Abstract
Sea ice is an important indicator and agent of changes in the global climate system. The ice is affected by waves that travel into the Marginal Ice Zone (MIZ) and cause floes to raft, deform and, potentially, fracture. The resulting change in the floe size distribution (FSD) influences the melting and freezing. Simultaneously, the ice floes affect the propagation of ocean waves. The motivation to study wave--ice interaction is therefore twofold: it plays a role in understanding climate change, and it is vital to wave forecasting models that have to be accurate to ensure the safety of research expeditions, coastal communities, etc. In the present thesis we investigate various models of ocean wave propagation in ice infested seas.
We distinguish between three classes of models: "floe models", "effective medium models", and "transport equation models", each of which assume a different set of fundamental degrees of freedom. Our goal is to systematically explore existing models of each type and extend them to advance our understanding of wave-ice interactions.
Floe models resolve individual ice floes as their fundamental degrees of freedom. We consider the scattering of water waves in a two-dimensional domain from a floating sea ice floe of uncertain length. The length is treated as a random variable governed by a prescribed probability distribution. In accord with the majority of wave-ice interaction models, a thin elastic plate that floats with Archimedean draught is used to represent the ice floe. We compute the expectation and variance of the reflection and transmission coefficients using two different methods derived from the framework of generalized polynomial chaos (gPC), which affords the expansion of unknown quantities of the problem in a basis of orthogonal polynomials of the random variable. The gPC methods are shown to be numerically efficient and exhibit desirable exponential convergence properties, as opposed to the slow algebraic convergence of the quasi Monte Carlo approach that we use for comparison. Finally, we employ one of the gPC methods to demonstrate that the FSD can have a significant impact on the expected transmission coefficient.
Effective medium models describe the surface ocean layer (including ice floes, brash ice, etc.) as a homogeneous viscoelastic material that causes waves to attenuate as they travel through the medium. We compare three ice layer models, namely a viscoelastic fluid layer model currently being used for studies in the spectral wave model WAVEWATCH III and two simpler viscoelastic thin beam models. A comparative analysis shows that one of the beam models provides similar predictions for wave attenuation and wavelength to the viscoelastic fluid model. We also calibrate the three models using wave attenuation data recently collected in the Antarctic MIZ. Although agreement with the data is obtained with all three models, several important issues related to the viscoelastic fluid model are identified that raise questions about its suitability to characterize wave attenuation in ice-covered seas.
Transport equation models describe the propagation of the wave action density (which is proportional to the wave energy density) in terms of a transport equation that is commonly used in ocean wave modelling. A term to represent the effect of floating sea ice is known for sparse collections of floes, but this is not valid at high concentrations. As a result, we derive the transport equation for a continuous ice cover of random thickness as a first step towards a transport equation model for high ice concentration. The attenuation coefficients predicted by this new equation turn out to be unrealistic. Hence, we outline an alternative derivation that may be explored in future work.