A Consistent Nonlinear Frequency Domain Model for Finite Depth Ocean Wave Propagation
Abstract
A new nonlinear second-order frequency-domain model based on the mild-slope equation is outlined. The model is an enhancement over previous work in that a closer correspondence between scaling of nonlinearity and horizontal variation of bathymetry is made relative to earlier models. This results in additional terms in the nonlinear summation terms of the model, as amplitude gradient terms are required in order to formulate a completely consistent model at second order. From the resulting elliptic model equation, a parabolic approximation is developed in order to efficiently model the equations for most applications. Comparisons between the present model, previously-formulated models, and experimental data show that the present model does evidence improvement in performance over previous, less-consistent models. It is also found that the “phase mismatch,” which arises from the dispersive nature of the resulting equations, can adversely impact performance; this is a potential problem with all models of this sort.
Using a scheme developed for stochastic formulations of these phase-resolved models, a hybrid consistent nonlinear mild-slope equation in frequency-domain is developed. Using this scheme, a newly simplified version of the present model retains quasi-cubic terms having a form of cubic term but originating from triad wave interaction terms is developed. Because of the quasi-cubic nonlinear summation having zero-mismatch, the hybrid model replicates the triad wave-wave interactions more accurately compared to the previous deterministic models.
A higher-order parabolic evolution equation is derived for high accuracy at large wave approach angles. As an alternative, a consistent nonlinear mild-slope equation based on the angular spectrum model is also developed. These two newly developed models are tested for accuracy in describing wave pattern by a refractive focal lens, elliptic shoal, and circular shoal with the several incidence angles. The newly developed models are further examined with field data in order to ensure the models’ capability in simulating two-dimensional irregular wave processes. Lastly, a source term for triad interactions is derived from the present model for implementation into operational phase-averaged wave models.
Citation
Kim, Inchul (2022). A Consistent Nonlinear Frequency Domain Model for Finite Depth Ocean Wave Propagation. Doctoral dissertation, Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /197252.