Olson, Eric; Titi, Edriss S. Determining modes for continuous data assimilation in 2D turbulence. (English) Zbl 1137.76402 J. Stat. Phys. 113, No. 5-6, 799-840 (2003). Summary: 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. Cited in 43 Documents MSC: 76F99 Turbulence Keywords:determining modes; continuous data assimilation PDFBibTeX XMLCite \textit{E. Olson} and \textit{E. S. Titi}, J. Stat. Phys. 113, No. 5--6, 799--840 (2003; Zbl 1137.76402) Full Text: DOI