Growth of small localized perturbations in Surface Quasi-Geostrophic turbulence

The ``butterfly effect’', i.e. the growth of a localized infinitesimal perturbation, is the fundamental property of chaotic systems. While the butterfly effect is today an obvious property of low-dimensional chaotic systems, its significance is more nuanced in extended systems with many spatial and temporal scales, such as geophysical flows. In this Letter we explore the butterfly effect, i.e., the fate of infinitesimal localized perturbations, in the Surface-Quasi-Geostrophic turbulence, a minimal model for mesoscale geophysical turbulence in the regime of strong stratification and rotation. We find that the evolution of a spatially localized perturbation exhibits strong variability, with an initial transient regime in which the perturbation energy decreases. The duration of this transient is broad and can persist for several small-scale characteristic times, depending on the initial location of the perturbation.