2017/02/14 by Sven Baars, S. Baars, Jan Viebahn +8
Computer Science · Earth and Planetary Sciences · Environmental Science · Mathematics · Physics and Astronomy · #Applied mathematics #Climate variability and models #Computer science #Continuation #Flow (mathematics) #Geometry #Lyapunov function #Mathematical analysis #Mathematics #Meteorological Phenomena and Simulations #Nonlinear system #Partial differential equation #Physics #Probability density function #Statistical Mechanics and Entropy #Statistics #Stochastic differential equation #cs.NA #math.NA #physics.comp-ph #physics.data-an #physics.flu-dyn #physics.geo-ph
paper · pdf · doi:10.1016/j.jcp.2017.02.021
published as Journal of Computational Physics 336 (2017) 627-643
openalex publication_date 2017/02/14 · arxiv created 2020/11/11 · arxiv updated 2020/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.