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Determining Modes for Continuous Data Assimilation in 2D Turbulence |
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| Authors: | Eric Olson Edriss S Titi |
| Institution: | (1) Department of Mathematics, University of California, Irvine, California, 92697;(2) Department of Mathematics, University of Nevada, Reno, Nevada, 89557;(3) Mechanical and Aerospace Engineering, University of California, Irvine, California, 92697;(4) Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel |
| 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. |
| Keywords: | determining modes continuous data assimilation |
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