准地转流的一个表面感知投影基
A surface-aware projection basis for quasigeostrophic flow
摘要：
最近的研究表明，海洋中尺度涡动场的高度观测反映了表面浮力和内部位渦异常的综合影响。前者有一个表面陷阱的结构，而后者有一个更严重的形式。为了评估每种对信号的贡献的相对重要性，将观察到的场投影到一组模式上是有用的，这些模式以自然的方式分离它们的影响。然而，表面捕获的动力学是不能很好地代表标准的斜压模态，而且，它们是依赖于水平尺度。在这里，我们推导出一个模态分解，结果从同时对角化的能量和概括的潜在拟能，包括从表面浮力场的贡献。这种方法产生了一个家庭的正交基，取决于两个参数：标准斜压模式恢复在一个限制的情况下，而其他选择提供的模式，代表表面和内部动力学在一个有效的方式。对于恒定分层，这些模式包括对称和反对称指数模式，捕捉表面动态，和一系列的振荡模式，代表内部动态。出于海洋，剪切集中在上表面附近，我们还考虑了一个静止的下表面的特殊情况。在这种情况下，内部模态与波数无关，并且有一个单一的指数表面模态代替正压模态。我们证明了这些模式的使用和有效性，通过投影的能量在一组模拟斜压湍流。
英文摘要：
Recent studies indicate that altimetric observations of the ocean's mesoscale eddy field reflect the combined influence of surface buoyancy and interior potential vorticity anomalies. The former have a surface-trapped structure, while the latter have a more grave form. To assess the relative importance of each contribution to the signal, it is useful to project the observed field onto a set of modes that separates their influence in a natural way. However, the surface-trapped dynamics are not well-represented by standard baroclinic modes; moreover, they are dependent on horizontal scale. Here we derive a modal decomposition that results from the simultaneous diagonalization of the energy and a generalisation of potential enstrophy that includes contributions from the surface buoyancy fields. This approach yields a family of orthonomal bases that depend on two parameters: the standard baroclinic modes are recovered in a limiting case, while other choices provide modes that represent surface and interior dynamics in an efficient way. For constant stratification, these modes consist of symmetric and antisymmetric exponential modes that capture the surface dynamics, and a series of oscillating modes that represent the interior dynamics. Motivated by the ocean, where shears are concentrated near the upper surface, we also consider the special case of a quiescent lower surface. In this case, the interior modes are independent of wavenumber, and there is a single exponential surface mode that replaces the barotropic mode. We demonstrate the use and effectiveness of these modes by projecting the energy in a set of simulations of baroclinic turbulence.
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