Linear theory for single and double flap wavemakers

TL;DR

This paper develops a linear theoretical model for wave generation in hydrodynamic labs using single and double flap wavemakers, deriving relations for wave height and wavemaker stroke to optimize wave production.

Contribution

It introduces a comprehensive linear theory based on dispersive water wave equations for both single and double flap wavemakers, including operational guidelines.

Findings

Derived explicit relations between wave height and wavemaker stroke.

Provided methods for efficient wave generation with minimal disturbances.

Extended the theory to both single-flap and double-flap configurations.

Abstract

In this paper, we are concerned with deterministic wave generation in a hydrodynamic laboratory. A linear wavemaker theory is developed based on the fully dispersive water wave equations. The governing field equation is the Laplace equation for potential flow with several boundary conditions: the dynamic and kinematic boundary condition at the free surface, the lateral boundary condition at the wavemaker and the bottom boundary condition. In this work, we consider both single-flap and double-flap wavemakers. The velocity potential and surface wave elevation are derived, and the relation between the propagating wave height and wavemaker stroke is formulated. This formulation is then used to find how to operate the wavemaker in an efficient way to generate the desired propagating waves with minimal disturbances near the wavemaker.