Vernon A. Squire

The Flexural Response of a Tabular Ice Island to Ocean Swell

Measurements of surface strain and vertical heave responses to swell were made on a tabular ice island in Kong Oscars Fjord, east Greenland, in September 1978 . At two sites surface strain was measured with a wire strainmeter of 2 m gauge length, and heave was measured with a vertical accelerometer. While the first site was occupied a simultaneous measurement of ambient wave energy was made with a wave buoy. The results show that the ice island flexes and heaves in response to the longest component only of the forcing wave field, at periods above 16 s, and wit h a mean strain amplitude of the order of S x 107 • The results are compared with theoretical calculations of the response of a thick floating beam. In the light of the theory, t he flexural behaviour of tabular icebergs and seaice floes is considered and their critical size ranges in relation to sea state are estimated. LIST OF SYMBOLS A wave amplitude under the ice block A wave amplitude on the sea surface c typical crack length D Eh3/(l-V 2 ) E Young s modulus g acceleration due to gravity h ice-block thickness k incident wave number

Ocean surface wave evolvement in the Arctic Basin

[1]xa0Recent basin-scale changes to the compactness and thickness of Arctic sea ice foreshadow that encroaching swells and locally generated waves will exert more influence there in the future. Indeed, it is conceivable that waves may have already hastened the adjustments observed by breaking up ice floes. Yet waves advancing in sea ice attenuate due to being scattered from ice thickness variations and damped by ice inelasticity, turbulence and friction. While past research focuses on scattering by unnaturally perfect features in the ice, the model reported herein assimilates realistic basin-scale swathes of heterogeneous ice and parameterizes damping. By way of example, we show how an ocean wave train evolves during its passage in an 1670-km-long Arctic sea ice profile obtained from submarine.

Strain in shore fast ice due to incoming ocean waves and swell

Using a development from the theoretical model presented by Fox and Squire (1990), this paper investigates the strain field generated in shore fast ice by normally incident ocean waves and swell. After a brief description of the model and its convergence, normalized absolute strain (relative to a 1-m incident wave) is found as a function of distance from the ice edge for various wave periods, ice thicknesses, and water depths. The squared transfer function, giving the relative ability of incident waves of different periods to generate strain in the ice, is calculated, and its consequences are discussed. The ice is then forced with a Pierson-Moskowitz spectrum, and the consequent strain spectra are plotted as a function of penetration into the ice sheet. Finally, rms strain, computed as the incoherent sum of the strains resulting from energy in the open water spectrum, is found. The results have implications to the breakup of shore fast ice and hence to the floe size distribution of the marginal ice zone.

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. 50u2009km) 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.

Ocean wave scattering by natural sea ice transects

[1]xa0Ocean waves propagate in continuous sea ice as flexural-gravity waves, so named because their dispersion is influenced by bending of the ice plate and by buoyancy. Such waves are scattered by topographic heterogeneity in the ice, e.g., features like pressure ridges, yet current models fail to account for the complexity that is symptomatic of sea ice. Here a two-dimensional wave scattering model is described that allows real data from natural sea ice to be assimilated rather than synthetic ice terrain. On the basis of linear wave theory and the elastic thin plate equation, the model assumes an unbroken compliant sea ice cover with no free edges and uses Greens Functions to obtain an integral equation that is solved numerically. While scattering in physical stretches of sea ice can vary greatly, all transects behave as low-pass filters and can display resonances that relate to how features are separated or to transect length, the latter being an undesirable trait of the model. In the paper an association is made between the statistical properties of the sea ice terrain and the nature of the scattering that results. Not unexpectedly, sea ice with greater relative draft variation is more reflective. It is proposed that this observation can be used to identify the draft variation for an unknown transect if its scattering response is known. Finally, the progression of median energy density for ensembles of similarly sampled transects is examined at wave periods of less than 10 s and is found to decay exponentially with distance traveled, in accord with the few observations available.