  This paper reports the first measurement of the relationship between
turbulent velocity and cloud size in the diffuse circumgalactic medium (CGM) in
typical galaxy halos at redshift z~0.4-1. Through spectrally-resolved
absorption profiles of a suite of ionic transitions paired with careful
ionization analyses of individual components, cool clumps of size as small as
l_cl~1 pc and density lower than nH = 0.001 cm^-3 are identified in galaxy
halos. In addition, comparing the line widths between different elements for
kinematically matched components provides robust empirical constraints on the
thermal temperature T and the non-thermal motions bNT, independent of the
ionization models. On average, bNT is found to increase with l_cl following bNT
\propto l_cl^0.3 over three decades in spatial scale from l_cl~1 pc to l_cl~1
kpc. Attributing the observed bNT to turbulent motions internal to the clumps,
the best-fit bNT-l_cl relation shows that the turbulence is consistent with
Kolmogorov at <1 kpc with a roughly constant energy transfer rate per unit mass
of epsilon~0.003 cm^2 s^-3 and a dissipation time scale of <~ 100 Myr. No
significant difference is found between massive quiescent and star-forming
halos in the sample on scales less than 1 kpc. While the inferred epsilon is
comparable to what is found in CIV absorbers at high redshift, it is
considerably smaller than observed in star-forming gas or in extended
line-emitting nebulae around distant quasars. A brief discussion of possible
sources to drive the observed turbulence in the cool CGM is presented.
