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 $alphasim 0.5$ 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.
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