Abstract
We present a unified, quantitative description of transport across the crossover between hydrodynamic weak-link flow and tunneling-dominated Josephson dynamics in a three-dimensional quantum fluid. Using an atomic Josephson junction realized in a Bose-Einstein condensate, we continuously tune the barrier strength to access both regimes within a single, well-controlled system. Measurements of the critical current and Josephson oscillations are in quantitative agreement with numerical simulations and analytical modeling, enabling a consistent inference of the microscopic mechanisms governing dissipation. In the weak-link regime, dissipative transport is consistent with vortex-ring-mediated phase slips, whereas in the tunneling regime it is consistent with rarefaction-pulse excitations. The crossover is further reflected in a transition from a multi-harmonic to a predominantly single-harmonic current-phase relation, signaling the emergence of tunneling-dominated transport. These results establish a general framework linking nonlinear excitations to coherent quantum transport across distinct dynamical regimes. More broadly, they provide insight into the microscopic origin of dissipation in driven quantum fluids, a problem that remains difficult to access in conventional solid-state systems.