models, focusing on two topics that remain only partially understood: (i) the long-time dynamics and (ii) the hydrostatic limit. As a guiding example I will use the classical 2d Euler-Boussinesq system. I will try to connect these two questions for this model, highlighting the role of...

16. Western intensified turbulence

Antoine Venaille

19/05/2026 16:40

Co-authors: Lennard Miller, Bruno Deremble
Abstract: We first investigate numerically the vanishing-viscosity limit of a two-dimensional wind-driven ocean model. Instead of forming a large-scale condensate, the flow remains strongly out of equilibrium, organizing into a highly energetic turbulent vortex gas coexisting with western-intensified gyres. When stratification is introduced, coherent...

17. Unstable internal waves

Roberta Bianchini (Consiglio Nazionale delle Ricerche)

20/05/2026 09:30

Abstract: Stably stratified fluids (e.g., oceans and atmosphere) support internal waves that are fundamental to oceanic circulation and atmospheric dynamics. We present the first rigorous proof of instability for small-amplitude internal waves, establishing the existence of an unstable spectrum for the Boussinesq equations linearised about a traveling wave. The analysis combines a...

20. Cascade transition in geophysical flows

Alexandros Alexakis (ENS)

20/05/2026 10:50

Abstract: I will discuss how a cascade can transition from a forward to an inverse cascade in geophysical flows as a parameter is varied. I will review some of the past results and present some of the most resent results in rotating flows and stratified flows.

12. MHD turbulence and weak solutions

Laszlo Szekelyhidi (Max Planck Institute for Mathematics in the Sciences)

20/05/2026 11:20

Co-author: Matteo Giardi
Abstract: The ideal magnetohydrodynamic system in three space dimensions consists of the incompressible Euler equations coupled to the Faraday system via Ohm’s law. This system has a wealth of interesting structure, including three conserved quantities : the total energy, cross-helicity and magnetic helicity. Whilst the former two are analogous to the total kinetic...

26. Hamiltonian Dysthe equation for hydroelastic waves in a compressed ice sheet

Catherine Sulem (University of Toronto)

20/05/2026 13:30

Co-authors: Philippe Guyenne, Adilbek Kairzhan
Abstract: This study concerns the motion of nonlinear hydroelastic waves along a com- pressed ice sheet lying on top of a two-dimensional fluid of infinite depth. Applying tech- niques of Hamiltonian perturbation theory, a Hamiltonian Dysthe equation is derived for the slowly varying envelope of modulated wavetrains. The derivation is further...

28. Rythmic patterns: dunes, ripples & more

Bruno Andreotti (LPENS)

20/05/2026 14:20

Abstract: Periodic patterns spontaneously emerge due to sublimation, erosion/deposition and sediment transport, dissolution, or—when it comes to waves—mechanical deformation of an interface. Starting with sand ripples and dunes, I will thoroughly discuss the various aspects of how these patterns form: linear instability vs pattern coarsening; laminar vs turbulent flow; mixing vs normal stress...

32. Bore wave solutions to Navier-Stokes

Ian Tice (Carnegie Mellon University)

20/05/2026 15:20

Abstract: In this talk we will discuss the construction of two-dimensional traveling bore wave solutions to the free boundary incompressible Navier-Stokes equations for a single finite depth layer of constant density fluid. Our construction is based on a rigorous justification of the formal shallow water limit, which postulates that in a certain scaling regime the full free boundary traveling...

33. Gibbon flow and the d'Alembert's paradox

Miguel Bustamante (University College Dublin)

20/05/2026 16:10

Co-authors: Yinshen Xu (UCD), Tiziana Comito (UCD), Johan Hoffman (KTH), John D. Gibbon (Imperial)
Abstract: Consider incompressible inviscid flow past an object. D'Alembert (1752) proved that for potential flow, the object experiences no drag force. However, experimental observations find significant drag at high Reynolds numbers, leading to the famous d'Alembert's paradox in fluid...

30. Exact Energy Transfers in Turbulence

Mahendra Verma (IIT Kanpur, India)

20/05/2026 16:40

We developed a mathematical framework called “mode-to-mode energy transfer” to compute energy transfers in fluid flows, in particular turbulence. In this talk, I will describe this general framework and illustrate its application to incompressible and compressible turbulence, turbulent convection, magnetohydrodynamics, dynamo, and quantum turbulence. This is a general framework that...

18. Rayleigh-Benard on a logarithmic lattice

Keaton Burns (Massachusetts Institute of Technology)

21/05/2026 09:30

Co-authors: Steven Tobias (Univ. Edinburgh), Curtis Saxton (Univ. Leeds), Richard Kerswell (Univ. Cambridge)
Abstract: Our ability to numerically study turbulent convection is limited by the high cost of direct numerical simulations (DNS) in the regimes relevant to geophysical and astrophysical flows. This motivates the development of alternatives to DNS which enable faster computation by...

21. Solutions to conservation laws unique?

Sam Krupa (École normale supérieure)

21/05/2026 10:50

Co-authors: László Székelyhidi, Jr.
Abstract: For hyperbolic systems of conservation laws in 1-D, fundamental questions about uniqueness and blow up of weak solutions still remain even for the apparently “simple” systems of two conserved quantities such as isentropic Euler and the p-system. Similarly, in the multi-dimensional case, a longstanding open question has been the uniqueness of weak...

24. Unstable Manifolds of Euler Equations

Chongchun Zeng (Georgia Institute of Technology)

21/05/2026 11:20

Co-authors: Zhiwu Lin and Yanbo Wang
Abstract: Consider a spectrally unstable steady state $(\rho_0(x), v_0(x))$ of the incompressible stratified Euler equation in certain $d$-dim domain $\Omega$. Assuming the linearized equation satisfies a linear exponential dichotomy with a reasonably large spectral gap relative to the maximal Lyapunov exponent of $v_0(x)$, we construct a local unstable...

2. Reduced and rescaled equations for RRRBC

Edgar Knobloch (University of California-Berkeley, Department of Physics)

21/05/2026 13:30

Co-authors: K. Julien, A. van Kan, B. Miquel, G. Vasil
Abstract: Geophysical flows are characterized by parameter values that are far outside those that can be studied in the laboratory or via state of the art numerical simulations. I will describe a formal multiscale asymptotic procedure for rapidly rotating convection that leads to a reduced system of equations valid in the limit of...

35. Congestion phenomena in fluids

charlotte perrin (Institut de Mathématiques de Marseille)

21/05/2026 14:20

Abstract: This talk addresses recent developments on fluid models with a maximal density constraint. Such constraints arise in the modeling of congestion effects, with applications to geophysical flows such as dense granular avalanches and sea ice dynamics.
I will focus on the main theoretical and numerical difficulties induced by this framework, including strong nonlinear effects,...

27. On the Instability of Small Stokes Waves

Miguel Rodrigues (Univ Rennes)

21/05/2026 15:20

Co-authors: Ziang Jiao, Zhao Yang (Beijing, China), Changzhen Sun (Besançon, France)
Abstract: We report on a recent proof that all irrotational planar periodic travelling waves of sufficiently small-amplitude are spectrally unstable as solutions to three-dimensional inviscid finite-depth gravity water-waves equations. The associated temporal growth scales sharply with respect to the...

29. Instabilities around mesoscale eddies

Michael Le Bars (CNRS, IRPHE UMR 7342)

21/05/2026 16:10

Co-authors: Antoine Chauchat (IRPHE), Patrice Meunier (IRPHE), Keaton Burns (MIT)
Abstract: Our current understanding of ocean mixing remains insufficient to balance the global ocean energy budget, pointing to overlooked local mechanisms. At the edges of mesoscale eddies, horizontal density layering is observed, suggesting enhanced vertical mixing. To investigate its origin, we examine the...

31. The Dynamical Landscape of the AMOC

Louis-Philippe Nadeau (Université du Québec à Rimouski)

21/05/2026 16:40

Abstract: While AMOC stability is traditionally viewed through simple box models, these models exhibit a diverse range of behaviors dictated by the background climate. These can be classified into two regimes: abrupt tipping points (saddle-node bifurcations) and millennial-scale oscillations (Hopf bifurcations). This presentation reviews the evolution of conceptual models of the AMOC,...

19. Transition in Stratified Shear Flows

Colm-cille Caulfield (DAMTP, University of Cambridge)

22/05/2026 09:30

Abstract: (Vertically) stratified shear flows, where both the background horizontal velocity and buoyancy distribution vary in the vertical (i.e. the direction parallel to gravity) are ubiquitous in geophysical fluid dynamics. A key question is how such flows undergo the transition to turbulence and hence irreversibly mix vigorously. Intuitively, if the buoyancy increases upwards...

22. Ekman-inertial instability

Nicolas Grisouard (University of Toronto)

22/05/2026 10:50

Abstract: Ekman-inertial instability (EII) occurs in Ro=O(1) jets when the magnitude of the anticyclonic vertical vorticity exceeds that of the Coriolis parameter, and when surface stress differs from interior viscous stress of the thermal wind shear immediately under the surface. EII is to Ekman spirals what symmetric instability is to internal waves. It can grow explosively fast at first due...

25. Long time dynamics 2D Navier-Stokes

Nader Masmoudi (nyuad)

22/05/2026 11:20

Abstract : In this talk, we study the long-time behavior of solutions to the two-dimensional Navier-Stokes equations in the presence of Couette flow on the half plane with Navier-slip boundary conditions. We construct the profile that describes the leading order term when time goes to infinity.