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Application of power law to vertical distribution of longshore currents

Zhang, Zhen-wei, Zou, Zhi-li
Water Science and Engineering 2019
beaches, field experimentation, spatial distribution
The vertical profiles of longshore currents have been examined experimentally over plane and barred beaches. In most cases, the vertical profiles of longshore currents are expressed by the logarithmic law. The power law is not commonly used to describe the profile of longshore currents. In this paper, however, a power-type formula is proposed to describe the vertical profiles of longshore currents. The formula has two parameters: the power law index (a) and the depth-averaged velocity. Based on previous studies, power law indices were set as a = 1/10 and a = 1/7. Depth-averaged velocity can be obtained through measurement. The fitting of the measured velocity profiles to a = 1/10 and a = 1/7 was assessed for the vertical longshore profiles. The vertical profile of longshore currents is well described by the power-type formula with a = 1/10 for a plane beach. However, for a barred beach, different values of a needed to be used for different regions. For the region from the bar trough to the offshore side of the bar crest, the vertical profiles of longshore currents given by the power-type formula with a = 1/10 and a = 1/7 fit the data well. However, the fit was slightly better with a = 1/10 than that with a = 1/7. For the data over the trough region of cross-shore distribution of the depth-averaged longshore currents, the power formula with a = 1/3 provided a good fit. The formulas with a = 1/10 and a = 1/7 were further examined using published data from four sources covering laboratory and field experiments. The results indicate that the power-type formula fits the data well for the laboratory and field data with a = 1/10.