Water wave transmission by an array of floating disks

An experimental validation of theoretical models of transmission of regular water waves by large arrays of floating disks is presented. The experiments are conducted in a wave basin. The models are based on combined potential-flow and thin-plate theories, and the assumption of linear motions. A low-concentration array, in which disks are separated by approximately a disk diameter in equilibrium, and a high-concentration array, in which adjacent disks are almost touching in equilibrium, are used for the experiments. The proportion of incident wave energy transmitted by the disks is presented as a function of wave period, and for different wave amplitudes. Results indicate that the models predict wave energy transmission accurately for small-amplitude waves and low-concentration arrays. Discrepancies for large-amplitude waves and high-concentration arrays are attributed to wave overwash of the disks and collisions between disks. Validation of model predictions of rigid-body motions of a solitary disk are also presented

Seasonal and spatial variations in the ocean-coupled ambient wavefield of the Ross Ice Shelf

© The Author(s), 2019. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Baker, M. G., Aster, R. C., Anthony, R. E., Chaput, J., Wiens, D. A., Nyblade, A., Bromirski, P. D., Gerstoft, P., & Stephen, R. A. Seasonal and spatial variations in the ocean-coupled ambient wavefield of the Ross Ice Shelf. Journal of Glaciology, 65(254), (2019): 912-925, doi:10.1017/jog.2019.64.The Ross Ice Shelf (RIS) is host to a broadband, multimode seismic wavefield that is excited in response to atmospheric, oceanic and solid Earth source processes. A 34-station broadband seismographic network installed on the RIS from late 2014 through early 2017 produced continuous vibrational observations of Earth's largest ice shelf at both floating and grounded locations. We characterize temporal and spatial variations in broadband ambient wavefield power, with a focus on period bands associated with primary (10–20 s) and secondary (5–10 s) microseism signals, and an oceanic source process near the ice front (0.4–4.0 s). Horizontal component signals on floating stations overwhelmingly reflect oceanic excitations year-round due to near-complete isolation from solid Earth shear waves. The spectrum at all periods is shown to be strongly modulated by the concentration of sea ice near the ice shelf front. Contiguous and extensive sea ice damps ocean wave coupling sufficiently so that wintertime background levels can approach or surpass those of land-sited stations in Antarctica.This research was supported by NSF grants PLR-1142518, 1141916, 1142126, 1246151 and 1246416. JC was additionally supported by Yates funds in the Colorado State University Department of Mathematics. PDB also received support from the California Department of Parks and Recreation, Division of Boating and Waterways under contract 11-106-107. We thank Reinhard Flick and Patrick Shore for their support during field work, Tom Bolmer in locating stations and preparing maps, and the US Antarctic Program for logistical support. The seismic instruments were provided by the Incorporated Research Institutions for Seismology (IRIS) through the PASSCAL Instrument Center at New Mexico Tech. Data collected are available through the IRIS Data Management Center under RIS and DRIS network code XH. The PSD-PDFs presented in this study were processed with the IRIS Noise Tool Kit (Bahavar and others, 2013). The facilities of the IRIS Consortium are supported by the National Science Foundation under Cooperative Agreement EAR-1261681 and the DOE National Nuclear Security Administration. The authors appreciate the support of the University of Wisconsin-Madison Automatic Weather Station Program for the data set, data display and information; funded under NSF grant number ANT-1543305. The Ross Ice Shelf profiles were generated using the Antarctic Mapping Tools (Greene and others, 2017). Regional maps were generated with the Generic Mapping Tools (Wessel and Smith, 1998). Topography and bathymetry data for all maps in this study were sourced from the National Geophysical Data Center ETOPO1 Global Relief Model (doi:10.7289/V5C8276M). We thank two anonymous reviewers for suggestions on the scope and organization of this paper

Moored elastic sheets under the action of nonlinear waves and current

This study is concerned with the interaction between nonlinear water waves and uniform current with moored, floating elastic sheets, resembling floating solar panels, floating airports, tunnels and bridges, and floating energy systems. The Green-Naghdi theory is applied for the nonlinear wave-current motion, the thin plate theory is used to determine the deformations of the elastic sheet and Hooke’s law defines the effect of the mooring lines. The horizontal displacement of the floating sheet is determined by substituting the forces induced by the fluid flow and the tensions generated in the mooring lines into the equations of motion of the floating body. The resulting governing equations, boundary and matching conditions are solved in two dimensions with a finite-difference technique. The results are compared with the available numerical data. Overall, very good agreement is observed. In the model developed here, the sheet is allowed to drift due to the wave-current impact, and hence the mooring lines partially restrict both deformation and the horizontal motions of the sheet. The influence of the mooring lines on the dynamics of the floating sheet is assessed in terms of wave- and current-induced elastic deformations and surge movements of the sheet. It is demonstrated that the mooring lines attached to the leading and trailing edges of the sheet can be highly effective in mitigating the horizontal oscillations and vertical elastic deformations of the floating sheet subjected to the wave and current actions. Special attention is given to the horizontal periodic motions of the sheet, which are analysed by use of a Fourier transform technique. It is shown that the moored elastic sheet can oscillate at a frequency different from its exciting frequency as a result of restoring forces from the mooring lines, exciting resonance when both frequencies meet. Extensive study in a broad range of sheet parameters, mooring stiffnesses and wave-current conditions established the location of resonant regimes of different configurations of the moored systems. Analysis of wave reflection and transmission coefficient revealed that mooring lines of increasing stiffness intensify the wave reflection and, consequently, result in smaller energy transformation downwave

Hydroelastic waves and their interaction with fixed structures

A selection of problems are presented which study the interaction of hydroelastic waves with fixed structures. A thin floating elastic plate model is considered which primarily represents a continuous floating ice sheet, but may also be applied to very large floating platforms. The incident hydroelastic waves are assumed to either propagate from long–distance towards the structures or be generated by a moving load. All aspects of the subsequent interaction are studied in detail. The elastic plate is clamped to the fixed vertical structures to model an ice sheet frozen to the structure boundary. Both linear and nonlinear formulations are admitted for a selection of two– and three–dimensional problems. For the linear problems, selection of appropriate integral transforms leads to explicit analytical solutions in terms of integral quadratures. For the nonlinear case, the numerical solution is found by application of Green’s second identity combined with a boundary element method. The resulting deflection fields are analysed as well as the strain in the ice sheet due to curvature from the hydroelastic waves. Particular attention is paid to the strain at the ice–structure boundary. The integral transforms also lead to concise expressions for the horizontal and vertical wave forces impacting on the structure. It is shown that these forces may reach a substantial magnitude and must be taken into account for the design of structures in ice–covered water. Several assumptions are utilised which allow the problems to be mathematically treatable while retaining accuracy. Realistic effects such as viscoelasticity and fluid stratification are studied. The solutions are investigated in detail under the variation of physical parameters of the fluid, the ice sheet and the incident/load–generated waves, based on realistic values from cold climate regions

Oblique wave scattering by a system of floating and submerged porous elastic plates

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