Hallerberg Sarah, Pazó Diego, López Juan M, Rodríguez Miguel A
Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, E-39005 Santander, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jun;81(6 Pt 2):066204. doi: 10.1103/PhysRevE.81.066204. Epub 2010 Jun 9.
Bred vectors are a type of finite perturbation used in prediction studies of atmospheric models that exhibit spatially extended chaos. We study the structure, spatial correlations, and the growth rates of logarithmic bred vectors (which are constructed by using a given norm). We find that, after a suitable transformation, logarithmic bred vectors are roughly piecewise copies of the leading Lyapunov vector. This fact allows us to deduce a scaling law for the bred vector growth rate as a function of its amplitude. In addition, we relate growth rates with the spectrum of Lyapunov exponents corresponding to the most expanding directions. We illustrate our results with simulations of the Lorenz 1996 model.
繁殖向量是一种有限扰动，用于具有空间扩展混沌特性的大气模型预测研究。我们研究了对数繁殖向量（通过使用给定范数构建）的结构、空间相关性和增长率。我们发现，经过适当变换后，对数繁殖向量大致是主导李雅普诺夫向量的分段副本。这一事实使我们能够推导出繁殖向量增长率作为其幅度函数的标度律。此外，我们将增长率与对应于最扩张方向的李雅普诺夫指数谱联系起来。我们用洛伦兹1996模型的模拟来说明我们的结果。
