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and to avoid drawing attention away from the overall desire to find a rough estimate for the mean velocities, detailed "undertow" velocity profile models will not be used. However, simple calculations can still be done to give an estimation of the strength of mass transport and the return flow based on the amount of flow going over the island. This modeling effort is consistent with the level of laboratory current data collected.
Mass transport calculations for this experiment are based on linear wave theory and Svendsen's (1984b) mass flux equation for non-overwash conditions. In linear wave theory, mass transport per unit width is defined as:
M = E (5.1)
C
where E is defined as the wave energy and C the wave celerity. It is considered a nonlinear quantity because the wave height is raised to the second power in the energy term. However, it is derived from linear wave theory. There are two approaches for determining mass transport in linear theory: Eulerian and Lagrangian. The Eulerian frame will be utilized since it is consistent with the Eulerian velocity data taken by the current meter during each trial.
Calculations of mass transport using linear wave theory will be performed at and prior to the break point. The nonlinearities and the additional mass flux in the breaking waves warrant a separate formulation. Values of mass transport in deep water do not have a significant bearing on the sediment transport processes and therefore will not be studied.
Using the measured wave heights, the mass transport for each of the six trials was calculated. Since there are no current measurements over the island for trials 2 and 6, these trials were not used. The mass transport values were then converted to volumetric units by multiplying these values with the width of the tank and then dividing them by the density of the water.