By trapping sediment in reservoirs, dams interrupt the continuity of sediment transport through rivers, resulting in loss of reservoir storage and reduced usable life, and depriving downstream reaches of sediments essential for channel form and aquatic habitats. With the acceleration of new dam construction globally, these impacts are increasingly widespread. There are proven techniques to pass sediment through or around reservoirs, to preserve reservoir capacity and to minimize downstream impacts, but they are not applied in many situations where they would be effective. This paper summarizes collective experience from five continents in managing reservoir sediments and mitigating downstream sediment starvation. Where geometry is favorable it is often possible to bypass sediment around the reservoir, which avoids reservoir sedimentation and supplies sediment to downstream reaches with rates and timing similar to pre-dam conditions. Sluicing (or drawdown routing) permits sediment to be transported through the reservoir rapidly to avoid sedimentation during high flows; it requires relatively large capacity outlets. Drawdown flushing involves scouring and re-suspending sediment deposited in the reservoir and transporting it downstream through low-level gates in the dam; it works best in narrow reservoirs with steep longitudinal gradients and with flow velocities maintained above the threshold to transport sediment. Turbidity currents can often be vented through the dam, with the advantage that the reservoir need not be drawn down to pass sediment. In planning dams, we recommend that these sediment management approaches be utilized where possible to sustain reservoir capacity and minimize environmental impacts of dams.

The topological pressure is defined for sub-additive potentials via separated sets and open covers in general compact dynamical systems. A variational principle for the topological pressure is set up without any additional assumptions. The relations between different approaches in defining the topological pressure are discussed. The result will have some potential applications in the multifractal analysis of iterated function systems with overlaps, the distribution of Lyapunov exponents and the dimension theory in dynamical systems.

Abstract. In this paper, using thermodynamic formalism for the sub-additive potential, upper bounds for the Hausdorff dimension and the box dimension of non-conformal repellers are obtained as the sub-additive Bowen equation. The map f only needs to be C 1 , without additional conditions. We also prove that all the upper bounds for the Hausdorff dimension obtained in earlier papers coincide. This unifies their results. Furthermore we define an average conformal repeller and prove that the dimension of an average conformal repeller equals the unique root of the sub-additive Bowen equation.

Given a non-conformal repeller Λ of a C 1+γ map, we study the Hausdorff dimension of the repeller and continuity of the sub-additive topological pressure for the sub-additive singular valued potentials. Such a potential always possesses an equilibrium state. We then use a substantially modified version of Katok's approximating argument, to construct a compact invariant set on which the corresponding dynamical quantities (such as Lyapunov exponents and metric entropy) are close to that of the equilibrium measure. This allows us to establish continuity of the sub-additive topological pressure and obtain a sharp lower bound of the Hausdorff dimension of the repeller. The latter is given by the zero of the super-additive topological pressure. 0