Evolution of basic equations for nearshore wave field
Related Experiment Video
Updated: May 15, 2026

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
Published on: February 13, 2018
1Graduate School of Frontier Sciences, The University of Tokyo, Chiba, Japan. isobe@k.u-tokyo.ac.jp
Abstract:
In this paper, a systematic, overall view of theories for periodic waves of permanent form, such as Stokes and cnoidal waves, is described first with their validity ranges. To deal with random waves, a method for estimating directional spectra is given. Then, various wave equations are introduced according to the assumptions included in their derivations. The mild-slope equation is derived for combined refraction and diffraction of linear periodic waves. Various parabolic approximations and time-dependent forms are proposed to include randomness and nonlinearity of waves as well as to simplify numerical calculation. Boussinesq equations are the equations developed for calculating nonlinear wave transformations in shallow water. Nonlinear mild-slope equations are derived as a set of wave equations to predict transformation of nonlinear random waves in the nearshore region. Finally, wave equations are classified systematically for a clear theoretical understanding and appropriate selection for specific applications.(Communicated by Kiyoshi HORIKAWA, M.J.A.).
Related Concept Videos
Equations of Wave Motion
Velocity and Acceleration of a Wave
The velocity of the particles can be obtained by taking the partial derivative of the position equation with respect to time. We can...
Electromagnetic Wave Equation
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations: What...
Wave Parameters
Propagation of Waves
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
Graphing the Wave Function

