Inducing spanwise motions in the vicinity of solid boundaries alters the energy, mass and/or momentum transfer. Under some conditions, these motions are such that drag is reduced and/or transition to turbulence is delayed. There are several possibilities to induce those spanwise motions, be it through active imposition a predefined velocity distribution at the walls or by careful design of the wall shape, which corresponds to passive control.In this contribution, we investigate the effect that wavy walls might have on delaying transition to turbulence. Direct Numerical Simulation of both planar and wavy-walled channel flows at laminar and turbulent regimes are conducted. A pseudo laminar regime that remains stable until a Reynolds number $20\%$ higher that the critical is found for the wavy-walled simulations. Dynamic Mode Decomposition applied to the simulation data reveals that in these configurations, modes with wavelength and frequency compatible with the surface undulation pattern appear. We explain and visualize the appearance of these modes. At higher Reynolds numbers we show that these modes remain present but are not dominant anymore. This work is an initial demonstration that flow control strategies that trigger underlying stable modes can keep or conduct the flow to new configurations more stable than the original one.

In this work, a study of the relative equilibrium of a double pendulum whose point of suspension performs high frequency harmonic vibrations is presented. In order to determine the induced positions of equilibrium of the double pendulum at different gravity and vibration configurations, a set of experiments has been conducted. The theoretical analysis of the problem has been developed using Kapitsa’s method and numerical method. The method of Kapitsa allows to analyze the potential energy of a system in general and to find the values of the parameters of the problem that correspond to the relative extreme of energy — positions of stable or unstable equilibrium. The results of numerical and theoretical analysis of Hamilton equations are in good agreement with the results of the experiments.