Models Based on Space-Time Symmetries in Transitional Film Flows and Turbulent Wall-Bounded Shear Flows.

Falling film flows and turbulent shear flows are modeled by means of biorthogonal decomposition techniques and space-time symmetry considerations. The analysis of experimental data shows that fluid films falling down an inclined plane are subject to spatio-temporal modulations as the Reynolds number is increased; this leads to a process of splitting and coalescence of front waves in physical space. The study of the system in its subharmonic regime clearly shows the convective nature of the instability as well as intermittency in both space and time. It is shown that inhomogeneous wall-bounded shear turbulence can be decomposed in terms of families of spatial and temporal orthogonal modes. In each family there exists a mother function from which all the other modes can be generated by successive stretchings of the mother, and whose energies are exponentially related to that of the mother. This corresponds to an exponentially decaying spectrum law. Due to the presence of a wall, the stretching symmetry must adapt by acting across the spatial domain (in the direction normal to the wall) in a non-homogeneous manner which is explicitly computed analytically. The previous arguments are tested on statistical data obtained by direct numerical simulation of turbulent channel flow. A good agreement is found within the "inertial range" of the spectrum, excluding the first five modes or so. Within this range, two families of self-similar modes can be extracted and deduced from a mother mode via stretching. The latter persists among the first five modes, but the stretching law is slightly different from that valid in the "inertial range" of the spectrum.