A Monte Carlo Model Of Particle Dispersion Due To Wave Motion

Abstract

A three-dimensional small-scale probabilistic model of particle dispersion was developed to correlate the wave conditions with the depth of particle penetration and the horizontal area covered by particle motion. A particle transport model was used to simulate the upper surface layer motions of a large number of independent particles. These particles were driven by residual currents, wave orbital motion, wave turbulence, and buoyant, gravitational, and drag forces. Velocity components representing each of these motions in three-dimensions were linearly combined and the resultant velocities were used to move the particles. Wave velocity data, which had been modified to account for the depth of the specific particle, was used to represent the wave orbital motions. This data typified various wave conditions ranging from a building sea with a predominant period to a heavy sea and finally small waves superimposed upon swell. The mean range of a particle's motion was determined for each of several cases with different wave conditions and non-dimensionalized using the respective significant wave heights. The relationships developed between the mean range of a particle motion and the wave parameters were: for the vertical direction after 10.0-12.0 significant wave heights mean depth reached = 2.0- <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20.0^{-0.115time}</tex> for the horizontal direction aligned with the predominant direction of wave motion after 2.0 significant wave periods mean distance spanned = 0.14 time + 1.3 for the horizontal direction perpendicular to the predominant direction of wave motion after 3.0 significant wave periods mean distance spanned = 0.09 time + 1.0. The depth and distance must be normalized by the significant wave height and the time by the significant wave period. A mixing depth of 3 to 4 significant wave heights is suggested for the extent of maximum particle penetration and 1 to 2 significant wave heights for the average particle penetration.