Abstract
The treatment of diffusion due to the tidal current in the near-shore ocean, and the similitude in the hydraulic model experiment are studied.
In broad and shallow tidal bays and in the coastal seawaters near irregular boundaries, horizontal eddy-currents induced geometrically and turbulence caused by their cascading have predominant effect on dispersion of river and waste waters. These turbulent diffusion processes are similarly reproduced in the Froude models of turbulent resume, by adding the similitude for the self-similar structure of the spectral density of turbulence, or the eddy diffusivity. The similitude means to take the scale ratios of the time and the vertical length as the two-thirds power of the scale ratio of the horizontal length.
Similitudes are also derived for the system of the gravitational circulation, the stratification and the salt-mass transport in partially and well-mixed estuaries. Generally, the vertical eddy diffusivity must be exaggerated by a half power of the model distortion externally by some methods of agitation. When the tidal bay is broad and very shallow, the Rayleigh number and the Hansen number are small, and the effect of density current and stratification on the flushing is small. Instead the effect of local eddies, geometrically induced tidal residual circulations become predominant. In this special case, there is no need to satisfy the similitude for density difference and vertical shear effects on dispersion.
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Sugimoto, T. Similitude of the hydraulic model experiment for tidal mixing. Journal of the Oceanographical Society of Japan 30, 260–270 (1974). https://doi.org/10.1007/BF02109669
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DOI: https://doi.org/10.1007/BF02109669