Nonrobustness of the two-dimensional turbulent inverse cascade

Energy and enstrophy spectra and fluxes for the inertial-dissipation range of two-dimensional turbulence

In this paper, using Pao's conjecture [Y.-H. Pao, Phys. Fluids 8, 1063 (1965)10.1063/1.1761356], we derive expressions for the spectra and fluxes of kinetic energy and enstrophy for two-dimensional (2D) forced turbulence that extend beyond the inertial range. In these expressions, the fluxes and the spectra contain additional factors of the exponential form. To validate these model predictions, we perform numerical simulations of 2D turbulence with external force applied at wavenumber band (k_{f},k_{f}+1) in the intermediate range. The numerical results match with the model predictions, except for the energy and enstrophy fluxes for k<k_{f}, where the fluxes exhibit significant fluctuations. We show that these fluctuations arise due to the unsteady nature of the flow at small wavenumbers. For k<k_{f}, the shell-to-shell energy transfers computed using numerical data show forward energy transfers among the neighboring shells, but backward energy transfers among other shells.

Instability onset and scaling laws of an auto-oscillating turbulent flow in a complex plasma

We study a complex plasma under microgravity conditions that is first stabilized with an oscillating electric field. Once the stabilization is stopped, the so-called heartbeat instability develops. We study how the kinetic energy spectrum changes during and after the onset of the instability and compare with the double cascade predicted by Kraichnan and Leith for two-dimensional turbulence. The onset of the instability manifests clearly in the ratio of the reduced rates of cascade of energy and enstrophy and in the power-law exponents of the energy spectra.

Lattice Boltzmann simulation for forced two-dimensional turbulence

The direct numerical simulations of forced two-dimensional turbulent flow are presented by using the lattice Boltzmann method. The development of an energy-enstrophy double cascade is investigated in the two cases of external force of two-dimensional turbulence, Gaussian force and Kolmogorov force. It is found that the friction force is a necessary condition of the occurrence of a double cascade. The energy spectrum k(-3) in the enstrophy inertial range is in accord with the classical Kraichnan theory for both external forces. The energy spectrum of the Gaussian force case in an inverse cascade is k(-2); however, the Kolmogorov force drives the k(-5/3) energy in a backscatter cascade. The result agrees with Scott's standpoint, which describes nonrobustness of the two-dimensional turbulent inverse cascade. Also, intermittency is found for the enstrophy cascade in two cases of the external force form. Intermittency refers to the nonuniform distribution of saddle points in the two-dimensional turbulent flow.

Transition of the scaling law in inverse energy cascade range caused by a nonlocal excitation of coherent structures observed in two-dimensional turbulent fields

We numerically investigate the inverse energy cascade range of two-dimensional Navier-Stokes turbulence. Our focus is on the universality of the Kolmogorov's phenomenology. In our direct numerical simulations, two types of forcing processes, the random forcing and the deterministic forcing, are employed besides the systematically varied numerical parameters. We first calculate the two-dimensional Navier-Stokes equations and confirm that results in the quasi steady state are consistent with the classical phenomenology for both types of forcing processes. It is also found that the difference in forcing process appears after the inverse energy cascade range reaches the system size; the dipole coherent vortices emerge and grow only when the random forcing is adopted. Then we add a large-scale drag term to the Navier-Stokes equations to obtain the statistically stationary state. When the random forcing is used, the scaling exponent of the energy spectrum in the stationary state starts to differ from the predicted -5/3 in the inverse energy cascade range as the infrared Reynolds number Re(d) increases, where Re(d) is defined as k(f)/k(d) with the forcing wave number k(f) and the large-scale drag wave number k(d). That can be interpreted as a transition phenomenon in which the local maximum vorticity grows like an order parameter caused by excitation of strong coherent vortices. Strong coherent vortices emerge and grow after the quasi steady state and destroy the scaling law when Re(d) is over a critical value. These coherent vortices are not due to the finite-size effect, unlike the dipole coherent vortices. On the other hand, when the deterministic forcing is adopted, strong coherent vortices are hardly seen and the -5/3 scaling law holds independently of Re(d). We examine the cases of the combination of both types of forcing processes and find that formation of such coherent vortices is sensitive to the mechanism of the external forcing process as well as the numerical parameters. Several types of large-scale drag terms are also tested and their insignificant influence on these qualitative properties is revealed.

Fluid turbulence in quantum plasmas

Nonlinear fluid simulations are developed by us to investigate the properties of fully developed two-dimensional (2D) electron fluid turbulence in a very dense Fermi (quantum) plasma. We find that a 2D quantum electron plasma exhibits dual cascades, in which the electron number density cascades towards smaller turbulent scales, while the electrostatic potential forms larger scale eddies. The characteristic turbulent spectrum associated with the nonlinear electron plasma oscillations (EPO) is determined critically by a ratio of the energy density of the EPOs and the electron kinetic energy density of quantum plasmas. The turbulent transport corresponding to the large-scale potential distribution is predominant in comparison with the small-scale electron number density variation, a result that is consistent with the classical diffusion theory.