One-dimensional hydrodynamic model generating a turbulent cascade.
As a minimal mathematical model generating cascade analogous to that of the Navier-Stokes turbulence in the inertial range, we propose a one-dimensional partial-differential-equation model that conserves the integral of the squared vorticity analog (enstrophy) in the inviscid case. With a large-scale random forcing and small viscosity, we find numerically that the model exhibits the enstrophy cascade, the broad energy spectrum with a sizable correction to the dimensional-analysis prediction, peculiar intermittency, and self-similarity in the dynamical system structure.
Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto, 606-8502, Japan.
Takeshi
T
Matsumoto
Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto, 606-8502, Japan.
Takashi
T
Sakajo