We present an analysis of the gas dynamics of star-forming galaxies at z~1.5 using data from the KMOS Galaxy Evolution Survey (KGES). We quantify the morphology of the galaxies using $HST$ CANDELS imaging parametrically and non-parametrically. We combine the H$alpha$ dynamics from KMOS with the high-resolution imaging to derive the relation between stellar mass (M$_{*}$) and stellar specific angular momentum (j$_{*}$). We show that high-redshift star-forming galaxies at z~1.5 follow a power-law trend in specific stellar angular momentum with stellar mass similar to that of local late-type galaxies of the form j$_*$$propto$M$_*^{0.53 pm 0.10}$. The highest specific angular momentum galaxies are mostly disc-like, although generally, both peculiar morphologies and disc-like systems are found across the sequence of specific angular momentum at a fixed stellar mass. We explore the scatter within the j$_{*}$-M$_{*}$ plane and its correlation with both the integrated dynamical properties of a galaxy (e.g. velocity dispersion, Toomre Q$_{rm g}$, H$alpha$ star formation rate surface density $Sigma_{rm SFR}$) and its parameterised rest-frame UV/optical morphology (e.g. Sersic index, bulge to total ratio, Clumpiness, Asymmetry and Concentration). We establish that the position in the j$_{*}$-M$_{*}$ plane is strongly correlated with the star-formation surface density and the Clumpiness of the stellar light distribution. Galaxies with peculiar rest-frame UV/optical morphologies have comparable specific angular momentum to disc-dominated galaxies of the same stellar mass, but are clumpier and have higher star-formation rate surface densities. We propose that the peculiar morphologies in high--redshift systems are driven by higher star formation rate surface densities and higher gas fractions leading to a more clumpy inter-stellar medium.
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