An Efficient Continuous Data Assimilation Algorithm for the Sabra Shell Model of Turbulence

Abstract

Complex nonlinear turbulent dynamical systems are ubiquitous in many areas. Recovering unobserved state variables is an important topic for the data assimilation of turbulent systems. In this article, an efficient continuous in time data assimilation scheme is developed, which exploits closed analytic formulae for updating the unobserved state variables. Therefore, it is computationally efficient and accurate. The new data assimilation scheme is combined with a simple reduced order modeling technique that involves a cheap closure approximation and a noise inflation. In such a way, many complicated turbulent dynamical systems can satisfy the requirements of the mathematical structures for the proposed efficient data assimilation scheme. The new data assimilation scheme is then applied to the Sabra shell model, which is a conceptual model for nonlinear turbulence. The goal is to recover the unobserved shell velocities across different spatial scales. It has been shown that the new data assimilation scheme is skillful in capturing the nonlinear features of turbulence including the intermittency and extreme events in both the chaotic and the turbulent dynamical regimes. It has also been shown that the new data assimilation scheme is more accurate and computationally cheaper than the standard ensemble Kalman filter and nudging data assimilation schemes for assimilating the Sabra shell model.

References in corpus (8)

• An optimal shell model of turbulence
• Continuous Data Assimilation Using General Interpolant Observables
• Extreme learning machine for reduced order modeling of turbulent geophysical flows
• Data-Driven Variational Multiscale Reduced Order Models
• Continuous Data Assimilation for a 2D Bénard Convection System through Horizontal Velocity Measurements Alone
• Probabilistic description of extreme events in intermittently unstable systems excited by correlated stochastic processes
• Data-Driven Correction Reduced Order Models for the Quasi-Geostrophic Equations: A Numerical Investigation
• Anomalous scaling in a shell model of helical turbulence

Cited by in corpus (1)

• The Bleeps, the Sweeps, and the Creeps: Convergence Rates for Dynamic Observer Patterns via Data Assimilation for the 2D Navier-Stokes Equations