Abstract
In this Letter, we investigate the turbulence and energy injection in the extended nebulae surrounding two luminous obscured quasars, WISEA J100211.29013706.7 () and SDSS J165202.64172852.3 (). Utilizing high-resolution data from the NIRSpec IFU onboard the James Webb Space Telescope, we analyze the velocity fields of line-emitting gas in and around these quasars and construct the second-order velocity structure functions (VSFs) to quantify turbulent motions across different spatial scales. Our findings reveal a notable flattening in the VSFs from kpc up to a scale of 10--20 kpc, suggesting that energy injection predominantly occurs at a scale 10 kpc, likely powered by quasar outflows and jet-driven bubbles. The extended spatial range of flat VSFs may also indicate the presence of multiple energy injection sources at these scales. For J1652, the turbulent energy in the host interstellar medium (ISM) is significantly higher than in tidally stripped gas, consistent with the expectation of active galactic nucleus (AGN) activities stirring up the host ISM. Compared to the VSFs observed on spatial scales of 10--50 kpc around lower-redshift UV-bright quasars, these obscured quasars exhibit higher turbulent energies in their immediate surroundings, implying different turbulence drivers between the ISM and halo-scale gas. Future studies with an expanded sample are essential to elucidate further the extent and the pivotal role of AGNs in shaping the gas kinematics of host galaxies and beyond.