Wave height

About: Wave height is a research topic. Over the lifetime, 5920 publications have been published within this topic receiving 100257 citations.

Significant Wave Height for Shallow Water Design

Abstract: Wave height parameters used in coastal and ocean engineering are grouped into three classes according to their definition bases: height statistics, energy, and monochromatic. Parameters within each class are easily interrelated for most engineering purposes. However, parameters from different classes are difficult to interrelate, particularly for shallow water applications where waves are near breaking. The often-used parameter “significant wave height” has traditionally been based on height statistics but many modern estimates are based on wave energy. A simple empirical method is developed to relate statistical and energy based significant height estimates. The method is developed with CERC laboratory flume data from a 1:30 plane slope, two samples of field data, and stream function wave theory. Since the two significant height estimates differ by over 40% in some laboratory cases, engineers should clearly recognize the distinction between them.

Branch Cuts of Stokes Wave on Deep Water. Part I: Numerical Solution and Padé Approximation

Abstract: Complex analytical structure of Stokes wave for two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth is analyzed. Stokes wave is the fully nonlinear periodic gravity wave prop agating with the constant velocity. Simulations with the quadruple (32 digits) and variable precisions (more than 200 digits) are performed to find Stokes wave with high accuracy and study the Stokes wave approaching its limiting form with radians angle on the crest. A conformal map is used that maps a free fluid surface of Stokes wave into the real line with fluid domain mapped into the lower complex half-plane. The Stokes wave is fully characterized by the complex singularities in the upper complex half-plane. These singularities are addressed by rational (Pade) interpolation of Stokes wave in the complex plane. Convergence of Pade approximation to the density of complex poles with the increase in the numerical precision and subsequent increase in the number of approximating poles reveals that the only singularities of Stokes wave are branch points connected by branch cuts. The converging densities are the jumps across the branch cuts. There is one square-root branch point per horizontal spatial period λ of Stokes wave located at the distance from the real line. The increase in the scaled wave height from the linear limit to the critical value marks the transition from the limit of almost linear wave to a strongly nonlinear limiting Stokes wave (also called the Stokes wave of the greatest height). Here, H is the wave height from the crest to the trough in physical variables. The limiting Stokes wave emerges as the singularity reaches the fluid surface. Tables of Pade approximation for Stokes waves of different heights are provided. These tables allow to recover the Stokes wave with the relative accuracy of at least 10−26. The number of poles in tables increases from a few for near-linear Stokes wave up to about hundred poles to highly nonlinear Stokes wave with