Determining Modes for Continuous Data Assimilation in 2D Turbulence Conference Paper uri icon

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-1norm of f and computationally by considering a family of forcing functions with identical Grash of 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.

published proceedings

  • Journal of Statistical Physics

author list (cited authors)

  • Olson, E., & Titi, E. S.

citation count

  • 40

complete list of authors

  • Olson, Eric||Titi, Edriss S

publication date

  • December 2003