  In massive objects, such as galaxy clusters, the turbulent velocity
dispersion, $\sigma_\mathrm{turb}$, is tightly correlated to both the object
mass, $M$, and the thermal energy. Here, we investigate whether these scaling
laws extend to lower-mass objects in dark-matter filaments. We perform a
cosmological zoom-in simulation of a filament using an adaptive filtering
technique for the resolved velocity component and a subgrid-scale model to
account for the unresolved component. We then compute the mean turbulent and
thermal energies for all halos in the zoom-in region and compare different
definitions of halo averages. Averaging constrained by density and temperature
thresholds is favored over averages solely based on virial spheres. We find no
clear trend for the turbulent velocity dispersion versus halo mass, but
significant correlation and a scaling law with exponent $\alpha\sim 0.5$
between the turbulent velocity dispersion and thermal energy that agrees with a
nearly constant turbulent Mach number, similar to more massive objects. We
conclude that the self-similar energetics proposed for galaxy clusters extends
down to the CGM of individual galaxies.
