Optimal forces of entrainment for the flow past inclined plate in a uniform flow*

Phase reduction theory provides a simple and clear vision of the essential part of the dynamics around the limit cycle (LC), and has been applied to many rhythmic phenomena. LCs can be found in fluid mechanics problems, i.e. the Karman’s vortex street or the flow past the inclined plate in a uniform flow. Such periodic flows are also targets of the phase reduction theory which allows us to analyze the synchronization and the entrainment of the system.

 

However, its applications to incompressible fluid systems are limited because the computational cost of calculation of the fundamental functions in phase reduction theory is quite high. Here, we propose an equation-free algorithm to numerically calculate the phase sensitivity function, one of the fundamental functions in the phase reduction theory. This algorithm requires the time-evolution function alone, and can be used to wider range of problems which have not analyzed by the phase reduction theory.

 

In this presentation, we apply this method to analyze the entrainment to the periodic external force of the flow past the inclined plate in a uniform flow. We discuss the characteristics of the phase sensitivity function and optimal external forces in several conditions both theoretically and numerically.