In fluid dynamics, various scientific issues remain unsolved. Our capabilities to meet the present economic and/or societal challenges depend also on our ability to solve these scientific issues.

As a first example, we can mention the heat transfer problem. Indeed, it is important to be able to predict the temperature field in various applications. For instance, the prediction of heat transfer is a key point in design and safety of nuclear plants because of requirements of heat removal from the reactor core. Cooling systems are also an important issue for aerospace applications. It is well-known that the Ariane crash in December 2002 was due to an insufficient heat transfer between the cooling channel and the rocket nozzle.

An example concerning fluid dynamics and energy conversion are combustion processes [Pitsch et al., 2006]. Indeed, in the context of rising environmental concerns and record-high oil prices, the need for cleaner and more efficient combustion devices becomes pressing. Two main points have to be understood to design efficient combustion devices. Since the fuel is usually injected in the liquid form, we have to deal with multi-phase flows. Moreover, combustion processes are the result of chemical reactions that take place at the interfaces. Thus, the mixing of the species as well as the interface dynamics due to the fluid motions have to be understood.

Another example showing the impact of fluid dynamics research is environmental problems. Indeed, it is important to understand the transport of pollutant species in the atmosphere. The atmosphere is a complex dynamic natural gaseous system that is described by the fluid dynamics science.

In all these examples, the numerical simulation of the fluid dynamic equations is an important tool for engineers and researchers. Indeed, experimental access to relevant data can be very difficult (for instance, the temperature fields in nuclear plants). The goal of numerical simulations is to predict accurately the behavior of the studied system to be able to optimize this system. One major problem for numerical simulations is often that the considered flow is turbulent with a large number of scales of motion.

The common issue to the applications given above is the prediction of the dynamics of a scalar advected by a turbulent flow. The scalar field is used to describe the temperature field (heat transfer), the concentration of species (reacting flow or pollutant transport) or a function to indicate the considered phase (multiphase flows).

The goal of this project is to study the scalar dynamics in turbulent flows, and to develop an accurate modelling procedure that is able to predict the observed scalar behavior. For various applications, it is important to compute not only statistical means but also extreme values. For example, the 2002 Ariane crash was due to a deficient prediction of the temperature peaks. There is therefore a crucial need to have available accurate prediction tools of an unsteady scalar field. Moreover, the numerical tools used have to be accurate also. For instance, excess numerical dissipations in the transported pollutant concentration significantly deteriorate the computed pollutant productions, with consequences in the predictions of these flows.