An Efficient Continuous Data Assimilation Algorithm for the Sabra Shell Model of Turbulence
release_jwgcjsmybrg3hopgpjkv343qki
by
Nan Chen, Yuchen Li, Evelyn Lunasin
2021
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.
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