Stream Function Wave Theory with Profile Constraints

Abstract

Numerical stream function wave theory with inclusion of inequality profile constraints is presented in this paper. This theory is applicable to waves in shallow to intermediate to deep waters with a coflowing Eulerian current or Stokes mass flux. Numerical algorithm is modified and expanded from previous code with two equality profile constraints, while the changes are kept to a minimum; i.e., the system unknowns are still solved in a least‐squares approximation to a transformed penalty function. This modified numerical stream function wave theory avoids the invalid triple‐crested wave predictions in shallow waters, while its solution characteristics in intermediate to deep waters remain the same as the previous least‐squares algorithms.