Probability Distribution of Near-Bed Water Particle Velocity Under Wave Action on a Sandy Beach

Articles in Press

Authors

1 Department of Civil Engineering, Faculty of Engineering, University of Guilan, Guilan, Iran

2 Faculty of Civil Engineering, K.N. Toosi University of Technology, Tehran, Iran

10.22034/ceej.2026.70206.2470

Abstract

This study investigates the most suitable probability distribution function for near-bed water particle velocity under wave action on a sandy beach. Initially, an experimental study was conducted to measure near-bed particle velocities under irregular wave conditions. Based on these measurements, six different probability distribution functions were proposed to characterize particle velocity. Four of these distributions were derived by integrating the probability distribution of wave height with two wave theories: long wave theory and second-order Stokes theory. The remaining two distributions were developed by combining the probability distribution of sea surface displacement with the same wave theories. A detailed comparison between the proposed distributions and the experimental data indicated that the probability distribution based on sea surface displacement, combined with second-order Stokes theory, provides the highest accuracy. This distribution is particularly valuable for practical engineering applications, as it can be derived from readily available sea surface displacement data, which can be easily obtained using standard buoy measurements.

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Journal of Civil and Environmental Engineering

Articles in Press, Accepted Manuscript
Available Online from 28 July 2026

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