EFFECT OF SURFACE TENSION ON KELVIN-HELMHOLTZ INSTABILITY

The effect of surface tension on Kelvin Helmholtz instability which is the object of our study, takes place within three layers of immiscible fluids and in the absence of capillary phenomena. Our work begins with a classical study of this instability caused by a relative motion between the different layers of the mixture and. Later we formulate the problem using the fundamental equations of fluids dynamics, knowing that the velocity profile at the base is linear. We obtain a rotational part and the irrotational part of velocity which can be expressed as a potential gradient. By applying certain hypothesis and boundary conditions we then obtain a dispersion equation which is a polynomial of degree 4 of the speed. The numerical resolution of this polynomial shows that longer wavelengths stabilize the flow where as shorter wavelengths destabilize the flow.