Good quality model testing requires an understanding of the wave tank environment, most importantly the wave maker and the beach. A wave maker is similar to most other structures moving in the ocean, and is actually very similar to a wave energy converter. For most applications, a simple closed-analytical theory describes the wave maker to good accuracy. This theory is based on the assumptions of inviscid, incompressible and irrotational flow. A velocity potential can be formulated that satisfies the following boundary conditions:

Here, ϕ(x, z) is the velocity potential in the coordinate system (x, z), and the horizontal (u) and vertical (w) velocities can be expressed as

u = ∂ϕ/∂x

and

w = ∂ϕ/∂z

The general form of the velocity potential for the wave maker solution is

ϕ(x, z, t) = A₀cosh k₀(h + z)sin (k₀x − ωt) + ∑_{j = 1…∞}C_jexp ( − k_jx)cos k_j(h + z)cos (ωt)

The first part of this solution represents a progressive water wave, and the second part represents so-called evanescent modes. The evanescent modes are also often referred to as standing wave modes. The wave numbers k₀ and k_j can be found as the solution to two forms of dispersion equations, which are illustrated below.

The coefficients c_j can also be obtained analytically (see our publications for detail or contact us), with a typical solution patters as illustrated below

In the above figure, the horizontal axis represents a non-dimensional water depth. In shallow water (left of figure), a typical wave maker produces mostly progressive waves (ϕ_p). In deeper water (right of figure), the wave maker also produces a large amount of evanescent waves.

First, with little evanescent wave modes, the wave elevation (normalized by the progressive wave amplitude) looks fairly consistent: