Introduction Room: Amphithéâtre Hermite

Stable regime singularity for the Muskat problem

• Andrej Zlatos (UCSD)

Room: Amphithéâtre Hermite 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 geometries than even prior whole plane results, and crucially allows the interface to touch the bottom. The latter can be used to model physically relevant scenarios where the heavier fluid invades a region occupied by the lighter fluid along the impermeable layer. We also show that finite time singularities do arise in this setting, including from arbitrarily small smooth initial data, by obtaining "maximum principles" for the height, slope, and potential energy of the fluid interface.

A model for breaking of surface waves

• Maria Kazakova (LAMA, USMB)

Room: Amphithéâtre Hermite 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 capturing the main features of wave breaking. The governing equations, the associated breaking criterion, and the numerical strategy used for their approximation are presented. Particular attention is paid to the persistence of the dissipation once activated, and to its influence on the behaviour of solutions. Several test cases illustrate the properties of the model.

A Great Red Spot: Models vs Observations

• Philip Marcus (California at Berkeley, University of)

Room: Amphithéâtre Hermite 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 vortex can be claimed to uniquely model the GRS. However, by requiring that the computed vortices also reproduce new cloud-top temperature observations, a unique solution to the equations of motion is obtained. This GRS solution has a vertical thickness of only $1\%$ of its east-west diameter, does not penetrate the underlying convection zone, and has a large Rossby number beneath its observable velocities, so it violates the quasi-geostrophic and shallow-water approximations. The 3D GRS is poorly approximated by 2D models, models based on potential vorticity dynamics, statistical models based on maximum entropy, and solitary wave models. Like an iceberg, upper surface observations of the GRS are misleading.

On local energy conservation

• Helena Nussenzveig Lopes (Universidade Federal do Rio de Janeiro)

Room: Amphithéâtre Hermite 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, is p-th power integrable or even a nonnegative Radon measure. The vanishing viscosity limit in domains with boundary is a classical open problem due mostly to the formation of large gradients near the walls. These may propagate into the bulk of the fluid through boundary layer separation and have the potential to yield anomalous dissipation. In this talk we will discuss the absence of local anomalous dissipation in the vanishing viscosity limit in a bounded domain.

Progress towards the inviscid dynamo

• Andy Jackson

Room: Amphithéâtre Hermite 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. Taylor (1963) proposed a reduced model by neglecting inertia and viscous force. A modified model that partially re-introduces the inertia term back is termed the torsional wave (TW) dynamo model, since it admits torsional oscillations, a special type of Alfven wave. In this study, we present progress to date in our studies of inviscid dynamo simulation.

Short presentations Posters Room: Amphithéâtre Hermite

Poster session Room: Amphithéâtre Hermite

Ocean Transit Times

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

Room: Amphithéâtre Hermite 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 Lagrangian parcels, particularly within ocean gyres, significantly enhance dispersion beyond the levels attributed to mesoscale eddies alone. Additionally, trapping by ocean gyres leads to multimodal distributions of Lagrangian transit times. These processes are illustrated in three complementary contexts: eddy-permitting ocean state estimates, simplified spatially extended three-dimensional flows and diffusively coupled two-dimensional pipe models.

Reduced models for bubbly flows

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

Room: Amphithéâtre Hermite 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 shape constraints on the bubbles through their evolution. This imposes in turn to relax the usual constraints at the gas/liquid interface. We shall present a method to determine the appropriate relaxed interface conditions, based on a least action principle. This is joint work with Cosmin Burtea.

Solutions near monotone vortices

• Ángel Castro (Instituto de Ciencias Matemáticas)

Room: Amphithéâtre Hermite 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 is related with the stability of shear flows and the existence of stationary and traveling waves solution near them. We also review some results on this topic.

Stratified turbulence

• Pascale Garaud (UC Santa Cruz)

Room: Amphithéâtre Hermite 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 model leverages the anticipated flow anisotropy in the limit of small Froude number / large Reynolds number to derive scaling laws for the turbulence properties. Several distinct regimes are investigated.

3D-2D asymptotics for the rotating MHD

• Frédéric Charve (UPEC)

Room: Amphithéâtre Hermite 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 incomplete. Reaching a more complete limit requires adding to some classical initial data a non-conventional component linked to the special structure of the limit system. Then we study (for both weak and strong solutions) the asymptotics when the Rossby number goes to zero (i.-e. for strong rotation) of the 3D-rotating (MHD) system when the initial velocity and magnetic field both feature some 2D-part (i.-e. depending only on the horizontal space variables). We show this limit is the 2D-MHD system *with three components* supplemented with an additional 3D magnetic field transported by the 2D limit velocity.

The deep-seated solar dynamo

• Toby Wood (Newcastle University)

Room: Amphithéâtre Hermite 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 recent studies have even questioned whether the tachocline is involved in the dynamo at all. We present an alternative hypothesis, in which both the toroidal and poloidal field are generated in the tachocline by a combination of shear and magnetic buoyancy instability. We demonstrate a proof-of-concept Cartesian model and ongoing efforts to identify the effects of spherical geometry and other instabilities, such as MRI.

Linear Stability of small BGK waves

• Benoit Pausader (Brown University)

Room: Amphithéâtre Hermite 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, perturbations are damped, when the Penrose criterion is violated, the situation is more complicated and related to another class of steady states: the (inhomogeneous) BGK waves.

QG convection on the f-plane

• Benjamin Miquel (CNRS, Ecole Centrale Lyon)

Room: Amphithéâtre Hermite 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 in a local model: the tilted f-plane. Employing non-orthogonal coordinates, we obtain a natural formulation for geostrophy and a set of governing equations for the non-hydrostatic quasi-geostrophic dynamics on the tilted f-plane (fNHQGE), valid in the asymptotic limit of rapid rotation. We conduct a systematic parametric study by varying the Rayleigh number and the tilt angle. As the tilt increases, the barotropic condensate transitions from large scale vortices (near the pole) to East-West jets (near the equator), with bistability at intermediate latitudes. Concomitantly, both heat transport and the vertical kinetic energy decrease monotonically with colatitude.

Couette flow and rotation/stratification

• Klaus Widmayer

Room: Amphithéâtre Hermite 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 discuss how their combined effect leads to a quantitatively improved stability This is based on joint work with M. Coti Zelati and A. Del Zotto.

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

• Javier Gomez-Serrano (Brown University)

Room: Amphithéâtre Hermite 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 extend the range of problems on which it can be brought to bear, often by searching spaces that are too large or too irregular for human intuition alone.

Data-driven reduced order models

• Taraneh Sayadi (Conservatoire National Arts et Métiers)

Room: Amphithéâtre Hermite 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, these architectures still face challenges when confronted with systems exhibiting variable dynamics, bifurcations, or chaotic behaviour. In this talk, we present a shift in perspective that unifies complex dynamical systems with nonintrusive, data-driven reduced-order modelling approaches, thereby broadening the range of applications that can be addressed effectively.

Data-driven dynamo equations

• Anna Guseva (Polytechnic University of Catalonia)

Room: Amphithéâtre Hermite 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 very challenging and their reduced-order models of oscillatory dynamos are of interest. In this work, we develop a framework to recover such models directly from numerical data using a combination of Hankel Dynamic Mode Decomposition (DMD) to identify magnetic structures, and Sparse Identification of Nonlinear Dynamics (SINDy) to model their dynamics, and compare it to classic mathematical method of weakly nonlinear analysis (WNL). We implement this approach on a one-dimensional idealized mean-field dynamo model parametrizing the main components of convective dynamo in a low-mass star, helical convection and differential rotation.

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

• Matthew Juniper (University of Cambridge)

Room: Amphithéâtre Hermite 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 modellers respond? In this talk, I will show that von Neumann's quote is more nuanced than it sounds. I will then frame a response within a Bayesian framework, in which physical principles such as conservation of mass, momentum, and energy are treated as high quality prior information, with quantified uncertainty, expressed as PDEs or low order models. The information content of data can then be quantified and the likelihood of different candidate models can be compared after the data arrives. I will show how Bayesian inference becomes computationally tractable when combined with adjoint methods. I will demonstrate this through assimilation of 3D Flow-MRI data in complex geometry into Finite Element CFD. The main message of the talk is "keep the physics in the model if you can."

Generative modeling of QG solutions

• Louis Thiry (Sorbonne Universite)

Room: Amphithéâtre Hermite 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 the north-atlantic ocean with a western-boundary (gulf-stream like) current, viewing the numerical solutions of QG equations as a stochastic process that we learn without using explicitly physical priors.

Post-Geostrophy: Numerics, Computation, AI

• Peter Korn (Max Planck Institute for Meteorology)

Room: Amphithéâtre Hermite 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 computational approaches to ocean modelling, new experimental strategies and reflects on how machine learning can be integrated into this endeavour.

Thoughts on Machine Learning

• Rupert Klein (Freie Universität Berlin)

Room: Amphithéâtre Hermite 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 safety-critical applications, we should know how to guarantee their compliance with pre-defined guardrails. Moreover, when they are utilized as building blocks in scientific research, it would violate scientific standards if these building blocks were used without a thorough understanding of their functionality, including inaccuracies, uncertainties, and other pitfalls. In this context, I will juxtapose (a subset of) deep neural network methods with the family of entropy-optimal ML techniques developed recently by Illia Horenko (RPTU Kaiserslautern-Landau) and colleagues.

Intermittency & dissipation in turbulence

• Theodore Drivas (Stony Brook University)

Room: Amphithéâtre Hermite 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.

Exact solutions to Euler's equations

• Nick Pizzo (University of Rhode Island)

Room: Amphithéâtre Hermite 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 infinitesimal canonical transformations. The associated compatibility conditions of these maps restrict the label dependence to be harmonic maps from cartesian label space to these two dimensional surfaces, connecting the rotational relabelling symmetry with harmonic maps. Using a frame equation approach on the sphere, harmonic maps from the plane to the sphere are associated with a negative sinh Laplace equation and the associated family of these maps, which rotate the Hopf differential, are shown to generate the time evolution. Simpler solutions with label dependent rotations are also presented.

Simple model for the strength of the ACC

• David Marshall (University of Oxford)

Room: Amphithéâtre Hermite 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 wind stress. A new model - building on the recent GEOMETRIC parameterisation of mesoscale eddies - is developed relating ACC transport to three length scales divided by the residence time of Southern Ocean eddy energy (set by bottom drag), and independent of the wind stress. Observation-based estimates of the parameters give an ACC transport of realistic magnitude.

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

• Sergey Gavrilyuk (Aix-Marseille University)

Room: Amphithéâtre Hermite 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 dispersive shock. Its speed and amplitude are defined analytically through the solitary limit of the corresponding Whitham modulation equations. In such a limit, Whitham's equations form a system of quasi-linear equations for which Riemann's invariants can be determined. The numerical results are in accordance with the analytical prediction.

Water-waves problem with contact angles

• Mei Ming (Yunnan University, China)

Room: Amphithéâtre Hermite 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 short time interval. As a result, we have fixed contact points and contact angles. To prove the energy estimate, a conformal mapping is used to transform the equation for the mean curvature into an equivalent equation in a flat strip with some weights. Moreover, the weighted limits at contact points for the velocity, the pressure etc. are tracked and discussed. Our formulation can be adapted to deal with more general cases.

Wave resonances in bounded domains

• Paul Milewski (Penn State University)

Room: Amphithéâtre Hermite 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 the past 60-years, almost always on domains that are large (or infinite) compared to the characteristic wavelength. In this case, the dispersion relation dictates that only quartic (4-wave) resonances can occur. In contrast, wave resonances in confined three-dimensional geometries have received relatively little attention, where, perhaps surprisingly, stronger 3-wave resonances of gravity waves can occur. We will present the results characterizing the configuration and dynamics of resonant triads in cylindrical basins of arbitrary cross sections. Extensions to internal waves and other geometries will also be discussed.

Metriplectic ocean thermodynamics

• Francisco Beron-Vera (University of Miami)

Room: Amphithéâtre Hermite 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 buoyancy's vertical average and gradient) is governed by its (Lie-)Poisson bracket with the Hamiltonian, plus a symmetric bracket with a Casimir that incorporates dissipation. The symmetric bracket is constructed in two ways: algebraically and using the metric on the flow domain, the latter justifying the term 'metriplectic bracket.' This is joint work with Erwin Luesink (University of Amsterdam).

Boundary layer around a rotating cylindre

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

Room: Amphithéâtre Hermite 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, and compare our findings with the geometric Feynman–Lagerstrom criterion recently revisited by Drivas–Iyer–Nguyen. New features seem to arise from the competition between the vorticity production and rotation-induced tangential transport, leading to boundary layer behaviour distinct from the classical Prandtl or Stokes layers. This is a joint work with Y. Maekawa, Kyoto University.

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

• David Lannes (Institut de Mathématiques de Bordeaux)

Room: Amphithéâtre Hermite 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 surface of the fluid and the surface of the solid. The presence of this boundary induces new difficulties such as the derivation and analysis of boundary conditions but also the analysis of the motion of the boundary itself. In this talk we review some known results on the treatment of boundary conditions for hyperbolic systems (such as the nonlinear shallow water equations), and propose some extensions motivated by wave-structure interactions. We will comment also on the treatment of boundary conditions for dispersive perturbations of hyperbolic systems (such as the Boussinesq equations) and introduce the notion of dispersive boundary layers. Finally, we will comment on the dynamics of the contact line, which is not always a kinematic boundary condition in the sense that a particle located on the contact line can detach from it. **Basque translation:** Uhin-egitura elkarrekintzetarako muga-baldintzak eta muga aske ez-zinematikoak Uhinen deskribapena, ur-uhinen ekuazioen edo eredu asintotiko sinpleagoen bidez (sakonera txikiko uraren ekuazio ez-linealak edo Boussinesq sistema, adibidez), ondo ulertzen da mugarik gabeko domeinu batean. Uhin-egitura elkarrekintzen kasuan, hala nola itsasertzaren edo objektu flotatzaileen dinamika, surfaze libreak fluidoaren surfazea eta solidoaren surfazearen arteko kontaktu-lerroak osatutako muga bat du. Muga horren presentziak zailtasun berriak eragiten ditu, hala nola muga-baldintzen deribazioa eta analisia baina baita mugaren beraren higiduraren analisia ere. Hitzaldi honetan, sistema hiperbolikoetarako muga-baldintzen tratamenduari buruzko emaitza ezagun batzuk berrikusiko ditugu, eta uhin-egitura elkarrekintzek eragindako hedapen batzuk proposatuko ditugu. Sistema hiperbolikoen perturbazio dispertsiboen muga-baldintzen tratamendua ere aipatuko dugu (Boussinesq-en ekuazioak, adibidez), eta muga-geruza dispertsiboen nozioa sartuko dugu. Azkenik, kontaktu-lerroaren dinamikari buruz hitz egingo dugu, ez baita beti muga-baldintza zinematikoa, kontaktu-lerroan kokatutako partikula batek linea horretatik aska dezakeen zentzuan.

Scaling Trends in Rotating Convection

• Paula Wulff (University of California, Los Angeles)

Room: Amphithéâtre Hermite 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 asymptotic scalings using a broad compilation of laboratory-numerical rotating convection experiments in planar, cylindrical, and spherical systems. We find good agreement between the different rapidly (Ro_c≪1) and slowly (Ro_c≫1) rotating trends for convective heat transfer, velocities, length scales, and dynamic Rossby numbers in Boussinesq fluids. Further, we show that the predicted trends also hold in anelastic systems, albeit with an additional dependence on the density stratification. Our tests demonstrate that, given reasonable estimates of Ro_c in a geo- or astrophysical fluid system, accurate first-order predictions of the convective dynamics can be made.

Polar Vortex Crystals

• William Young (University of California, San Diego)

Room: Amphithéâtre Hermite 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 structures, with vastly different space and time scales, can be reproduced by a maximally simplified ‘quasigeostrophic’ (QG) model to two-dimensional turbulence model. The QG model shows that vortex crystals form from the free evolution of randomly excited two-dimensional turbulence on an idealized polar cap. Once formed, the crystals are long lived and survive until the end of the simulations (300 crystal-rotation periods). We identify a fundamental length scale characterizing the size of the crystal in terms of the mean-square velocity of the fluid and a parameter characterizing the variation of the Coriolis parameter close to the pole.