Svendsen's equation will be utilized in determining the mass transport values in the surf zone and over the island. His theory is based on the assumption that a breaking wave can be divided into two sections: the surface roller of the breaking wave and the water column below the roller. Accounting for the fact that the total mean volume flux is zero for non-overwashing cases, the total volume of water created by mass transport must be returned by a equal but opposite return flow volume. Using the notation from his roller assumptions, Svendsen's solved for the mass transport volume as shown in equation 5.2.
Q f (B + A d). (5.2)
Q =- C 2 "' L h
where
" C = speed of wave propagation.
" Bo = nondimensional time averaged energy flux.
* A = area of the roller and can be approximated as A-0.9W.
* d = depth of the water from the bottom to the trough level. L = wave length
h = water depth at the mean water line.
Several assumptions were made for the variables in Svendsen's equation. d, was approximated by taking the depth at the wave height measurement and subtracting the value of the wave height divided by two. B. was determined by taking the average of the I1-dLo values from all the measurements and finding the corresponding value from the graph in Svendsen (1984b). This value was estimated at B. = 0.07.
Substituting in the values for the wave height and the variables above, the mass transport for the surf zone and island was calculated. In order to equate this mass transport with the mass transport solved using linear wave theory, the value was multiplied by the tank width.