Semigeostrophic Particle Motion and Exponentially Accurate Normal forms
Semigeostrophic Particle Motion and Exponentially Accurate Normal forms
复制标题
半地转粒子运动和指数精确的范式
DOI：
10.1137/05064326x
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
S. Reich
中科院分区：
文献类型：
--
作者：
C. Cotter;S. Reich
我们给出了一个半转极限下在旋转浅水系统中运动的拉格朗日粒子的指数精确范式，它描述了指数精确的慢流形区域内的运动（快尺度动力学在罗斯比数中呈指数小的相空间区域）。我们证明了这个结果是如何与[M]的变分渐近方法相关联的。奥利弗，J.流体机械师。， 551 (2006), pp. 197-234]；不同之处在于，在哈密顿方面，有可能获得远离（但接近）慢流形的快速运动增长的强界。我们的范式方法通过反向误差分析扩展到数值近似，并扩展到浅水方程的粒子方法，其中结果表明，粒子在半转极限下长时间保持接近平衡。
We give an exponentially accurate normal form for a Lagrangian particle moving in a rotating shallow-water system in the semigeostrophic limit, which describes the motion in the region of an exponentially accurate slow manifold (a region of phase space for which dynamics on the fast scale are exponentially small in the Rossby number). We show how this result is related to the variational asymptotics approach of [M. Oliver, J. Fluid Mech., 551 (2006), pp. 197-234]; the difference is that on the Hamiltonian side it is possible to obtain strong bounds on the growth of fast motion away from (but close to) the slow manifold. Our normal form approach extends to numerical approximations via backward error analysis and extends to particle methods for the shallow-water equations, where the result shows that particles stay close to balance over long times in the semigeostrophic limit.