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Determining Modes for Continuous Data Assimilation in 2D Turbulence

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Abstract

We study the number of determining modes necessary for continuous data assimilation in the two-dimensional incompressible Navier–Stokes equations. Our focus is on how the spatial structure of the body forcing affects the rate of continuous data assimilation and the number of determining modes. We treat this problem analytically by proving a convergence result depending on the H −1 norm of f and computationally by considering a family of forcing functions with identical Grashof numbers that are supported on different annuli in Fourier space. The rate of continuous data assimilation and the number of determining modes is shown to depend strongly on the length scales present in the forcing.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Irvine, California, 92697

    Eric Olson & Edriss S. Titi

  2. Department of Mathematics, University of Nevada, Reno, Nevada, 89557

    Eric Olson

  3. Mechanical and Aerospace Engineering, University of California, Irvine, California, 92697

    Edriss S. Titi

  4. Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel

    Edriss S. Titi

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  1. Eric Olson
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Olson, E., Titi, E.S. Determining Modes for Continuous Data Assimilation in 2D Turbulence. Journal of Statistical Physics 113, 799–840 (2003). https://doi.org/10.1023/A:1027312703252

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