Derivation of solute-transport equations for a turbulent natural-channel flow

The continuity equation of water and the convection-diffusion equation for a solute are derived by use of an orthogonal curvilinear (natural) coordinate system, which follows the meandering and irregular pattern of natural channel geometry. The solute is assumed to be neutrally buoyant, conservative, and passive. The three-, two-, and one-dimensional equations derived herein represent one of the most satisfactory descriptions of solute transport by turbulent flow in a natural channel.