AN ACCESSIBLE POTENTIAL ENERGY BUDGET (APEB) FOR DENSITY CURRENTS IN STRATIFIED DAM RESERVOIRS

Abstract

Density currents in stratified dam reservoirs play a central role in sediment transport, water quality, and reservoir operation, yet existing models primarily describe how such currents evolve once established rather than whether they can persist as coherent flows. Classical gravity-current formulations rely on local force balances, geometric intrusion criteria, or empirical entrainment closures, and do not explicitly quantify the energetic feasibility of sustaining a density current in a stratified environment.

In this study, we introduce an Accessible Potential Energy Budget (APEB) framework that explicitly links reservoir stratification to the mechanical energy available to drive and maintain density currents. The word “budget” is used in a strict physical and energetic sense, accounting of sources and sinks of mechanical energy derived from buoyancy. Thus, the term "Budget" used in this study should be understood as "Balance, Accounting, or Quantification”. Starting from classical layer-averaged formulations for mass, buoyancy dilution, and momentum, we identify the neutral depth as a stratification constraint and define a new quantity: the accessible buoyancy work per unit mass, obtained by integrating the ambient density profile along the vertical adjustment path of the inflow. This quantity converts a measured density stratification into an energetic scale directly comparable to dissipation processes.

By multiplying the accessible buoyancy work by the inflow mass flux, we obtain a buoyancy-derived power input that represents the maximum mechanical energy available from stratification. We then introduce an explicit decomposition of the dissipation demand, including (1) internal turbulent mixing and entrainment power, (2) bed-friction losses, and (3) interfacial drag with the ambient fluid. The resulting APEB persistence criterion states that a coherent density current can exist only if accessible buoyancy power exceeds the total dissipation demand.

A worked numerical example using real reservoir temperature-depth data demonstrates how the framework is applied in practice. The example shows how the shape of the ambient density profile strongly controls the accessible energy through a dimensionless stratification factor, explaining why currents with identical inflow density and discharge may persist in some reservoirs but collapse rapidly in others.

The proposed framework extends classical density-current theory by introducing an explicit energetic gatekeeper for current formation and persistence. It unifies underflows and interflows within a single energy-based perspective and provides a physically interpretable criterion that can be evaluated directly from field data, offering new predictive capability for reservoir management and environmental hydraulics.