Laminar and Turbulent flow Behaviors in a 3-D Kinetic-based Discrete Dynamical System *

A 3-D discrete dynamical system (DDS) has been derived in Fourier space based on the lattice Boltzmann equation (LBE) involving four bifurcation parameters, the relaxation time τ from the LBE, and the three wave-vector components k_x, k_y, and k_z. Numerical experiments employing combinations of these bifurcation parameters have produced laminar and turbulent flow behaviors such as periodic, subharmonic, n-period, quasiperiodic, noisy periodic with harmonics, noisy subharmonic, noisy quasiperiodic, and broadband. We now explore the underlying physics behind the observed flow behaviors in terms of the interactions among scales of motion, energy transport from large scale to small scale, etc. This DDS will be used to generate sub-grid scale (SGS) information in the large-eddy simulation of pulsatile turbulence in the LBE. The kinetic-based DDS, by nature of its construction, carries some large-scale information (as observed) not typically found in other similar DDSs. It is important to account for this when constructing SGS models so as not to count intermediate scales repeatedly.