Author(s): Georgios M. Horsch

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Keywords: Density currents; sloping bottom; scales; similarity; initial conditions; fully developed state

Abstract: The structure of steady, laminar, two-dimensional density currents, emanating from a slot of height h 0 and flowing down an incline, is examined. It is shown that neglecting the stream-wise buoyancy-induced pressure gradient is compatible with the boundary layer approximation. Two regions are distinguished: the developing region, where the growth of the current is determined by its initial conditions, and the fully developed region where it is independent of them. The nature of the developing region is shown to depend on the parameter Re 0 tan2 θ /Ri 0, where Re 0 and Ri 0 are the entrance Reynolds and Richardson numbers, respectively, and θ is the angle of inclination, and its length scales are determined. In the fully developed region, balance is found to be between buoyancy and viscous forces if the Schmidt number, Sc, is larger than one, and between the buoyancy and inertia forces if Sc is less than one. The boundary layer thickness as well as the velocity and salinity scales are determined, and using these scales similarity solutions are found. The similarity shape functions are found to depend strongly on Sc. Finally, the resulting scales are found to be compatible with the outcome of two-dimensional numerical simulations. These simulations further indicate that the asymptotic progression towards the similarity profiles is increasingly slow with increasing Sc number, so that some features of the similarity solutions may never be fully attained in experimental tanks of restricted length.

DOI: https://doi.org/10.1080/00221686.2004.9728380

Year: 2004