Models for hydraulics of open-channel flows: hydraulic jumps and roll waves.


Coastal Waves

Coastal waves from the shoaling zone to the surf zone and to the swash zone.


Thin Films

Newtonian thin films in laminar flows with capillarity.


Drops of water

Propagation and spreading of drops of water on aircraft windscreens.



The fundamental model in hydraulics of open-channel flows is due to Adhémar Barré de Saint-Venant, who published in 1871 the equations which are known today as Saint Venant equations or under the english name of nonlinear shallow water equations. These equations are successful to describe the gradually varied flows but are unable to describe the rapidly varied flows (hydraulic jumps, breaking waves...) where shearing and turbulence play a great role.

An important part of my research activities is to develop a new approach taking into account shearing and turbulence, incorporating the energy equation as an independent equation, modelling correctly the energy dissipation in the flow and able to describe the rapidly varied flows. In this new depth-averaged model, the large scale turbulence is explicitly resolved and its anisotropic character is captured by the enstrophy tensor.

Modelling the coastal waves implies to include dispersion, which plays a predominant role before breaking and dissipation which is the dominant effect after breaking. The Saint-Venant equations are dissipative but not dispersive whereas the dispersive equations (Boussinesq, Serre) are not dissipative. The strategies to combine both effects have various drawbacks, in particular the necessity of a breaking criterion which reduces the robustness and the predictive character of the model. One of my the subjects of my research work is to develop a predictive model, both dispersive and dissipative, capable to describe fully the coastal waves. The elimination of the breaking criterion and the development of a model for sedimentary transport are major objectives to obtain an operational model in the field of extreme coastal events and coastal erosion. The optimization of the dispersive properties of the Serre equations and their numerical resolution are also included in my research work.

In the field of thin films (Kapitsa waves for example), the challenge is to obtain an accurate model having a good mathematical structure leading to a reliable and robust numerical resolution with stable numerical schemes. Such a model would have applications in the domain of renewable energy. It would make easier to optimize plate exchangers with falling films to develop  absorption refrigerators which use solar energy or waste heat.

This whole combination of subjects comes down to develop and expand the initial idea of V. M. Teshukov (2007) to obtain advanced models of open-channel flows, to implement them numerically and to study their applications inf the field of engineering and environmental sciences.