## Research

* *

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**.