The longitudinal dispersion due to the shear effect of a current is examined theoretically in the idealized two-dimensional case. This study reveals the process whereby the dispersion reaches a stationary stage after the release of the dispersing substance as an instantaneous line source in steady and in oscillatory currents. In addition, the relation between the stationary dispersion coefficients in steady and oscillatory currents is given analytically. Analysis of the dispersion during the initial stage needs a clear definition of the vertical average of the variance. We can understand the problem of the negative dispersion coefficient, which is obtained by the usual vertical average, through introduction of a new vertical average.
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Hidekazu Yasuda (1984) studied this question.
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