非均匀正压体积强迫产生的内潮
Internal tide generation from non-uniform barotropic body forcing
AI总结：
本文提出耦合模态系统建模非均匀正压潮受一维地形强迫产生的线性内潮，解析恢复WTA并数值刻画任意地形下的能量辐射与临界性规律。
摘要：
我们对正压潮与一维地形相互作用所产生的线性、无黏内潮进行建模。从该水动力学问题的体积强迫公式出发，我们利用流函数的局部本征函数展开，推导出一个耦合模态系统（Coupled-Mode System, CMS）。对于微小地形，我们解析求解该CMS，恢复了正压至斜压能量转换率的经典弱地形近似（Weak Topography Approximation, WTA）公式。对于任意地形，我们数值求解该CMS。与现有模态解相比，CMS具有更快的收敛性，并可同时应用于次临界和超临界区域中的海脊与陆架剖面。我们表明，非均匀正压潮会在大坡度地形上局部影响斜压场，并研究辐射能量转换率对临界性的依赖。我们表明，非辐射或弱辐射地形在次临界区域很常见。我们还评估了WTA近似在常用高斯海脊以及本文首次研究的紧支撑凸包海脊上的有效区域。最后，我们提供数值证据表明，在强超临界区域，海脊（分别地，陆架）的能量转换率趋近于刀刃形（分别地，阶梯形）地形所得的值。
英文摘要：
We model linear, inviscid, internal tides generated by the interaction of a barotropic tide with one-dimensional topography. Starting from the body-forcing formulation of the hydrodynamic problem, we derive a Coupled-Mode System (CMS) using a local eigenfunction expansion of the stream function. For infinitesimal topography, we solve this CMS analytically, recovering the classical Weak Topography Approximation (WTA) formula for the barotropic-to-baroclinic energy conversion rate. For arbitrary topographies, we solve this CMS numerically. The CMS enjoys faster convergence with respect to existing modal solutions and can be applied in the subcritical and supercritical regimes for both ridges and shelf profiles. We show that the non-uniform barotropic tide affects the baroclinic field locally over topographies with large slopes and we study the dependence of the radiated energy conversion rate on the criticality. We show that non-radiating or weakly radiating topographies are common in the subcritical regime. We also assess the region of validity of the WTA approximation for the commonly used Gaussian ridge and a compactly supported bump ridge studied here for the first time. Finally, we provide numerical evidence showing that in the strongly supercritical regime the energy conversion rate for a ridge (resp. shelf) approaches the value obtained by the knife-edge (resp. step) topography.
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