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An efficient continuous data assimilation algorithm for the Sabra shell model of turbulence.

Nan Chen1, Yuchen Li1, Evelyn Lunasin2

  • 1Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA.

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This study introduces an efficient continuous-time data assimilation scheme for complex turbulent systems. The method accurately recovers unobserved variables, outperforming standard techniques for nonlinear turbulence models.

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Area of Science:

  • Physics
  • Applied Mathematics
  • Complex Systems

Background:

  • Complex nonlinear turbulent dynamical systems are prevalent across scientific disciplines.
  • Accurate recovery of unobserved state variables is crucial for data assimilation in turbulent systems.

Purpose of the Study:

  • To develop an efficient continuous-in-time data assimilation scheme for nonlinear turbulent systems.
  • To enhance the computational efficiency and accuracy of state variable recovery.

Main Methods:

  • Development of a continuous-in-time data assimilation scheme utilizing closed analytic formulas.
  • Integration with a reduced-order modeling technique featuring closure approximation and noise inflation.
  • Application to the Sabra shell model, a conceptual model for nonlinear turbulence.

Main Results:

  • The proposed scheme accurately captures nonlinear turbulence features, including intermittency and extreme events.
  • Demonstrated effectiveness in both chaotic and turbulent dynamical regimes.
  • Outperformed standard ensemble Kalman filter and nudging schemes in accuracy and computational cost for the Sabra shell model.

Conclusions:

  • The novel data assimilation scheme offers a computationally efficient and accurate solution for analyzing complex turbulent systems.
  • The method shows significant promise for applications requiring the assimilation of partial observations in nonlinear dynamics.
  • Successfully recovers unobserved shell velocities, providing insights into turbulence across various spatial scales.