Project: Dispersion of fifth order stokes waves

Stokes wave theory is particularly useful in the design of offshore structures as it helps in determining the wave loads on a structure. In order to estimate the design loads for an offshore structure, two parameters – wavelength (L) and the amplitude parameter (a) of gravity waves are needed. These two parameters are obtained by solving two coupled nonlinear fifth order stokes equations.

The attached manuscript provides a numerical method to solve this set of stokes equations iteratively. Develop an R code and solve the system of equations to determine L and a. 

Given: water depth (d) = 9 m, Wave period (T) = 7 sec, Crest to trough height (H) = 5.67 m. 

Initial Guesses (L0,a0) = (60, 2.5)