Chapter VII
Wave flume
87
This motion describes the displacement of the wave board at a position 𝑧 = 0 and time 𝑡, where
𝑆 represents the amplitude of the motion and 𝜔 represents the angular frequency.
By implementing this sinusoidal motion, the wavemaker can generate waves with controlled
amplitudes and frequencies, enabling precise simulation of various wave conditions in a wave
flume.
Figure VII-1 Two-Dimensional Wave Flume Definition Sketch.
VII.2.2. Mathematical model
The problem can be formulated mathematically as a set of five equations considering an inviscid
and irrotational fluid flow (Steve,1993). These equations are the Laplace equation (Equation
VII-2), along with four auxiliary boundary conditions. These conditions include the bottom
boundary condition (Equation VII-3) , the kinematic and dynamic free surface conditions
(Equation VII-4,Equation VII-5), and the boundary condition at the wavemaker board (Equation
VII-6).
The primary equation used in the mathematical model is the Laplace equation, which governs the
velocity potential (ϕ) in the fluid domain.
𝜕
2 𝜑
𝜕𝑥 2 +
𝜕
2 𝜑
𝜕𝑧 2 = 0
Equation VII-2
𝜕𝜑
𝜕𝑧
= 0, 𝑎𝑡 𝑧 = −ℎ
Equation VII-3