Calculation of wave-induced turbulent flows in estuaries

The k-ε turbulence model which relates the eddy viscosity to turbulent kinetic energy, k, and to the rate of its dissipation, ε, and determines the distribution of these two quantities from modeled transport equations, is employed in calculating the vertical structure of wave-induced turbulent flows in two-dimensional estuaries. The empirical constants in this model are given the standard values cited in the literature and used successfully for calculating a large variety of steady flows; they are not tuned to the oscillating flows. The free surface elevation and the eddy-viscosity distribution are also calculated as a part of the solution. First, calculations performed for oscillatory laminar flows are compared with analytic solutions to ensure the proper performance of the numerical scheme. The turbulent flow in a laboratory-estuary model with one end closed, and in the Humber Estuary is simulated with the numerical model, and the results are compared with the corresponding flume and field measurements. The influence of frequency and roughness is thereby investigated. The results indicate that the time and space variation of the velocity field and the phase lag between the surface slope and the horizontal velocity can be predicted satisfactorily in wave-induced turbulent flows.