This study hypothesises that the motion of binary tropical cyclones (TCs) can be modified by diabatic heating (DH) asymmetry associated with self-induced vertical wind shear. To demonstrate this hypothesis in the quiescent environment, a set of the idealised f -plane numerical experiments such as identical (varied in the initial separation distance) and non-identical (varied in TC intensity and size) experiments are conducted. Results show that the binary TC tracks are affected by the initial separation distance, and TC intensity and size, that is, TC influence radius. Identical experiments show that the critical distance for separating, merging or repelling motion is 8 • (where 1 • ≃ 111 km). The binary TC interaction shows that single large-scale cyclonic and anticyclonic circulations can develop as a result of the superposition of the circulation of the binary TCs in the lower and upper troposphere. These two different large-scale circulations result in a vertically sheared environment in each TC. Potential vorticity (PV) tendency diagnosis shows that the TC motion is consistent with a positive region of the local tendency of PV. To quantify the contribution of each PV diagnostic term to the TC motion, we calculate each vector of the PV tendency diagnostic equation. In the merger case, the horizontal advection vector (HADV) appears to be greater than the DH vector (DHV) due to attraction. In the repulsion case, the DHV is largely compensated by the HADV. Specifically, the strong shear-induced DH generated in the lower troposphere and downshear or downshear-left quadrant can modify the TC motion in collaboration with the transport of PV to the middle and upper troposphere by offsetting the PV imbalance via the HADV. Overall, these results validate our hypothesis, which we refer to as the three-dimensional Fujiwhara effect.