Generation of internal waves by ocean tides

IDES是海洋对众所周知的太阳和月球引力的反应。这些巨大的能量振荡影响着地球系统的各个部分，如月球轨道的历史，大规模海洋环流的热量输送，以及流入极地海洋的冰盖。当潮流流经海洋底部地形时，它们在密度分层的海洋内部产生潮汐频率的重力内波。虽然从海洋表面几乎看不到这些内部潮汐，但它们在一系列沿海和开阔海洋的动力学中发挥着重要作用。特别令人感兴趣的是从(表面)潮汐转化为内潮的能量(以及隐含的内潮阻力对深度平均流动的影响)，以及这种能量如何在海洋内部传输。在这个博士项目中，将在以前的二维研究的基础上，在理想化的三维几何中开发简单的内潮产生和传播的数学模型。这涉及到对运动(例如，线性、弱非线性、时间周期)、密度分层(例如，均匀、分段恒定)和海底地形(例如，小幅度、阶跃)的简化假设的某种组合，以便可以将非线性运动偏微分方程组简化为更容易处理的系统。然后，可以通过解析或简单的数值计算来寻求解决方案，从而允许探索广泛的参数空间。这将使我们更好地理解在不同的强迫情况下从(表面)潮汐到内潮的能量转移，这与地形宽度和高度有很大的关系。一个特别的重点将是将[7]的解决方案和方法推广到三维环境中，该方法解释了任意大的地形变化，但仅在二维情况下。主要目标是：1。了解由二维地形(代表大陆坡度)上方的三维表面潮汐(特别是开尔文波)产生的内潮。在许多沿海地区，开尔文波是表层潮汐的主要形式，所隐含的能量转移在全球范围内是重要的。了解沿海岸方向的地形起伏的作用，即在完全三维地形之上的三维潮汐。从观测中得知，峡谷(例如)导致内部潮汐产生(和消散)增强。

ides are the oceanic response to well-known gravitational forcing by the Sun and Moon. These hugely energetic oscillations influence various parts of the Earth system, such as the history of the lunar orbit, the transport of heat by the large-scale ocean circulation, and ice sheets flowing into the polar oceans.As tidal currents flow over the bottom topography of the ocean, they generate internal gravity waves of tidal frequency in the density-stratified ocean interior. Although almost invisible from the ocean surface, these internal tides play an important role in a range of coastal and open-ocean dynamics. Of particular interest is the amount of energy converted from the (surface) tide to internal tides (along with the magnitude of the implied internal tide drag on the depth-averaged flow), and how this energy is transported within the ocean interior.In this PhD project, simple mathematical models of internal tide generation and propagation will be developed in idealised three-dimensional geometries, building on previous two-dimensional studies. This involves making some combination of simplifying assumptions about the motion (e.g., linear, weakly nonlinear, time-periodic), density stratification (e.g., uniform, piecewise constant), and sea-floor topography (e.g., small-amplitude, stepped), so that the nonlinear partial differential equations of motion can be reduced to a more tractable system. Solutions can then be sought analytically or via simple numerical computations, allowing a wide range of parameter space to be explored. This gives a better understanding of the energy transfer from (surface) tides to internal tides in different forcing scenarios, which is known to have a non-trivial dependence upon topographic width and height.A particular focus would be on extending the solutions and methods of [7], which accounted for arbitrarily large topographic variations but only in two dimensions, to three-dimensional settings. The main targets are to1. Understand internal tides generated by a three-dimensional surface tide (in particular, the Kelvin wave) above a two-dimensional topography (representing a continental slope). The Kelvin wave is the dominant form of the surface tide in many coastal zones, and the implied energy transfers are significant on a global scale.2. Understand the role of topographic undulations in the along-shore direction, i.e., for a three-dimensional tide above a fully three-dimensional topography. It is known from observations that canyons (for exam-ple) lead to enhanced internal tide generation (and dissipation).