The interaction of aircraft exhaust jet and wake vortex is numerically studied. Following the preceding numerical study of wake vortex evolution from roll-up until vortex decay, we aim to simulate the jet-vortex interaction from the early phase until the complete roll-up. For numerical simulation we employ an unstructured mesh Reynolds-averaged Navier-Stokes solver for a flow around an aircraft model, while a Cartesian mesh large-eddy simulation solver implemented on the framework of the Building-Cube Method (BCM) is used for the mid- to far-field wake. Here we investigate a coupling approach of the above solvers to simulate the roll-up of exhaust jet and aircraft wake. The results show that a multi-level Cartesian mesh of the BCM is effective to capture the evolution of aircraft wake including exhaust jet.