Evolution of density variations in a trapped atomic superfluid driven into turbulence
In this work, we study the free decay of a turbulent trapped Bose gas by analyzing the temporal evolution of density variations extracted from absorption images. We introduce a parameter $\delta$ as a simple and experimentally accessible observable that captures the amplitude of density variations. After the driving is turned off, this parameter exhibits a clear decay, which enabled us to identify a characteristic relaxation time. Interestingly, this timescale remains nearly constant across the range of excitation amplitudes explored, while the magnitude of $\delta$ varies with the injected energy. Numerical simulations based on the Gross-Pitaevskii equation reveal a qualitatively similar behavior, both showing a decay of density variations over time.