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Jérôme Fontane


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 Instabilities and transition of inhomogeneous flows at high Froude number

Industrial flows exhibit numerous mixing and injection configurations that present density variations. These inhomogeneities of mass induce momentum variations which modify in return the local-rotational dynamics under the action of the baroclinic torque. The resulting mixing can be significantly changed through the modification of coherent structures that develop naturally in the unstable shear regions.

To address this issue, we carry out modal and nonmodal linear stability analysis in order to obtain perturbations fields. The study follows with the nonlinear development of these disturbances by use of direct numerical simulations. Two simplified model flows are considered :

  • the plane mixing layer (opposite image)
  • the round jet with or without swirl and/or co-flow

 Vortex dynamics and aircraft wakes

Vortex dynamics plays a crucial role in aeronautical and geophysical flows but it also deals with the behaviour of eddies considered as the elementary bricks of fully developped turbulence. We address vortex stability and vortex interactions. The expected outcomes of this research are the mixing promotion (in direct link with previous topic) and the reduction of the lifetime of aircraft trailing vortices which limit airports productivity for safety reasons and also play a central role in the amount of persistent condensates emitted by the aircraft engines.

 Geophysical flows and 2D turbulence

Density stratification and planetary rotation place strong constraints on geophysical flows in a wide range of situations. These flows can be represented to a good approximation by layer-wise two-dimensional flow with varying degrees of vertical coherence. High Reynolds number,
2D turbulence is commonly considered as one of the simplest models to assess qualitative aspects of their dynamics. Due to the existence of two invariants, energy and enstrophy, this model exhibits the most
remarkable feature of 2D flows, namely a dual cascade in which energy (resp. enstrophy) is transferred preferentially to large (resp. small) scales.

In collaboration with David Dritschel and Richard Scott of the University of St Andrews, we characterise this dual cascade with high resolution numerical simulations using a powerful algorithm specially designed for geophysical flows : the Combined Lagrangian Advective Methods (CLAM).

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