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.
An experimental model of reflection and transmission of ocean waves by an ice floe is presented. Evolution of mechanically-generated, regular waves is monitored in front and in the lee of a solitary, square floe, made of a synthetic material. Results confirm dependence of reflection and transmission on the period of the incident wave. Results also indicate that wave overwash on the floe affects reflection and transmission.
Wave attenuation by ice floes is an important parameter for modelling the Arctic Oceans. At present, attenuation coefficients are extracted from linear models as a function of the incident wave period and floe thickness. Recent explorations in the Antarctic Mixed Ice Zone (MIZ) revealed a further dependence on wave amplitude, suggesting that nonlinear contributions are non-negligible. An experimental model for wave attenuation by a single ice floe in a wave flume is here presented. Observations are compared with linear predictions based on wave scattering. Results indicate that linear models p…
An optimisation scheme is developed to accurately represent the sub-grid scale forcing of a high dimensional chaotic ocean system. Using a simple parameterisation scheme, the velocity components of a 30km resolution shallow water ocean model are optimised to have the same climatological mean and variance as that of a less viscous 7.5km resolution model. The 5 day lag-covariance is also optimised, leading to a more accurate estimate of the high resolution response to forcing using the low resolution model. The system considered is an idealised barotropic double gyre that is chaotic at both reso…
A new ocean wave/sea-ice interaction model is proposed that simulates how a directional wave spectrum evolves as it travels through an arbitrary finite array of circular ice floes, where wave/ice dynamics are entirely governed by wave scattering effects. The model is applied to characterise the wave reflection and transmission properties of a strip of ice floes, such as an ice edge band. A method is devised to extract the reflected and transmitted directional wave spectra produced by the array. The method builds upon an integral mapping from polar to Cartesian coordinates of the scattered wave…
A modified version of the wave-ice interaction model proposed by Williams et al (2013a,b) is presented for an idealised transect geometry. Wave attenuation due to ice floes and wave-induced ice fracture are both included in the wave-ice interaction model. Subgrid spatial and temporal discretisations are not required in the modified version of the model, thereby facilitating its future integration into large-scaled coupled models. Results produced by the new model are compared to results produced by the original model of Williams et al (2013b).
Direct phase-resolved simulations are performed to investigate the propagation and scattering of nonlinear ocean waves in fragmented sea ice. The numerical model solves the full time-dependent equations for nonlinear potential flow coupled with a nonlinear thin-plate representation of the ice cover, and neglects dissipative processes. The two-dimensional setting with incident wave groups on deep water is considered, in view of applications to wave attenuation along transects of the marginal ice zone. A spatially-varying weight is assigned to the surface pressure so that irregular distributions…
Modeling and understanding sea ice dynamics in marginal ice zones relies on acquiring Lagrangian ice floe measurements. However, optical satellite images are susceptible to atmospheric noise, leading to gaps in the retrieved time series of floe positions. This paper presents an efficient and statistically accurate nonlinear dynamical interpolation framework for recovering missing floe observations. It exploits a balanced physics-based and data-driven construction to address the challenges posed by the high-dimensional and nonlinear nature of the coupled atmosphere-ice-ocean system, where effec…
We present a discrete element method (DEM) model to simulate the mechanical behavior of sea ice in response to ocean waves. The interaction of ocean waves and sea ice can potentially lead to the fracture and fragmentation of sea ice depending on the wave amplitude and period. The fracture behavior of sea ice is explicitly modeled by a DEM method, where sea ice is modeled by densely packed spherical particles with finite size. These particles are bonded together at their contact points through mechanical bonds that can sustain both tensile and compressive forces and moments. Fracturing can be n…
Particle, kinetic and hydrodynamic models for sea ice floes. Part II: Rotating floes with environmental forces
Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）；School of Computing, Australian National University（澳大利亚国立大学计算学院）；Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University（首尔大学数学科学系与数学研究所）；Department of Mathematical Sciences, Seoul National University（首尔大学数学科学系）；School of Engineering, Mathematics and Physics, University of East Anglia（东英吉利大学工程、数学与物理学院）；School of Mathematics and Statistics, The University of Melbourne（墨尔本大学数学与统计学院）
The marginal ice zone is the dynamic interface between the open ocean and consolidated inner pack ice. Surface gravity waves regulate marginal ice zone extent and properties, and, hence, fluxes between the atmosphere and ocean, and ice advance and retreat. Over the past decade, seminal experimental campaigns have generated much needed measurements of wave evolution in the marginal ice zone, which, notwithstanding the prominent knowledge gaps that remain, are underpinning major advances in understanding the region's role in the climate system. Here, we report three-dimensional imaging of waves …
A model of ice floe breakup under ocean wave forcing in the marginal ice zone (MIZ) is proposed to investigate how floe size distribution (FSD) evolves under repeated wave breakup events. A three-dimensional linear model of ocean wave scattering by a finite array of compliant circular ice floes is coupled to a flexural failure model, which breaks a floe into two floes provided the two-dimensional stress field satisfies a breakup criterion. A closed-feedback loop algorithm is devised, which (i)~solves wave scattering problem for a given FSD under time-harmonic plane wave forcing, (ii)~computes …
Lagrangian data assimilation of complex nonlinear turbulent flows is an important but computationally challenging topic. In this article, an efficient data-driven statistically accurate reduced-order modeling algorithm is developed that significantly accelerates the computational efficiency of Lagrangian data assimilation. The algorithm starts with a Fourier transform of the high-dimensional flow field, which is followed by an effective model reduction that retains only a small subset of the Fourier coefficients corresponding to the energetic modes. Then a linear stochastic model is developed …
Increased knowledge about wave attenuation processes in sea ice, and hence atmosphere-wave-ice-ocean energy transfer, is necessary to improve sea ice dynamics models used for climate modeling and offshore applications. The aim of this study is to generate such much needed data by investigating colliding ice floes dynamics in a large-scale experiment and directly measuring and quantifying the turbulent kinetic energy (TKE). The field work was carried out at Van Mijen Fjord on Svalbard, where a 3x4 m ice floe was sawed out in the fast ice. Wave motion was simulated by pulling the ice floe back a…
High temporal resolution in--situ measurements of pancake ice drift are presented, from a pair of buoys deployed on floes in the Antarctic marginal ice zone during the winter sea ice expansion, over nine days in which the region was impacted by four polar cyclones. Concomitant measurements of wave-in-ice activity from the buoys is used to infer that pancake ice conditions were maintained over at least the first seven days. Analysis of the data shows: (i)~unprecedentedly fast drift speeds in the Southern Ocean; (ii)~high correlation of drift velocities with the surface wind velocities, indicati…
A two-dimensional model for eddy saturation and frictional control in the Southern Ocean
The University of Edinburgh（爱丁堡大学）；University of Oxford（牛津大学）；Hong Kong University of Science and Technology（香港科技大学）；National Oceanography Centre, Southampton（南安普顿国家海洋中心）
We present a set of idealised numerical experiments of a solstitial aquaplanet ocean and examine the thermodynamic and dynamic implications of surface gravity waves (SGWs) upon its mean state. The aquaplanet's oceanic circulation is dominated by an equatorial zonal jet and four Ekman driven meridional overturning circulation (MOC) cells aligned with the westerly atmospheric jet streams and easterly trade winds in both hemispheres. Including SGW parameterization (representing modulations of air-sea momentum fluxes, Langmuir circulation and Stokes-Coriolis force) increases mixed layer vertical m…
Irregular, unidirectional surface water waves incident on model ice in an ice tank are used as a physical model of ocean surface wave interactions with sea ice. Results are given for an experiment consisting of three tests, starting with a continuous ice cover and in which the incident wave steepness increases between tests. The incident waves range from causing no breakup of the ice cover to breakup of the full length of ice cover. Temporal evolution of the ice edge, breaking front and mean floe sizes are reported. Floe size distributions in the different tests are analysed. The evolution of …
A wave-ice interaction model for the marginal ice zone (MIZ) is reported, which involves both the attenuation of ocean surface waves by sea ice and the concomitant breaking of the ice by waves. It is specifically designed to embed wave-ice interactions in an operational ice/ocean model for the first time. We investigate different methods of including the wave forcing, and different criteria for determining if they cause floes to break. We also investigate and discuss the effects of using various attenuation models, finding that predicted MIZ widths are quite sensitive to the choice of model. A…
Increased research interest and economic activity in the Arctic raise the need for new observations of sea ice dynamics. Remote sensing as well as mathematical and numerical models of wave propagation in sea ice would benefit from more in situ data for validation. This study presents wave measurements in the marginal ice zone (MIZ) obtained from ship mounted sensors. The system combines altimeter readings from the ship bow with ship motion correction data to provide estimated single point ocean surface elevation. Significant wave height and mean wave period, as well as one-dimensional wave spe…
Young sea ice composed of grease and pancake ice (GPI), as well as thin floes, considered to be the most common form of sea ice fringing Antarctica, is now becoming the 'new normal' also in the Arctic. Investigations to determine how an increase in GPI is affecting the climate in the far north and globally, require specific tools to monitor the GPI's thickness distribution. Directional wave spectra from satellite SAR imagery are used to determine the change in wave dispersion as a wave train enters GPI fields. The ice cover thickness is then estimated by fitting the dispersion data with two mo…
Increased economic activity and research interest in the Arctic raise the need for better wave forecasts in the marginal ice zone (MIZ). Mathematical and numerical models of wave propagation in sea ice would benefit from more in situ data for validation. This study presents shipborne wave measurements from the MIZ where altimeter readings are corrected for ship motion to obtain estimated single point ocean surface elevation. From the combined measurements, we obtain significant wave height and zero up-crossing period, as well as one-dimensional wave spectra. In addition, we provide spectra and…
