[abridged] Aims: We test the effects of re-orienting jets from an active galactic nucleus (AGN) on the intracluster medium in a galaxy cluster environment with short central cooling time. We investigate appearance and properties of the resulting cavities, and the efficiency of jets in providing near-isotropic heating to the cooling cluster core. Methods: We use numerical simulations to explore four models of jets over several active/inactive cycles. We keep the jet power and duration fixed, varying only the jet angle prescription. We track the total energy of the intracluster medium (ICM) in the cluster core over time, and the fraction of the jet energy transferred to the ICM, paying attention to where the energy is deposited. We also compare synthetic X-ray images of the simulated cluster to actual observations. Results: Jets whose re-orientation is minimal ($lesssim 20^{circ}$) typically produce conical structures of interconnected cavities, with the opening angle of the cones being $sim 15-20^{circ}$, extending to $sim 300$ kpc from the cluster centre. Such jets transfer about $60%$ of their energy to the ICM, yet they are not very efficient at heating the cluster core, as the jet energy is deposited further out. Jets that re-orient by $gtrsim 20^{circ}$ generally produce multiple pairs of detached cavities. Although smaller, these cavities are inflated within the central 50~kpc and are more isotropically distributed, resulting in more effective heating of the core. Such jets, over few hundreds Myr, can deposit up to $80%$ of their energy where it is required. Consequently, these models come the closest to an heating/cooling balance and to mitigating runaway cooling of the core, even though all models have identical power/duration profiles. Additionally, the corresponding synthetic X-ray images exhibit structures closely resembling those seen in real cool-core clusters.
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