ABSTRACT
There are many internal and external flows which display exponential temporal growth of very small omnipresent disturbances by a linear mechanism. As these disturbances grow in amplitude, nonlinearity intervenes decisively in taking the system from one equilibrium state to another. Vortex shedding behind a circular cylinder represents this scenario for which flow instability begins with the growth of disturbances by a linear temporal mechanism followed by nonlinear saturation. This flow has been identified as an example of a nonlinear dynamical system representing phase transition and instabilities for external flows in [284, 353, 387]. For this dynamical system, it was considered until very recently that the transfer function is central, with the input spectrum playing only a residual role at the equilibrium stage (as incidental for systems representing intrinsic dynamics). Such flows are also referred to as hydrodynamic oscillators at any post-critical Reynolds number. Here the criticality refers to primary temporal instability, which is also described mathematically as a Hopf bifurcation in the parameter space in [129].
