Determining modes and Grashof number in 2D turbulence: a numerical case study Academic Article uri icon

abstract

  • We study how the number of numerically determining modes in the Navier-Stokes equations depends on the Grashof number. Consider the two-dimensional incompressible Navier-Stokes equations in a periodic domain with a fixed time-independent forcing function. We increase the Grashof number by rescaling the forcing and observe through numerical computation that the number of numerically determining modes stabilizes at some finite value as the Grashof number increases. This unexpected result implies that our theoretical understanding of continuous data assimilation is incomplete until an analytic proof which makes use of the non-linear term in the Navier-Stokes equations is found. 2008 Springer-Verlag.

published proceedings

  • Theoretical and Computational Fluid Dynamics

altmetric score

  • 3

author list (cited authors)

  • Olson, E., & Titi, E. S.

citation count

  • 22

complete list of authors

  • Olson, Eric||Titi, Edriss S

publication date

  • August 2008