  We present the first empirical constraints on the turbulent velocity field of
the diffuse circumgalactic medium around four luminous QSOs at
$z\!\approx\!0.5$--1.1. Spatially extended nebulae of $\approx\!50$--100
physical kpc in diameter centered on the QSOs are revealed in
[OII]$\lambda\lambda\,3727,3729$ and/or [OIII]$\lambda\,5008$ emission lines in
integral field spectroscopic observations obtained using MUSE on the VLT. We
measure the second- and third-order velocity structure functions (VSFs) over a
range of scales, from $\lesssim\!5$ kpc to $\approx\!20$--50 kpc, to quantify
the turbulent energy transfer between different scales in these nebulae. While
no constraints on the energy injection and dissipation scales can be obtained
from the current data, we show that robust constraints on the power-law slope
of the VSFs can be determined after accounting for the effects of atmospheric
seeing, spatial smoothing, and large-scale bulk flows. Out of the four QSO
nebulae studied, one exhibits VSFs in spectacular agreement with the Kolmogorov
law, expected for isotropic, homogeneous, and incompressible turbulent flows.
The other three fields exhibit a shallower decline in the VSFs from large to
small scales. However, with a limited dynamic range in the spatial scales in
seeing-limited data, no constraints can be obtained for the VSF slopes of these
three nebulae. For the QSO nebula consistent with the Kolmogorov law, we
determine a turbulence energy cascade rate of $\approx\!0.2$ cm$^{2}$ s$^{-3}$.
We discuss the implication of the observed VSFs in the context of QSO feeding
and feedback in the circumgalactic medium.
