Relative efficiency of three mechanisms of vector field growth in a random media

We consider a model of a random media with fixed and finite memory time with abrupt losses of memory (renovation model). Within the memory intervals we can observe either amplification or oscillation of the vector field in a given particle. The cumulative effect of amplifications in many subsequent intervals leads to amplification of the mean field and mean energy. Similarly, the cumulative effect of intermittent amplifications or oscillations also leads to amplification of the mean field and mean energy, however, at a lower rate. Finally, the random oscillations alone can resonate and yield the growth of the mean field and energy. These are the three mechanisms that we investigate and compute analytically and numerically the growth rates based on the Jacobi equation with a random curvature parameter.