In this paper we present the first observations of the Ophiuchus molecular cloud performed as part of the James Clerk Maxwell Telescope (JCMT) Gould Belt Survey (GBS) with the SCUBA-2 instrument. We demonstrate methods for combining these data with previous HARP CO, Herschel, and IRAM N$_{2}$H$^{+}$ observations in order to accurately quantify the properties of the SCUBA-2 sources in Ophiuchus. We produce a catalogue of all of the sources found by SCUBA-2. We separate these into protostars and starless cores. We list all of the starless cores and perform a full virial analysis, including external pressure. This is the first time that external pressure has been included in this level of detail. We find that the majority of our cores are either bound or virialised. Gravitational energy and external pressure are on average of a similar order of magnitude, but with some variation from region to region. We find that cores in the Oph A region are gravitationally bound prestellar cores, while cores in the Oph C and E regions are pressure-confined. We determine that N$_{2}$H$^{+}$ is a good tracer of the bound material of prestellar cores, although we find some evidence for N$_{2}$H$^{+}$ freeze-out at the very highest core densities. We find that non-thermal linewidths decrease substantially between the gas traced by C$^{18}$O and that traced by N$_{2}$H$^{+}$, indicating the dissipation of turbulence at higher densities. We find that the critical Bonnor-Ebert stability criterion is not a good indicator of the boundedness of our cores. We detect the pre-brown dwarf candidate Oph B-11 and find a flux density and mass consistent with previous work. We discuss regional variations in the nature of the cores and find further support for our previous hypothesis of a global evolutionary gradient across the cloud from southwest to northeast, indicating sequential star formation across the region.
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