This work examines computationally the Mach 3 ow eld structure of the external shock-wave/turbulentboundary-layerinteraction caused by a cylinder/offset-are juncture. The theoretical model employs the full mean compressible Navier-Stokes equations. Several turbulence closures are employed, with particular emphasis placed on predictions obtained with a two-equation k-² model. The calculations are validated by comparison with a range of qualitative and quantitative data. The ow eld is characterized by several of the complex features associated with three-dimensional separation. The surface pattern exhibits an intricate sequence of critical points and is analyzed in terms of its topological portrait through comparison with experimental observations. Fluid separates around the entire periphery upstream of the juncture. Near the upper symmetry plane, this separating uid rolls up to form a horseshoe-like vortical structure. The legs of this structure wrap around the juncture and are turned streamwise near the lower symmetry plane. In conjunction with the displaced oncoming boundary-layer uid, a dual scroll-like structure is observed straddling the lower symmetry plane. Nomenclature BB = Baldwin-Barth turbulence model BL = Baldwin-Lomax turbulence model C f = skin-friction coef cient I L ; J L ; K L = numbers of points in » ,´, and directions, respectively k = turbulence kinetic energy LC = line of coalescence LD = line of divergence M1; M2; M3 = mesh designator N = nodal point or focus on surface NC = node on centerline NPBL = number of mesh points in the incoming boundary-layer n = nodal point or focus on symmetry plane S = saddle point on surface SA = Spalart-Allmaras turbulence model SEP = separatrix s = saddle point on symmetry plane u; v; w = Cartesian velocity components u µ = velocity component in µ direction x; r; µ = cylindrical coordinates measured with reference to cylinder axis x; y; z = Cartesian coordinates y C= distance normal to surface in wall units 1 = physical spacing normalized by ± cm ± = incoming boundary-layer thickness, 1.1 cm ² = turbulence energy dissipation µ = angle in degrees »;´;= computational coordinates