Results and the database from a direct numerical simulation of turbulent flow in a square duct are used to investigate the dissipation processes in a flow with two inhomogeneous directions. First, the effect of the corner on small-scale topological patterns is identified, and second, information for the assessment and development of turbulence closure models is provided by calculating all of the terms in the transport equations for the turbulent dissipation rate and enstrophy. It is shown that, with the exception of two production terms, these budgets have the same dynamics down to the wall. The effects of the corner are manifested by vanishing turbulence production in the viscous sublayer very close to the corner, and reduced dissipation of turbulent vorticity along the diagonal, farther away from the corner. IRECT numerical simulation (DNS) of simple shear flows has proven to be an effective and important tool for studying turbulence structures and near-wall effects.1 The present paper extends this idea to complex turbulent flows by using the database from a recent DNS of turbulent square-duct flow2 to investigate the influence of the corner on the structure of small-scale turbulence. These effects are manifested by vanishing turbulence production as well as reduced turbulence energy and dissipation along the diagonal (corner bisector).2 The imbalance between the turbulence along the corner bisector and the midchannel (wall bisector) creates the stress-driven secondary flow, defined as secondary flow of the second kind.24 Of particular interest in this paper is the turbulence dissipationrate (and enstrophy) budget because the dissipation rate contributes significantly to the Reynolds stress balance.3 An order-of-magnitude analysis of the dissipation process is provided by Tennekes and Lumley5 by estimating the terms in the turbulence enstrophy budget. Mansour et al.6 presented all of the terms in the dissipation-rate budget from the DNS of turbulent channel flow and demonstrated the significance of these terms in a wall-bounded flow. The work of Rodi and Mansour7 also indicates the importance of all terms in the dissipation-rate budget near the wall, including the transport and diffusion. Because of their connection to the dissipation processes,8 the small-scale topological structures also are considered. By displaying scatter plots of the invariants of the local deformation tensor obtained in the homogeneous direction and in time, we can deduce the preferred small-scale topologies and dissipation production processes in the square duct. The present results document all of the terms in the turbulence dissipation rate and enstrophy equations that are essential for both the modeling of Reynolds stress transport equations and the development of subgrid-scale models.