The laminar flowfield and performance of clusters of two-dimensional vertical axis wind turbines are analyzed by idealizing the rotors as momentum sources. The flowfield dominated by the pressure field of the operating turbines is determined by solving the incompressible Navier-Stokes equations and mutual interference is observed to be elliptic in nature. Physical positioning of the turbines with respect to each other significantly affects the aerodynamic performance of the turbines. Several cases are examined starting with one pair of turbines to a cluster as big as 21 turbines. From the two-dimensional cases presented here, it is concluded that downwind turbine performance can be improved by judiciously choosing the angular relative orientation of the turbines. Qualitative analysis of the laminar flowfield is conducted with the help of streamlines and pressure contours. Performance comparisons of the turbines are made with a stand-alone turbine operating under similar flow conditions. This investigation lays the groundwork for the optimization of a wind farm.