Complex Wave Dynamics in Falling Films and Surface Turbulence

par Evgeny A. Demekhin, Laboratory of electrohydrodynamics of micro- and nanoscales (Kuban State University, Russian Federation)

Le MARDI 25 novembre à 14h, salle des séminaires, bâtiment A4, 3e étage

Investigation of thin liquid films is one of the most important hydrodynamic problems. Numerous studies of this problem are connected with wide practical application in industry, engineering and biology. Besides practical importance, there is a general theoretical interest. The flow is convectively unstable, its complex and rich dynamics have also attracted considerable scientific attention: it is the “simplest” example of an open-flow system that exhibits a sequence of transitions of wavy regimes that are generic to the more complex hydrodynamic systems. The simplest 2D waves can be of sinusoidal form or solitary type; they attracted attention for four last decades and their behavior was eventually deciphered.
Much more important from a practical view-point and intrigues from a theoretical view-point, the case of irregular 3D waves (or “surface turbulence”) has been untouched. Such a regime was studied both theoretically and experimentally.
The evolution of unstable natural disturbances in open systems undergoes several changings in each regime. At sufficiently large Reynolds numbers it eventually reaches the last stage when the surface is randomly covered by 3D nonlinear structures or “quasi-particles” which are robust and interact with each other in a chaotic way. Such a stage is often called “surface turbulence” and it occurs when Reynolds numbers in liquid are small for Tollmien-Schlichting instability and usual turbulence. We constructed theoretically “quasi-particle” of surface turbulence, its shape, amplitude and speed. Sophisticated experiments were done to measure these parameters experimentally. The last were successfully compared with our theory. Turbulence in open-flow systems is a phenomenon which is far from understanding. Hence, the results of our investigation are a promising break into the theory of turbulence and nonlinear waves in an active medium. Moreover, taking into account striking likeness between coherent structures in falling films and Lambda-vortices in the boundary layer, our “simple” example can elucidate the behavior of much more complex structures of turbulence.