2016/04/07 by Mohammad Farazmand, Themistoklis Sapsis · 2 citations
Mathematics · Physics and Astronomy · #math.DS #nlin.CD #physics.comp-ph #physics.flu-dyn
paper · pdf · doi:10.1103/physreve.94.032212
published as Phys. Rev. E 94, 032212 (2016)
arxiv created 2016/04/07 · arxiv updated 2016/09/21
Drawing upon the bursting mechanism in slow-fast systems, we propose indicators for the prediction of such rare extreme events which do not require a priori known slow and fast coordinates. The indicators are associated with functionals defined in terms of Optimally Time Dependent (OTD) modes. One such functional has the form of the largest eigenvalue of the symmetric part of the linearized dynamics reduced to these modes. In contrast to other choices of subspaces, the proposed modes are flow invariant and therefore a projection onto them is dynamically meaningful. We illustrate the application of these indicators on three examples: a prototype low-dimensional model, a body forced turbulent fluid flow, and a unidirectional model of nonlinear water waves. We use Bayesian statistics to quantify the predictive power of the proposed indicators.