Numerical simulation of two-dimensional turbulence based on Immersed Boundary Lattice Boltzmann method

Abstract

The two-dimensional turbulence is numerically investigated using Immersed Boundary Lattice Boltzmann Method. The 2D turbulence should be considered as 2D channel flow where the flow is forced by the arrays of cylinders vertically placed in the inlet of 2D channel. The inverse cascade in two cases, the normal wall boundary case and rough wall boundary case, is obtained in the inertial range. The scaling behavior of energy spectrum in the inverse cascade is k−5/3, which is according with the Kraichnan theory of 2D turbulence. It is found that the time-evolving vortex number density distribution n(A)∼t−1A−1, based on the Rortex vortex definition criterion, which is in fair agreement with the theory of Burgess and Scott at intermediate scales sufficiently far from the forcing and the largest vortex scale. The energy flux of the normal wall boundary case cascades to the large scale. The energy flux of the rough wall boundary case cascades to large scale when the scale l < D. The energy flux at l > D cascades to the small scale. The energy dissipation filed εl coarse grained at the scale l has the pow-law behaviors with the scale. The intermittency measured by PDF exists in the inverse inertial range of 2D turbulence. On the basis of the vortex scaling law of Burgess and Scott and our simulation results, the universal scaling law of velocity structure function in the inverse cascade is obtained by extending the 3D turbulent S-L intermittency model to the inverse inertial range of 2D turbulence.