The predictability/unpredictability of nonlinear internal gravity waves in the ocean: generation, shoaling and dissipation

当重力恢复力作用于垂直位移流体时，密度分层流体中存在重力内波。它们发生在流体的内部，例如，在海洋表面以下，密度变化。它们在我们的海洋、湖泊和大气中无处不在，它们在水平和垂直方向上传播。内波通过混合热量和营养物影响海洋环流和海洋地球化学过程，它们重新悬浮和运输沉积物和营养物，其水流可以影响近海结构。他们被假设在塑造大陆架方面发挥作用，并观察到鱼类垂直迁移，以应对大型内波的通过，以优化其摄食策略。内波可以从其产生地点传播数千公里，因此在一个位置产生的波可以在很远的距离产生影响。内波主要是由流过山脊和大陆架斜坡等地形特征的潮流或作用于海洋表面的风产生的。潮汐-地形相互作用迫使流体在倾斜的底部上下流动，而海面上风应力的变化则驱动水平水流，将流体推到一起或分散开，从而导致向下和向上的运动。这些垂直运动驱动内波。内波是非线性色散波。非线性在不同波之间传递能量，而色散导致不同波以不同速度传播的能量。非线性将能量从注入的大尺度转移到耗散并发生混合的小尺度。海洋中的许多内波都是强非线性的，内孤立波就是最典型的例子。在这里，非线性和色散共同作用，产生一个可以传播很长距离的大相干波。这些波的极端例子具有接近200米的振幅（尼亚加拉福尔斯高度的四倍），尽管几十米的振幅是正常的。与内部孤立波相关联的电流修改表面波场，使得它们的存在可从空间检测到，并且可以影响离岸结构，使得这些波对离岸石油工业感兴趣。拟议的研究将通过数值模拟和数学建模解决内波的可预测性和不可预测性问题。它将解决由潮汐地形相互作用产生的内波，重点是能量转移到内部孤立波及其在垂直混合中的作用。一个案例研究将侧重于波生成的秘鲁大陆架上的观测表明，内波是负责垂直混合的热量和生物生产力的季节性变化。将研究内孤立波的变浅，重点是破裂的发生，并将调查内孤立波的剪切不稳定性，这种不稳定性导致热量和营养物的垂直混合。将研究这些波的可预测性的其他方面，包括潮汐频率的内波与海洋中的涡旋和漩涡的相互作用，这会影响内波的长距离传播，以及不同形式的内波的发生，例如，呼吸器是特殊的非线性脉动波包。这项研究将提高我们预测海洋内波场的能力，并将能够更好地预测大规模海洋环流、跨大陆架交换、生物生产力和大陆架形状等过程，并有助于设计和运营离岸结构。

Internal gravity waves exist in density-stratified fluids when gravitational restoring forces act on vertically displaced fluid. They occur in the interior of the fluid, e.g., below the ocean surface, where the density varies. They are ubiquitous in our oceans, lakes and atmosphere where they propagate both horizontally and vertically. Internal waves affect ocean circulation and biogeochemical processes by mixing heat and nutrients, they re-suspend and transport sediments and nutrients, and their currents can impact offshore structures. They have been hypothesized to play a role in shaping the continental shelf and fish have been observed to migrate vertically in response to the passing of large internal waves to optimize their feeding strategy. Internal waves can propagate thousands of kilometers from their generation site so wave generation in one location can have an impact at great distances. Internal waves are primarily generated by tidal currents flowing over topographic features such as ridges and the continental shelf slope, or by winds acting on the ocean surface. Tide-topography interaction forces fluid up and down the sloping bottom while variations in wind stress at the ocean surface drive horizontal currents which push fluid together or spread it apart resulting in downward and upward motion. These vertical motions drive internal waves. Internal waves are nonlinear-dispersive waves. The nonlinearity transfers energy among different waves while dispersion results in energy in different waves propagating with different velocities. Nonlinearity transfers energy from the large scales at which it is injected to small scales at which it is dissipated and mixing occurs. Many internal waves in the ocean are strongly nonlinear with internal solitary waves being the most striking example. Here nonlinearity and dispersion act in concert to create a large coherent wave that can propagate large distances. Extreme examples of these waves have amplitudes approaching 200 m (four times the height of Niagara Falls) though amplitudes of tens of meters are the norm. Currents associated with internal solitary waves modify the surface wave field making their presence detectible from space and can impact off-shore structures making these waves of interest to the off-shore oil industry. The proposed research will address aspects of the predictability and unpredictability of internal waves via numerical simulations and mathematical modelling. It will address the generation of internal waves by tide-topography interactions focussing on energy transfer to internal solitary waves and their role in vertical mixing. A case study will focus on wave generation on the Peruvian shelf where observations suggest that internal waves are responsible for the vertical mixing of heat and for the seasonal variability in biological productivity. The shoaling of internal solitary waves with an emphasis on the occurrence of breaking will be studied and shear instabilities in internal solitary waves, which result in the vertical mixing of heat and nutrients, will be investigated. Other aspects of the predictability of these waves will be investigated including the interaction of internal waves of tidal frequency with eddies and vortices in the ocean, which affects the long-distance propagation of internal waves, and the occurrence of different forms of internal waves, e.g., breathers which are special nonlinear, pulsating wave packets. This research will improve our capability to predict the internal wave field in the ocean and will enable better predictions of processes such as large scale ocean circulation, cross-shelf exchange, biological productivity and the shaping of our continental shelf and help in the design and operation of off-shore structures.