Water Wave Modeling Using Complete Solution of Laplace Equation

Abstract

Analytical solution of Laplace equation using variable separation method, consists of two velocity potentials. However, only one component has been used. This research used both velocity potential equation components. With the potential equation, water wave surface equation and the related wave constants were formulated using kinematic free surface boundary condition and surface momentum equation. The characteristic of water wave surface that was produced was observed, both in deep water and shallow water.

Applying Weighted Taylor Series on Time Series Water Wave Modeling

“…This value is constant for a given accuracy level 𝜀, unaffected by wavelength or wave period. As an example, calculations for a sloping bottom with nonuniform wavelength are presented in Table (5), where a wave period of 8 sec is used, and the grid calculation uses 𝜀 = 0.02.…”

“…In Table (5), 𝛿𝑡 is constant, while 𝛿𝑡 is not, but the resulting Courant number, is constant. The Finite Difference Method is formulated using a second-order Taylor series, where the Taylor series is truncated to second order only.…”

Development of Linear Water Wave Dispersion Equation using Critical wave Steepness Criteria

“…Analytically (using the Taylor series), were obtained = 3. However, if the = 3is used, a complete momentum equation should be used, Hutahaean (2019).…”

“…In the case of non-linear assumptions, namely the assumption of small amplitude and long wave, the nonlinear term equation in the momentum equation of ( 20) is also done. The formulation is not written here because the limited space, where the formulation can be seen in Hutahaean (2019). The nonlinear dispersion equation in deep water is, where is wave amplitude, = 3.0 while = 1.63.…”

“…The nonlinear dispersion equation in deep water is, where is wave amplitude, = 3.0 while = 1.63. Actually is function of , Hutahaean (2019), where for = 3then = 1.63will be obtained.…”