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Context. Turbulence plays an important role in shaping the interstellar medium, and it strongly influences star formation. Aims. We aim to identify the physical processes capable of sustaining H I turbulence in the solar neighborhood. Methods. We compare recent H I line-of-sight velocity observations within a volume of radius 70–500 pc centered on the Sun with a suite of 1 kpc numerical simulations that include two distinct turbulent drivers: (i) supernova (SN) feedback and (ii) imposed large-scale turbulent forcing. For each simulation, we constructed synthetic sky maps that closely mimic the observational one, allowing for a consistent comparison between the simulations and the observational data. Results. The H I observations show a median velocity dispersion of 11.1 km s −1 in the solar neighborhood. The SN-driven simulations systematically underpredict this value, yielding dispersions in the range 4.9–6.7 km s −1 . We find that the simulations with strong enough large-scale forcing can reproduce not only the median observed velocity dispersion but also the observed velocity distribution.