Abstract

A mathematical model describing the vertical structure of a partially mixed estuary has been developed, based on the laterally integrated momentum, continuity and salt balance equations. The dominant Reynolds stress and the vertical turbulent transport of salt were modelled by an effective diffusion hypothesis in which the eddy coefficients were determined from the solution of the turbulence energy equation. The effects of density stratification on the turbulence energy, the eddy viscosity and the turbulent Schmidt number were included. The model was applied to an idealized straight rectangular channel similar in dimensions to the Rotterdam Waterway. The dominant Reynolds stress and the turbulence energy distributions were calculated, in addition to the surface elevation, velocity and salinity distributions. Observations of an equilibrium turbulence structure near mid-tide and an inactive component of the turbulence energy were confirmed by the model. The dispersion coefficient was identified as an important parameter in quantifying both the horizontal and vertical structure of the flow and salinity distributions in laterally integrated representations of partially mixed estuaries.

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