Doubly transient chaos in a decaying open flow

Abstract

Abstract Doubly transient chaos was recently characterized as the general form of chaos in undriven dissipative systems. Here we study this type of complex behavior in the advective dynamics of decaying incompressible open flows. Using a decaying version of the blinking vortex-sink map as a prototype, we show that the resulting dynamics is markedly distinct from the one of mechanical systems addressed in previous works. In particular, the asymptotic codimension of the set of initial conditions of non-escaping particles is zero rather than one and the time-dependent escape rates either undergo an exponential decay rather than growth (for moderate and fast energy dissipation) or display a complex, possibly nonmonotonic behavior (for slow energy dissipation).