Hydro-kinetic, tidal stream, and ocean current energy turbines operate in flows subject to vertical shear, which has an influence on the turbines, especially ones located near the bed. The gravity applied on a fluid is proportional to its density, thus the static pressure induced by gravity is enhanced by the higher density of water than air. Turbines are expected to be placed in fast moving, shallow flows. Hence the Froude number may be relatively high and changes to the free surface are likely, leading to additional flow confinement. In order to investigate the combined effect of vertical shear and gravity on idealized turbines, an extension of linear momentum actuator disc theory (LMADT) is used to estimate the thrust and power extracted by an idealized turbine for two types of free surface inviscid flow. It is assumed that there is fast pressure recovery and that the core flow contains self-similar velocity profiles. Results from a parameter study in which the velocity profiles and turbine settings are varied show that idealized turbines operate at higher efficiency under the effect of gravity, but operate at either higher or lower efficiency under shear flow. The proposed model can also be used to investigate energy extracted by turbines in a periodically spaced array, enabling better evaluation of array efficiency.