Stream function solutions for steady water waves

Two stream function solutions for steady two-dimensional water waves are reviewed. The algorithm developed by Dalrymple (1974, Proc. 6th Conf. Offshore Tech., pp. 843–856) and used by Hudspeth and Slotta (1978, Proceedings of the American Society of Civil Engineers,104, 319–334) is compared with the algorithm developed by Chaplin (1980, Coastal Engineering,3, 179–205). By examining more closely the near-breaking wave conditions, it is shown that celerity does not increase monotonically with increasing dimensionless wave steepness. Numerical comparisons between the two algorithms indicate that the Dalrymple algorithm is more accurate for near-breaking waves and requires less computer programming effort. Neither algorithm appears to be able to predict breaking wave conditions as accurately as the Cokelet (1977, Philosophical Transactions of the Royal Society of London,A286, 183–230) algorithm. Numerical comparisons of the Dalrymple free surface error convergence criteria with the Chaplin significant figures convergence criteria indicate that the free surface error convergence criterion is more consistent for stream function representations.