Fluid dynamics

Our work in fluid dynamics combines experimental numerical and theoretical approaches to tackle questions of fundamental research intertwined with problems taking their roots in concrete situations, whether natural or industrial. Areas we are particularly interested in include, but are not limited to convection, turbulence, transitional flows and magnetohydrodynamics. These are not only fascinating themes of research in their own right, they are highly also relevant to the metallurgy or the oil industry, with whom we work in collaboration. They also concern the dynamics of planetary atmospheres and of the Earth deep interior, which we are attempting to model experimentally.

Research themes

Separated flows

Flow separation at the back of a tennis ball (NASA).
Shedding of hairpin vortices in the wake of a 3D rectangular obstacle, no magnetic field applied.
Vortex Shedding in the wake of a 3D rectangular obstacle, with a spanwise magnetic field.

Flow separation is one the classical phenomena of fluid dynamics and it is ubiquitous. Car manufacturers often display pictures of wind tunnels where the flow around the car is visualised with smoke filaments. These closely follow the contour of the car up to the sharp angles at the back, where they inevitably separate from it. A region of low pressure develops there that "pulls" the car back and increases petrol consumption. Low pressure sucks the flow in this region, where it generates complex vortex structures that soon shed downstream. Similar effects happen at all scales, around mountains, sky-scrapers, tennis balls or air-cooled computer components. The shape and orientation of the shed vortices determine the feedback force the flow exerts on the obstacle. But because vortices strongly mix the fluid and everything it carries, they also dictate the ability of the wake to transfer heat and chemicals. For this reason, it is common to place obstacles inside heat exchangers, or to alter the shape of ducts to control flow separation and increase the efficiency of the device. When the fluid is electrically conducting, these structures can be affected by an external magnetic field. This happens for instance in the cooling-breeding blankets of thermonuclear fusion reactors, which use a liquid metal as heat carrier, or when a probe is inserted in a liquid metal flow and generates unwanted vortices in its wake. We use shallow water models and 3D Direct Numerical Simulations to explore the fine structure of these flows, and dissect the vortex shedding mechanisms, in generic geometries such as 2D and 3D obstacles, and U-bends.

Turbulence dimensionality

Forced MHD turbulence in a periodic domain.
Experiment where MHD turbulence is electrically driven in a cubic vessel placed in the bore of a superconducting magnet.
Contours of electric potential on opposite walls of the vessel,both normal to the magnetic field. Large vortices extend between the walls whilst smaller ones don't.

Turbulence is a fascinating physical phenomenon which enables flows to dissipate very large amounts of kinetic energy. In laminar flows, energy can only be dissipated by viscous friction, which occurs in small and rather localised regions where strong velocity gradients exist, for instance near the walls of a pipe. In intense flows, these regions do not produce enough dissipation, yet, viscous friction is still the only mechanism available. Nature's answer to this paradox is to reorganise the flow in such a way that strong velocity gradients invade the bulk of the flow. Such gradients are created by intense flow fluctuations, over a spectrum of length scales ranging from that of the flow domain to very small ones where viscous dissipation is most efficient. One of the most remarkable features of turbulence is to operate in a radically different way in 2D and quasi-2D flows than it does in 3D flows. 3D turbulence is characterised by a direct energy cascade: inertial effects break down large vortices into smaller ones, and repeat the process until the energy is transfered to the dissipative scales where viscous dissipation acts. In 2D turbulence, on the contrary, vortices agglomerate into larger ones under the effect of 2D inertia, thus transferring their energy to the larger scales. These in turn exert considerable friction on the flow boundaries where dissipation is enhanced. 

If the fluid is electrically conducting, applying an external magnetic field to it elongates the vortices along the field direction, thus introducing a strong anisotropy.  Depending on the field strength, the flow can be either 3D or quasi-2D, if the vortices are elongated up to boundaries of the fluid domain. To exploit this possibility of studying both types of turbulence, we have built a an experimental platform, based at the Louis Neel Institute in Grenoble (part of the French CNRS).  With it, we are able to generate vortices and turbulence in liquid metals, and diagnose them by measuring electric potentials as well as by ultra-sound velocimetry. We are also developing a new type of spectral method that takes advantage of the mathematical properties of the governing equations to perform more efficient numerical simulations of MHD turbulence.

Quasi Two-dimensional flows

Atmospheric vortex
Jupiter's great red spot
Quasi-2D layer of Gallium in a transverse magnetic field with electric current injected at two electrodes of opposite polarities

Each of us has in mind a satellite picture from the 8pm news showing the large anticyclones that dictate tomorrow's weather. These are so much larger than the atmosphere thickness that we instinctively think of them as two-dimensional objects. Mostly, we are right to do so as their dynamics is essentially a 2D one, and not only so because they are so thin, but also because the Earth's rotation tends to smooth out any variation of velocity or pressure across their thickness. Nevertheless, our experience of bumpy plane descents tells us that strong wind gradients do exist close to the ground, albeit in a small layer compared to the atmosphere thickness. This layer, called the Ekman layer, and the different sublayers is it made of, play a key role in the overall dynamics of the atmospheric structures. Because of these 3D effects, atmospheric flows are not just 2D but rather quasi-2D. Understanding these departures to two-dimensionality and modelling the overall behaviour of quasi-2D flows is a fascinating physical and mathematical challenge that takes us even beyond atmospheric flows: experiments conducted in the 60's indeed revealed that similar phenomena took place in layers of electrically conducting fluids (such as mercury, or electrolytes), subject to a strong transverse static magnetic field. To understand these flows better and the natural or industrial processes they drive, we single out the mathematical structure behind this similarity. We also take advantage of the near invariance of these flows in their transversal direction to derive two-dimensional equations that govern their dynamics. Since, however, these flows aren't exactly 2D, these equations aren't exactly the 2D Navier stokes equations of fluid mechanics. They exhibit a wealth of additional properties, which we explore with numerical simulations and experiments. 

Geophysical flows

The magnetic field of the Earth is one of our planet's most intriguing features. It shields life on its surface from harmful particles emitted by the Sun. It is nevertheless unsteady and sometimes lets particles penetrate and cause severe damage to electrical equipment such as the electrical grid. Understanding its dynamics is one of the great challenges of modern science, and can also help us deal with these events.

The turbulent motion of hot liquid iron within the liquid core of the Earth sustains the magnetic field, but this "boiling pan" is in turn influenced by the Earth magnetic  field itself, by the rotation of the Earth, and by convection due to the heat released from the solid inner core. The key to understand the Earth magnetic field lies in how these complex phenomena interact.

The "Little Earth Experiment" is a laboratory reproduction of the motion of liquid metal in the core of the Earth in a large superconducting magnet, which we built to

- Reproduce and control the interaction between the Coriolis force (rotation), the electromagnetic force, and buoyancy forces (convection).
- Seek flow patterns in the core which are compatible with the structure
- of the magnetic field near the poles.
- Understand the physical mechanism that determines the structure of the magnetic field near the poles.

This collaborative work with IISc Bengalore is supported by the Royal Academy of Engineering and the Levehulme Trust.


We are also trying to understand some aspects of the behaviour of volcanoes. Observed volcanic activity is driven by motion in the magma deep within the earth, and in the volcanic conduits leading to the surface. This motion is characterised by (among other things) density contrasts and gas pockets. Modelling and understanding this motion is key to understanding how volcanoes behave.


Plasma flows

Energetic turbulent structures in real space, filtered according to size, for gyrokinetic turbulence.
Magnetic field-lines (in yellow) tracing turbulent structures denoted by the intensity of the magnetic energy (i.e. the blue cloud - lighter colors denoting larger values of the energy). To a good degree, electrons can be seen as traveling along the filed-lines, while energetic ions have a tendency to bounce off magnetic structures.

As electrically charged particles move, they generate electromagnetic fields that in turn affect the trajectories of the charged particles. Thus, plasmas represent the cumulative interplay occurring between charged particles and electromagnetic fields. The description of a plasma can range from the simpler fluid approaches (magnetohydrodynamics) to complex gyrokinetic formalisms.

Understanding the motion of a plasma medium is crucial for the study of solar and astrophysical phenomena (e.g. the solar wind, sun corona heating, cosmic rays transport), but also for the development of controlled fusion energy, one of the largest and most important engineering endeavors of this century. The work performed in this field is done in collaboration with the Max-Plank/Princeton Center for Plasma Physics, Germany/US.

Fusion plasmas  

In a controlled fusion toroidal vessel (i.e. a tokamak), plasmas are confined by strong magnetic fields as a mean to obtain the high temperature and density required for fusion reactions to take place. 

In the magnetized plasma core, dynamically represented by a gyrokinetic approximation, structures in the 5D-phase space become coupled, as strong nonlinear interactions develop for a turbulent state. As such, large-scale gradient instabilities interact with scales where collisional phenomena dominate. This nonlinear interaction in phase space stands at the basis of the problems we have with understanding heat and particle transport related process, which directly impact the required plasma confinement.     

At present, our research is centred on understanding the fundamental nature of gyrokinetic turbulence and the development of models. As the problem is in 5D-phase space and the magnetic filed possesses a non-trivial geometry, a series of complication arises compared to classical turbulence.

Astrophysical Plasmas  

One of our interests consists in describing the acceleration and transport of particles in balanced and imbalanced Alfvenic turbulence, relevant to the solar-wind problem. Heat or mass transport in a medium, perfectly understood in simple configurations, becomes near impossible to account for in turbulent states. At the basis of understanding the generalized transport problem, stands the ability to describe the acceleration behaviour of particles, as a result of force fields that possess intricate structures that are generated by turbulence. This is the case for the motion of charged particles in electromagnetic fields, generated self-consistently by the turbulent motion of a plasma flow. 



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