Eulerian indicators under continuously varying conditions

In this paper, we extend the notion of Eulerian indicators (EIs) for predicting Lagrangian mixing behavior previously developed for blinking flows to the continuous time setting. We apply the EIs to a study of mixing in a kinematic model of a time-dependent double-gyre with five different time dependencies—sinusoidal, sawtooth, square wave, triangular, and noise (which is constructed so that it is also periodic in time). Each of the five velocity fields is described by two parameters; the strength of the time dependence (e) and the period (T). Based on a trajectory based quality of mixing diagnostic (Danckwerts’ normalized variance of concentration) we find that noisy time dependence has the largest region of good mixing in the parameter space and triangular time dependence has parameter values corresponding to the most complete and fastest mixing. These Lagrangian based predictions are confirmed by the EIs (product of the transversality and mobility). Although not every feature of the mixing behavior is ...