- 學位論文
波浪通過連續黏彈性浮冰之理論分析
Theoretical analysis of waves propagating through a continuous viscoelastic ice cover
摘要
隨著氣候變遷以及全球暖化加劇，在極地區域冰溶化的速率大幅的增加，雖然說這讓航運以及海事工程在此區域看到了新的可能性，不過因為冰層減少、開放海域的增加也讓風吹拂海面所造成波浪的機率大大提升。為了能讓經濟發展能順利在此運行，關於海象、氣象方面的研究也勢必需要立即著手。此研究鎖定了連結開放海域以及長年結冰區域間的 Marginal ice zone (MIZ) 進行波浪與浮冰的理論模式分析，此區域的冰塊由剛結成冰的晶體、單塊浮冰，一直到連續的冰層所組成，且波浪在開放海域成形後大多能通過於此，使得此區域的冰-波動態交互模式變得相當複雜，也因大部分在極地的相關經濟活動大多通過於此，關於此區域的研究也日漸受到大家重視。 本研究將冰塊視為浮在海水面上的一層連續的黏彈性體，冰波交互作用的理論模式是依據冰、水雖然會有各自的運動模式，但在交界面處須滿足關於剪切應力、正向應力、垂直方向速率一致的邊界條件來達成，並透過求解波數來分析水動力的消散、冰層兩側週期震盪各自的振幅比值，以及其相位差。此研究分析了兩個具有差異的理論模式，其一我們將其內容延伸探討波浪水動力消散的現象以及對於延散方程式中複數根的解析提出了新的解釋，另一模式本是用來分析兩層黏性流體的交互作用，上層的黏性流體在此篇內容中被改成了黏彈性體，而兩種模式最大的不同在於海水黏滯效應納入與否，因此關於黏滯性的影響以及兩模式因為浮冰對水動力表現之差異也都將在此篇文獻中呈現。本篇研究也因振幅比、相位差在不同冰塊特性下與現實世界有一致的現象而進一步驗證了此冰波交互作用的可行性。
並列摘要
With the onset of climate change and global warming, the melting rate of sea ice in polar regions has significantly increased. While this presents new opportunities for shipping and marine engineering, it also leads to a higher occurrence of wind wave generation in areas with decreased ice cover. In order to facilitate smooth economic development in these regions, it is crucial to initiate research on ice-wave interaction and meteorology. The presented thesis focuses on analyzing theoretical models pertaining to waves and ice in the Marginal Ice Zone (MIZ), which connects open water areas with perennial ice-covered regions. The ice in this zone ranges from newly formed crystals and individual ice floes to continuous ice sheets. As most waves generate in the open sea and propagate through this area, the dynamic interaction between waves and ice becomes highly complex. Considering the significant economic activities taking place in this region, research in this field has gained increasing attention. In the presented two-layer theoretical models, the ice layer is treated as a continuous viscoelastic material floating on the sea surface. The theoretical model of ice-wave interaction is achieved by satisfying the boundary conditions of the shear stress, normal stress, and vertical velocity continuous at the ice-water interface. When waves propagate through the underlying seawater layer, the ice responds to wave disturbances, while the wave is influenced by both viscosity and elasticity effects from sea ice, resulting in hydrodynamic dissipation, amplitude ratio variation, and phase lag. By solving the complex wavenumbers, these effects are analyzed. Two different theoretical models are examined in this study: one originally developed for ice-wave interaction is extended to investigate the hydrodynamic and dissipation of water waves, and another model, originally designed for two viscous layers, is modified to include a viscoelastic fluid in the upper layer. The most significant difference between two models is whether the viscosity effect of seawater is involved or not. The impact of seawater viscosity and the comparison of two models are presented. Lastly, this study also further verifies the feasibility of the ice-wave interaction models because the amplitude ratio and phase difference are consistent with the real world under different ice characteristics.