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To illustrate some of the mechanisms and concepts of stability we choosed a classic problem: the Kelvin-Helmholtz instability. This phenomenon can be observed in nature when the wind is blowing on the water surface. Some waves are created and then are amplified until they deferlete.

This instability can be observed in less complicated situations: for instance with two liquids of different density in a rectangular channel and by putting down slightly this channel, we can observe regular waves on the interface between the two liquids.

In our study we used water and oil, two liquids whose density are very close.The two fluids have got different velocities. Then we used an initial sinusoïdal disturbance in order to induce the development of the instability.

Our study is divided into three parts: first, the study of the development of the instability, then the study of the instability versus the difference of velocity between the two fluids and then the study of the instability versus the frequency of the disturbance.