Tethered multirotor axial flow turbines have been proposed to overcome the many challenges associated with extracting ocean current energy where deep waters render seabed mounting strategies infeasible. However, flexible systems are inherently more susceptible to perturbation than fixed systems. The effects of flow misalignment on the hydrokinetic energy conversion of multirotor coaxial turbines have been investigated recently; however, the spatial dynamics and equilibrium behaviors of tethered coaxial turbines have not been well characterized, limiting the ability of designers to explicitly tailor the device behavior. In this work, a computational model of a dual-rotor coaxial turbine is presented, and the model is employed to explore the equilibrium behavior of the turbine with variations in parameters. A complete characterization of the hydrostatic state of the system and a comparative study of representative tethered turbine simulation cases is also presented. Two important findings are presented. First, that a positively buoyant dual-rotor turbine that is anchored to a surface-dwelling platform can operate where the turbine is located at some desired depth below the surface. Second, that more than one turbine system may be anchored to a single point while maintaining the desired orientation and position of each turbine to avoid collision and maximize energy production. The results and methods presented in this paper may be used to inform application-specific coaxial turbine design and to develop additional targeted empirical and simulation studies.