We present results from the KMOS Lens-Amplified Spectroscopic Survey (KLASS), an ESO Very Large Telescope (VLT) large program using gravitational lensing to study the spatially resolved kinematics of 44 star-forming galaxies at 0.6<z<2.3 with a stellar mass of 8.1<log(M$_star$/M$_{odot}$)<11.0. These galaxies are located behind six galaxy clusters selected from the HST Grism Lens-Amplified Survey from Space (GLASS). We find that the majority of the galaxies show a rotating disk, but most of the rotation-dominated galaxies only have a low $upsilon_{rot}/sigma_0$ ratio (median of $upsilon_{rot}/sigma_0sim2.5$). We explore the Tully-Fisher relation by adopting the circular velocity, $V_{circ}=(upsilon_{rot}^2+3.4sigma_0^2)^{1/2}$, to account for pressure support. We find that our sample follows a Tully-Fisher relation with a positive zero-point offset of +0.18 dex compared to the local relation, consistent with more gas-rich galaxies that still have to convert most of their gas into stars. We find a strong correlation between the velocity dispersion and stellar mass in the KLASS sample. When combining our data to other surveys from the literature, we also see an increase of the velocity dispersion with stellar mass at all redshift. We obtain an increase of $upsilon_{rot}/sigma_0$ with stellar mass at 0.5<z<1.0. This could indicate that massive galaxies settle into regular rotating disks before the low-mass galaxies. For higher redshift (z>1), we find a weak increase or flat trend. We investigate the relation between the rest-frame UV clumpiness of galaxies and their global kinematic properties. We find no clear trend between the clumpiness and the velocity dispersion and $upsilon_{rot}/sigma_0$. This could suggest that the kinematic properties of galaxies evolve after the clumps formed in the galaxy disk or that the clumps can form in different physical conditions.
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