An analysis of horizontal dispersion due to the drift current with an Ekman layer |
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| Authors: | Hidekazu Yasuda |
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| Institution: | (1) Chugoku National Industrial Research Institute, Hiro-Suehiro, 737-01 Kure, Japan;(2) Present address: National Fisheries University, 2-7-1 Nagata-Honmachi, Shimonoseki, 759-6595 Yamaguchi, Japan |
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| Abstract: | An analytical method for describing horizontal matter dispersion in shear currents is presented using a tensor expression
from the point of view that matter dispersion due to the shear effect should be one of the principal mixing dilution processes.
Although the behavior of horizontal dispersion is considerably more complicated than common longitudinal dispersion, the present
study elucidates the vertical structure of dispersion and the dispersing process from the initial to the stationary stage,
besides the usual depth-averaged dispersion coefficient at the stationary stage. As one of the typical applications of horizontal
dispersion, dispersion due to the pure drift current with an Ekman layer is examined theoretically using the present method.
This examination reveals that the displacement of the centroid and the major axis of dispersion are twisted in the vertical
direction more than the direction of the current vector forming the Ekman spiral; that the variance increases in proportion
to the third power of the elapsed time; and that the dispersion coefficient at the stationary stage remains constant, independent
of the depth normalized by an Ekman layer thickness. Such dependence of the dispersion coefficient in the steady current is
shown to be different from that in the oscillatory current, which is inversely proportional to the depth normalized by a Stokes
layer thickness. This is considered to be induced by the difference of the vertical profiles of the first order moment in
both currents, that is, the shear region of the first order moment is restricted around the floor by the alternation of the
current shear in the oscillatory current while it is diffused in the whole depth in the steady current. |
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| Keywords: | Horizontal dispersion dispersion coefficient tensor the drift current an Ekman layer |
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