A dispersion equation and dispersion coefficient for material transport in Inland Seas

Abstract

To analyse material transport in inland seas, a horizontal two-dimensional dispersion equation is derived, and the dispersion coefficient due to the combined effect of vertical turbulent mixing and vertical shear of both a steady current and a tidal current is studied. In the present study, the assumption that velocity is uniform in horizontal planes is not necessary, and velocity has a free vertical profile; thus the dispersion coefficient formulated is general, and is represented by a tensor of the second order. The properties of the dispersion coefficient in the horizontal two-dimensional dispersion model are also investigated, and it is shown that the time-averaged dispersion coefficient due to the tidal current over a tidal period is approximately half that due to the steady current, if the velocity amplitude and the vertical profile of the tidal current are the same as those of the steady current (a similar result was presented byBowden (1965) for horizontal one-dimensional models). Finally, the dispersion coefficient in Hiuchi-Nada (Hiuchi Sound) in the central part of the Seto Inland Sea is evaluated by using the model. The values of the dispersion coefficient in that region range from 103 cm2 s−1 to 105 cm2 s−1 when vertical turbulent diffusivity is taken to be 50 cm2 s−1.