Experiments on standing waves in a rectangular tank with a corrugated bed

Abstract

An experimental investigation of resonant standing water waves in a rectangular tank with a corrugated bottom is reported. The study was stimulated by the theory of Howard & Yu (J. Fluid Mech., vol. 593, 2007, pp. 209-234) predicting the existence of normal modes that can be significantly affected by Bragg reflection/scattering. As a result, the amplitude of the standing waves (normal modes) varies exponentially along the entire length of the tank, or from the centre out in each direction, depending on the phase of the corrugations at the tank endwalls. Experiments were conducted in a 5 m tank fitted with a sinusoidal bottom with one adjustable endwall. Waves were excited by small-amplitude sinusoidal horizontal movement of the tank using an electrical motor drive system. Simultaneous time-series data of standing oscillations were recorded at well-separated positions along the tank to measure the growth in amplitude. Waveforms over a section of the tank were filmed through the transparent acrylic walls. Except for very shallow depths and near the tank endwalls, the experimental measurements of resonant frequencies, mean wavelengths, free-surface waveforms and amplitude growth are found in essential agreement with the Bragg resonant normal mode theory.

Experiments on the synchronous sloshing in suspended containers described by shallow-water theory

“…The bifilar suspension system was constructed using three equal length 1/16-inch steel wire ropes with compression eyelet sleeves. Opposite ends of the eyelets were inserted into assemblies designed to house two SR3-ZZEEC Boca bearings separated to accommodate the eyelets using a shoulder bolt; a detailed sketch of the bearing assemblies may be found in Weidman et al (2015). One wire was located at the center front of a container and the two other wires were symmetrically disposed aft of the container.…”

Linear waves in two-layer fluids over periodic bottoms

“…In applying this work to a confined, continuously stratified sea, the present two-layer problem requires modification by adding (1) vertical sidewalls, as for the surface wave problem in Howard & Yu (2007) and Weidman et al (2015), (2) slopes to these sidewalls and (3) multiple layers. Three comments can be made regarding these additions.…”

“…Application to confined fluid domains is, even for the surface wave problem, non-trivial. It requires finding an appropriate combination of wave and evanescent modes (which together constitute a complete basis and are provided by Yu & Howard (2012) for a generally periodic bed), such that the impermeability at the side walls (lateral boundaries) can be satisfied (Weidman et al 2015). Before addressing this issue in layered systems, the existence of a similar, complete basis needs to be investigated.…”

“…Even with the restriction to linear dynamics, there are few exact analytical solutions but a broad range of approximated theories, most of which exploit the inhomogeneities of the medium by considering gentle slopes, small amplitudes or abrupt changes in bottom topographies. The complexity and difficulty in this type of problems arise in the intermediate case, where wavelength, depth and bottom variations have comparable scales, making the inhomogeneity of the medium neither gradual nor small nor localized (Rhines & Bretherton 1973;Weidman et al 2015).…”

“…The theory provides a set of exact linear modes for periodic bottoms that is analogous to the set of propagating and evanescent waves on a horizontal flat bed, becoming the second known complete basis for water waves. Applications have been made, demonstrating that this set of Floquet modes can indeed be used to construct solutions to various boundary value problems involving finite domains of an undulating bottom (Yu & Zheng 2012;Weidman et al 2015).…”