Nonlinear Wave-Ice-Interaction

本研究课题主要研究固体冰下非线性波-冰相互作用的基本问题，主要研究非线性波的传播和弥散。目的是验证非线性是否发生在固体冰下。因此，非线性波冰相互作用以及固体冰的特性对这种相互作用的影响将进行研究。调查包括数值模拟伴随着实验。将研究特殊的非线性波群和冰盖附近的典型涌浪条件。包络孤子和游隼呼吸器解决方案将被应用代表非线性薛定谔方程（NLSE）的精确解。这种非线性波群的应用是为了实现本研究提案的目标--验证非线性在固体冰下发生--因为只有在发生非线性波-波相互作用的情况下，才能在实验中观察到这些波群。这表明冰槽中存在这样的波群是直接的证据。实验的目的是第一次从实验上证实在固体冰下发生非线性，从而导致稳定的波群以及夸大的波幅。在Peregrine呼吸器的帮助下，应表明调制不稳定性将导致远离固体冰边缘的夸大波高。此外，根据数值模拟，选定的膨胀情况下，特别感兴趣的非线性现象将重现在冰槽。除了关注固体冰下的非线性波浪效应外，还将分别研究固体冰对波长和波能传播的影响，即测量由于固体冰的突然出现而引起的波长变化，并将其与理论结果进行比较。实验将在两种不同的冰类型中进行。一种是种子模型冰，其中波浪和冰的特性将根据现有技术进行缩放，即在保持弗劳德和柯西相似性的同时进行几何缩放，其中与自然生长的冰相比，阻尼特性可能会被夸大。第二种冰是盆地中规则的自然生长的冰，冰的强度可能很高，但弹性变形和相关的恢复力以及波浪的阻尼被认为更类似于海冰。这里的目的是评估两种冰类型之间可能存在的差异，并评估现有技术的模型冰是否允许按照现有技术的水平对问题进行缩放。

This research project addresses the fundamental question of nonlinear wave-ice interaction under solid ice focusing on nonlinear wave propagation and dispersion of waves. The objective is to verify if nonlinearity takes place under solid ice. Thereby, nonlinear wave-ice interaction as well as the impact of the solid ice characteristics on this interaction will be investigated. The investigations comprise numerical simulations accompanied by experiments. Special nonlinear wave groups and typical swell conditions in the vicinity of ice covers will be investigated. Envelope soliton and Peregrine breather solutions will be applied representing exact solutions of the Nonlinear Schrödinger Equation (NLSE). The application of such nonlinear wave groups are predestined for the objective of this research proposal – verification that nonlinearity takes place under solid ice – as these wave groups’ can only be observed within experiments if nonlinear wave-wave interaction takes place. This denotes that the existence of such wave groups in the ice tank is the direct proof.The goal of the experiments is to verify experimentally for the first time that nonlinearity takes place under solid ice resulting in stable wave groups as well as exaggerated wave amplitudes. With the help of the Peregrine breather it shall be shown that modulation instability will lead to an exaggerated wave height far away from the edge of the solid ice. In addition, and based on numerical simulations, selected swell cases of special interest regarding nonlinear phenomena will be reproduced in the ice tank. Besides focusing on nonlinear wave effects under solid ice, the effect of solid ice on the wave length and wave energy propagation, respectively, will also be investigated, i.e. the change of wave length due to the sudden presence of solid ice will be measured and compared to theoretical findings.The experiments will be conducted in two different ice types. One will be seeded model ice, where properties of waves and ice will be scaled according to the state of the art, i.e. geometrically scaled while maintaining Froude and Cauchy similitude, where damping properties might be exaggerated compared to naturally grown ice. The second ice type will be regular, naturally grown ice in the basin, where the ice strength might be high, but the elastic deformation and related restoring forces as well as the damping of waves is considered to be more similar to sea ice. The objective here is to assess possible differences between the two ice types and to evaluate whether the state of the art model ice does even allow a scaling of the problem following the current state of the art.