Three-Dimensional Quasi-Periodic Instabilities of Two-Dimensional Time-Periodic Flows

Three-dimensional synchronous instabilities of two-dimensional time-periodic wake flows, such as the so-called modes A and B of the circular cylinder wake, are now well-known. On the other hand, quasi-periodic three-dimensional instabilities are just as generic, but have as yet not received such wide-spread recognition, partly as a consequence of the predominance of attention given to flows, such as the cylinder wake, in which the synchronous modes happen to dominate at onset of three-dimensionality. Here we provide an introduction to the quasi-periodic modes, which can manifest either as modulated standing waves, or modulated travelling waves.