Emmanuel 
  Dormy


 
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Research interests: I am interested in the construction and analysis of Mathematical Models for Geophysical Fluid Dynamics. You will find below a list of my current research interests. My approach is characterised by the construction of simplified mathematical models, which are sometimes tackled numerically, sometimes with a joint asymptotic and numerical approach, but always motivated by real world problems.
Numerical simulation of convection in the Earth core
[E. Dormy].
Dynamo Theory: I am interested in the understanding of natural dynamos. The Earth core (approximatively 3000 km below our feet) consists largely of liquid iron in convection.
Slowest decaying mode in a conducting sphere [E. Dormy].
This convective flow is strongly influenced by the rapid rotation of the Earth. The magnetohydrodynamic flow in the core is thought to sustain a self excited dynamo, which generates the main part of the Earth magnetic field. Although the geodynamo theory was first proposed in 1919, the precise mechanism of the field generation remains unknown. The same mechanism, although under different conditions, is expected to account for the magnetic field of stars (like the Sun) or even galaxies (like the Milkyway).

Teahupoo, Tahiti [Picture
E. Dormy].
Numerical simulation of wave breaking using the vortex method
[E. Dormy & C. Lacave].
Water waves: Water waves at the surface of the ocean are familiar to everyone. Surprisingly several fundamental issues remain open concerning their generation, their evolution and their interaction with the environment. Possibly one of the most striking property of water waves is their ability to develop a sharp singularity from an initially smooth configuration. This is known as the wave breaking problem, which raises serious mathematical difficulties. Wave breaking often occurs as the waves approach land and the depth of water reduces, as the waves slows down, its amplitude increases. Wave breaking can however also occur away from the coast.

Tropical Cyclone Maysak (2015) [Picture T. Virts from the ISS].
Tropical Cyclones: Tropical Cyclones (TCs) are among the most deadly and destructive natural disasters on Earth, they are certainly the most energetic structures in the atmosphere. They present a large number of fascinating and unresolved problems. One of their most striking features is that they develop a so-called eye:
Sketch of a Tropical Cyclone (model of Oruba, Davidson, Dormy, JFM, 2017).
a region of reversed flow in and around the axis of the vortex. Much has been written about eye formation in the context of tropical cyclones, but the key dynamical processes are still poorly understood. I am working on this question as well as that of the rapid intensification often observed for tropical cyclones and which hinders the prediction of their consequences.

"Tea Cup Experiment", click on the picture!
[Mazelet & Dormy]
Flow in the Ekman layer (after Dormy & Soward, 2007).
Rotating Fluids: A key characteristic of geophysical fluids is the role played by the rotation of the Earth on their dynamics. Fluid dynamics in a non-inertial frame of reference is characterised by an additional term in the Navier-Stokes equation, known as the Coriolis term. Rotating fluids are full of surprises and the flow is often very counterintuitive.

The DTS experiment in Grenoble.
MHD shear layer in super-rotation (introduced in Dormy et al. 1998).
Magneohydrodynamic: (or MHD) consists in the study of flows in conducting liquids. The most extreme case, of dynamo action has been mentioned above. I am also interested in general in flows of liquid metal and understanding how the Lorentz force affects the dynamics of the fluid. MHD flows are often characterised by very thin shear layers, which raise mathematical and numerical difficulties.

Super-computer at one of the french national computing centers (CCRT).
Numerical Analysis: The study of the above problems, as well as many others in fluid dynamics, can benefit from efficient numerical simulations. Such simulations are only useful when they can be interpreted physically. This is often achieved through detailed comparisons with theoretical or experimental work. This requires high resolution simulations, varying parameters significantly. I am interested in the development of efficient numerical methods to allow such comparisons.
Asymptotic expansions can in some cases provide exact analytical solutions, usually in the form of special function expansions; however in many cases the asymptotic equations cannot be solved analytically,
Von Neumann amplification factor for the heat equation with an explicit Euler scheme.
and progress is only possible by numerical solution. This is far from straightforward: often regularising terms (such as viscous effects) are retained in one direction only (normal to a shear say) and great care must be taken in choosing the numerical scheme and building the resolution algorithm, in order to guarantee numerical stability.