Luke G. Bennetts

In situ measurements and analysis of ocean waves in the Antarctic marginal ice zone

In situ measurements of ocean surface wave spectra evolution in the Antarctic marginal ice zone are described. Analysis of the measurements shows significant wave heights and peak periods do not vary appreciably in approximately the first 80km of the ice-covered ocean. Beyond this region, significant wave heights attenuate and peak periods increase. It is shown that attenuation rates are insensitive to amplitudes for long-period waves but increase with increasing amplitude above some critical amplitude for short-period waves. Attenuation rates of the spectral components of the wavefield are calculated. It is shown that attenuation rates decrease with increasing wave period. Further, for long-period waves the decrease is shown to be proportional to the inverse of the period squared. This relationship can be used to efficiently implement wave attenuation through the marginal ice zone in ocean-scale wave models.

A multi-mode approximation to wave scattering by ice sheets of varying thickness

The problem of linear wave scattering by an ice sheet of variable thickness floating on water of variable quiescent depth is considered by applying the Rayleigh–Ritz method in conjunction with a variational principle. By using a multi-mode expansion to approximate the velocity potential that represents the fluid motion, Porter & Porter (J. Fluid Mech. vol. 509, 2004, p. 145) is extended and the solution of the problem may be obtained to any desired accuracy. Explicit solution methods are formulated for waves that are obliquely incident on two-dimensional geometry, comparisons are made with existing work and a range of new examples that includes both total and partial ice-cover is considered.

On the calculation of an attenuation coefficient for transects of ice-covered ocean

Exponential attenuation of ocean surface waves in ice-covered regions of the polar seas is modelled in a two-dimensional, linear setting, assuming that the sea ice behaves as a thin-elastic plate. Attenuation is produced by natural features in the ice cover, with three types considered: floes, cracks and pressure ridges. An inelastic damping parameterization is also incorporated. Efficient methods for obtaining an attenuation coefficient for each class of feature, involving an investigation of wave interaction theory and averaging methods, are sought. It is found that (i) the attenuation produced by long floes can be obtained from the scattering properties of a single ice edge; and (ii) wave interaction theory in ice-covered regions requires evanescent and damped-propagating motions to be included when scattering sources are relatively nearby. Implications for the integration of this model into an oceanic general circulation model are also discussed.

Wave scattering by multiple rows of circular ice floes

A three-dimensional model of ocean-wave scattering in the marginal ice zone is constructed using linear theory under time-harmonic conditions. Individual floes are represented by circular elastic plates and are permitted to have a physically realistic draught. These floes are arranged into a finite number of parallel rows, and each row possesses an infinite number of identical floes that are evenly spaced. The floe properties may differ between rows, and the spacing between the rows is arbitrary. The vertical dependence of the solution is expanded in a finite number of modes, and through the use of a variational principle, a finite set of two-dimensional equations is generated from which the full-linear solution may be retrieved to any desired accuracy. By dictating the periodicity in each row to be identical, the scattering properties of the individual rows are combined using transfer matrices that take account of interactions between both propagating and evanescent waves. Numerical results are presented that investigate the differences between using the three-dimensional model and using a two-dimensional model in which the rows are replaced with strips of ice. Furthermore, Bragg resonance is identified when the rows are identical and equi-spaced, and its reduction when the inhomogeneities, that are accommodated by the model, are introduced is shown.

Wave scattering by ice floes and polynyas of arbitrary shape

An efficient solution method is presented for linear and time-harmonic water-wave scattering by two classes of a three-dimensional hydroelastic system. In both cases, the fluid domain is of infinite horizontal extent and finite depth. The fluid surface is either open, except in a finite region where it is covered by a thin-elastic plate, which represents an ice floe, or fully covered by a plate, except in a finite region where it is open, which represents an ice polynya. The approach outlined herein permits the boundary between the ice-covered and free-surface fluid regions to be described by an arbitrary smooth curve. To solve the governing equations of the full three-dimensional linear problem, they are first projected onto the horizontal plane by using an approximation theory that combines an expansion of the vertical motion of the fluid in a finite set of judiciously chosen modes with a variational principle. This generates a system of two-dimensional partial differential equations that are converted into a set of one-dimensional integro-differential equations using matrices of Greens functions, which are solved numerically through an application of the Galerkin technique. A numerical results section justifies the consideration of an arbitrarily shaped boundary by comparing the response of differently shaped floes and polynyas over a range of relevant wavenumbers. Comparisons are made in terms of the magnitude and direction of the far-field scattering response, and also the maximum average curvature of the floe and the maximum wave elevation within the polynya.

Water wave transmission by an array of floating discs

An experimental validation of theoretical models of regular-water-wave transmission through arrays of floating discs is presented. The experiments were 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 discs are separated by approximately a disc diameter in equilibrium, and a high-concentration array, in which adjacent discs are almost touching in equilibrium, were used for the experiments. The proportion of incident-wave energy transmitted by the discs is presented as a function of wave period, and for different wave amplitudes. Results indicate 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 discs and collisions between discs. Validation of model predictions of a solitary discs rigid-body motions are also presented.

An idealised experimental model of ocean surface wave transmission by an ice floe

Abstract An experimental model of transmission of ocean waves by an ice floe is presented. Thin plastic plates with different material properties and thicknesses are used to model the floe. Regular incident waves with different periods and steepnesses are used, ranging from gently-sloping to storm-like conditions. A wave gauge is used to measure the water surface elevation in the lee of the floe. The depth of wave overwash on the floe is measured by a gauge in the centre of the floe’s upper surface. Results show transmitted waves are regular for gently-sloping incident waves but irregular for storm-like incident waves. The proportion of the incident wave transmitted is shown to decrease as incident wave steepness increases, and to be at its minimum for an incident wavelength equal to the floe length. Further, a trend is noted for transmission to decrease as the mean wave height in the overwash region increases.

The decay of flexural-gravity waves in long sea ice transects

Flexural oscillations of floating sea ice sheets induced by ocean waves travelling at the boundary between the ice and the water below can propagate great distances. But, by virtue of scattering, changes of ice thickness and other properties encountered during the journey affect their passage, notwithstanding attenuation arising from several other naturally occurring agencies. We describe here a two-dimensional model that can simulate wave scattering by long (approx. 50 km) stretches of inelastic sea ice, the goal being to replicate heterogeneity accurately while also assimilating supplementary processes that lead to energy loss in sea ice at scales that are amenable to experimental validation. In work concerned with scattering from solitary or juxtaposed stylized features in the sea ice canopy, reflection and transmission coefficients are commonly used to quantify scattering, but on this occasion, we use the attenuation coefficient as we consider that it provides a more helpful description when dealing with long sequences of adjoining scatterers. Results show that scattering and viscosity both induce exponential decay and we observe three distinct regimes: (i) low period, where scattering dominates, (ii) high period, where viscosity dominates, and (iii) a transition regime. Each regime’s period range depends on the sea ice properties including viscosity, which must be included for the correct identification of decay rate.

Sea ice floes dissipate the energy of steep ocean waves

A laboratory experimental model of an incident ocean wave interacting with an ice floe is used to validate the canonical, solitary floe version of contemporary theoretical models of wave attenuation in the ice-covered ocean. Amplitudes of waves transmitted by the floe are presented as functions of incident wave steepness for different incident wavelengths. The model is shown to predict the transmitted amplitudes accurately for low incident steepness but to overpredict the amplitudes by an increasing amount, as the incident wave becomes steeper. The proportion of incident wave energy dissipated by the floe in the experiments is shown to correlate with the agreement between the theoretical model and the experimental data, thus implying that wave-floe interactions increasingly dissipate wave energy as the incident wave becomes steeper.

Experimental and theoretical models of wave-induced flexure of a sea ice floe

An experimental model is used to validate a theoretical model of a sea ice floe’s flexural motion, induced by ocean waves. A thin plastic plate models the ice floe in the experiments. Rigid and compliant plastics and two different thicknesses are tested. Regular incident waves are used, with wavelengths less than, equal to, and greater than the floe length, and steepnesses ranging from gently sloping to storm-like. Results show the models agree well, despite the overwash phenomenon occurring in the experiments, which the theoretical model neglects.