衰减锋面暖心涡
Frictionally decaying frontal warm-core eddies
摘要：
利用非线性、非定常简化重力浅水方程，半解析地研究了受Rayleigh摩擦影响的非定常、非线性、轴对称、暖核地球物理表面锋面涡的动力学。在此框架下，发现径向速度呈线性分布、截面速度和方位速度呈任意结构的涡都可以用一组非定常、非线性的耦合常微分方程精确描述。一阶问题（即，描述以线性方位角速度场和二次截面为特征的涡旋）由4个微分方程组成，并且每进一步的阶在系统中引入3个附加的常微分方程和2个代数方程。为了说明的非定常衰减涡的行为，系统的解决方案的一阶和二阶的问题，然后获得数值使用龙格-库塔法。该解决方案表明，惯性振荡和指数衰减占主导地位的涡动力学：膨胀和变浅，收缩和加深交替在一个确切的惯性周期，而涡衰减。涡耗散率对初始半径的依赖关系是非单调的：小半径和大半径的涡耗散率都较高。我们的分析增加了现实主义以前的理论研究中尺度涡，代表了一个理想的工具，用于测试的数值模型的准确性，在模拟非线性，非平稳摩擦锋面现象在旋转的海洋，并铺平了道路，进一步扩展（半）分析解决方案的流体动力地球物理问题，更任意的形式和更复杂的密度分层。
英文摘要：
The dynamics of nonstationary, nonlinear, axisymmetric, warm-core geophysical surface frontal vortices affected by Rayleigh friction is investigated semi-analytically using the nonlinear, nonstationary reduced-gravity shallow-water equations. In this frame, it is found that vortices characterized by linear distributions of their radial velocity and arbitrary structures of their section and azimuthal velocity can be described exactly by a set of nonstationary, nonlinear coupled ordinary differential equations. The first-order problem (i.e., that describing vortices characterized by a linear azimuthal velocity field and a quadratic section) consists of a system of 4 differential equations, and each further order introduces in the system three additional ordinary differential equations and two algebraic equations. In order to illustrate the behavior of the nonstationary decaying vortices, the system's solution for the first-order and for the second-order problem is then obtained numerically using a Runge-Kutta method. The solutions demonstrate that inertial oscillations and an exponential attenuation dominate the vortex dynamics: Expansions and shallowings, contractions and deepenings alternate during an exact inertial period while the vortex decays. The dependence of the vortex dissipation rate on its initial radius is found to be non-monotonic: It is higher for small and large radii. Our analysis adds realism to previous theoretical investigations on mesoscale vortices, represents an ideal tool for testing the accuracy of numerical models in simulating nonlinear, nonstationary frictional frontal phenomena in a rotating ocean, and paves the way to further extensions of (semi-) analytical solutions of hydrodynamical geophysical problems to more arbitrary forms and more complex density stratifications.
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