Corrected Wavemaker Theory, Momentum Flux and Vorticity

TL;DR

This paper identifies flaws in traditional wavemaker theory due to an unjustified assumption, introduces an exact microjet-based wavemaker model, and clarifies momentum flux and vorticity effects in wave generation.

Contribution

It presents a corrected wavemaker theory with an exact microjet model, clarifies momentum flux contributions, and analyzes vorticity effects in realistic wave generation.

Findings

Traditional wavemaker theory has an unjustified assumption.

The microjet model allows exact force and flux calculations.

Vorticity sources significantly affect fluid motion in wavemakers.

Abstract

The usual wavemaker theory hides an unjustified integration constant assumption that renders it invalid. We discuss some surprising subtleties of momentum flux in infinite waves, packets and some counterintuitive examples where "hidden" flux contributions can arise. From here, we construct an ideal wavemaker that builds Airy waves from a series of microjets that allows an exact calculation of the forces on boundaries. This allows us to also compute the fluxes of all conserved quantities directly and rule out some of these hidden contributions to momentum flux. We then discuss some realistic flapper wavemakers and the trouble vorticity sources can create in the resulting fluid motion. Along the way we present a completely local derivation of the group velocity using fluxes.