Ghost manifolds in slow–fast systems, with applications to unsteady fluid flow separation

Abstract

Consider a structurally stable nonhyperbolic critical manifold in a nonautonomous dynamical system. Despite the lack of hyperbolicity and slow dynamics, sharp moving spikes can develop and move along this critical manifold. An important physical example of this phenomenon is moving separation behind a cylinder in accelerating crossflow. Using a combination of analytic and numerical methods, we uncover the geometric structure responsible for moving spikes. This structure, a ghost manifold, turns out to have a footprint on the critical manifold even though the two manifolds are separated by a boundary layer. We illustrate our results on analytical and numerical examples of off-wall fluid flow separation.