On Wave-Driven “Shingle” Beach Dynamics in a Table-Top Hele-Shaw Cell

Abstract

The primary evolution of beaches by wave action takes place during storms. Beach evolution by non-linear breaking waves is 3D, multi-scale, and involves particle-wave interactions. We will show how a novel, three-phase extension to the classic "Hele-Shaw" laboratory experiment is designed to create beach morphologies with breaking waves in a quasi-2D setting. Idealized beaches emerge in tens of minutes due to several types of breaking waves, with about 1s periods. The thin Hele-Shaw cell simplifies the inherent complexity of three-phase dynamics by reducing the turbulence. Given the interest in the Hele-Shaw table-top demonstrations at ICCE2014, we will also discuss how different versions of the Hele-Shaw cell have been constructed. Construction can be inexpensive thus yielding an accessible and flexible coastal engineering demonstration as well as research tool. Beach evolution is sufficiently fast and can start very far from equilibrium, allowing an unusually large dynamical range to be investigated.

Variational Water Wave Modelling: from Continuum to Experiment

“…We use this expansion in the variational principle (26) and retain terms up to order O( 2 µ, 3 ). After integration in z, the resulting leading-order principle becomes…”

“…It adds explicit time-dependence to the principle. In Bokhove et al [3] and Thornton et al [17], this was investigated for water wave dynamics in a vertical Hele-Shaw cell with a moving interface between water and air, concerning damped motion with a wave pump and with damped wave sloshing, respectively. The Hele-Shaw cell is a narrow wave tank with a wave-maker, e.g., it has a width of 2 mm, length of 0.6 to 1 m, and depth of circa 0.1 m, between two closely spaced glass plates.…”

“…The bulk damping due to the dominant friction against these glass plates leads to an exponential time dependent factor e γt in the variational principle. Its inverse expresses the exponential decay due to friction with γ > 0 proportional to both the viscosity and the square inverse of the gap width between the glass plates (e.g., Bokhove et al [3]).…”

“…While some techniques have been published before [3,6,7,17], the derivation of the modified Benney-Luke equations, the systematic way to lift non-autonomous to autonomous variational principles in time, and the use of this lifting in finding extended time discretisations are novel. Also new is the soliton splash simulation.…”