A NEW THEORETICAL ENVELOPE FRAMEWORK IN THE HAMILTONIAN THEORY OF NONLINEAR DEEP- AND FINITE-WATER SURFACE GRAVITY WAVES

An extensive body of literature has addressed the question that how we can accurately and efficiently predict the spatial-temporal evolution of surface gravity waves in the open ocean and coastal waters. The main methods for an answer to it can be partitioned into two groups: (i) theoretical frameworks which make use of Fourier transforms such as a nonlinear Schrödinger (NLS) equation-based model [1], the High-Order Spectral method (HOS) [2,3], and Zakharov integral equations[4,5], and (ii) direct numerical solvers which propose to obtain the numerical solution of the fully nonlinear potential flow equations like OceanWave3D[6], Reef3D[7], and a harmonic polynomial cell method [8]. Generally, the first group has been known to excel at numerical efficiency[9].