Periodic motion representing isotropic turbulence

  title={Periodic motion representing isotropic turbulence},
  author={Lennaert van Veen and Shigeo Kida and Genta Kawahara},
  journal={Fluid Dynamics Research},
We investigate unstable periodic motion embedded in isotropic turbulence with high symmetry. Several orbits of different period are continued from the regime of weak turbulence into developed
Unstable periodic motion in turbulent flows
Recently found unstable time-periodic solutions to the incompressible Navier-Stokes equation are reviewed to discuss their relevance to plane Couette turbulence and isotropic turbulence. It is shown
Irreversible mixing by unstable periodic orbits in stratified turbulence
We consider turbulence driven by a large scale horizontal shear in Kolmogorov flow (i.e. with sinusoidal body forcing) and a background linear stable stratification with buoyancy frequency $N_B^2$
Recently both shear turbulence and isotropic turbulence have been investigated by means of unstable periodic orbits. These orbits are embedded in a high dimensional chaotic attractor that represents
Quasi-cyclic evolution of turbulence driven by a steady force in a periodic cube
The quasi-cyclic evolution of turbulence driven by a steady force in a periodic cube is investigated by means of large-eddy simulations with vanishing kinematic viscosity. By constraining the domain
Irreversible mixing by unstable periodic orbits in buoyancy dominated stratified turbulence
We consider turbulence driven by a large-scale horizontal shear in Kolmogorov flow (i.e. with sinusoidal body forcing) and a background linear stable stratification with buoyancy frequency
A vortex interaction mechanism for generating energy and enstrophy fluctuations in high-symmetric turbulence
Turbulent vortex dynamics is investigated in triply periodic turbulent flow with Kida’s high symmetry (Kida, J. Phys. Soc. Japan, vol. 54, 1985, pp. 2132–2136) by means of unstable periodic motion
Transitions in large eddy simulation of box turbulence
Abstract One promising decomposition of turbulent dynamics is that into building blocks such as equilibrium and periodic solutions and orbits connecting these. While the numerical approximation of
The Significance of Simple Invariant Solutions in Turbulent Flows
Recent remarkable progress in computing power and numerical analysis is enabling us to fill a gap in the dynamical systems approach to turbulence. One of the significant advances in this respect has
Unstable periodic orbits in turbulent hydrodynamics
A novel parallel space-time algorithm for the computation of periodic solutions of the driven, incompressible Navier-Stokes equations in the turbulent regime is described and the potential for this approach to become a new paradigm in the study of driven, dissipative dynamical systems is discussed.


Spatiotemporal intermittency and instability of a forced turbulence
The time development of an infinitesimal disturbance and the relation to the spatiotemporal intermittency of a developed turbulence is studied by solving numerically the Navier–Stokes equation and
Periodic motion embedded in plane Couette turbulence: regeneration cycle and burst
Two time-periodic solutions with genuine three-dimensional structure are numerically discovered for the incompressible Navier–Stokes equation of a constrained plane Couette flow. One solution with
Lyapunov exponents and the dimension of periodic incompressible Navier—Stokes flows: numerical measurements
In this paper we study the quasi-stationary turbulent state developed by an incompressible flow submitted to a constant periodic force. The turbulent state is described by its Lyapunov exponents and
Structures and structure functions in the inertial range of turbulence
The deviations from the Kolmogorov 1941 laws of inertial range of turbulence are investigated using the results from the direct numerical simulations of an unforced flow starting from a high-symmetry
A route to chaos and turbulence
Kolmogorov similarity in freely decaying turbulence
A direct numerical simulation of the three‐dimensional Navier–Stokes equation at high Reynolds numbers is performed by the spectral method with 3×3403 effective modes (853 independent degrees of
Short-time Lyapunov exponent analysis and the transition to chaos in Taylor–Couette flow
Short-time Lyapunov exponent analysis is a new approach to the study of the stability properties of unsteady flows. At any instant in time the Lyapunov perturbations are the set of infinitesimal
Unstable periodic solutions embedded in a shell model turbulence.
  • S. Kato, M. Yamada
  • Physics, Environmental Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2003
An approach to intermittency of a shell model turbulence is proposed from the viewpoint of dynamical systems and the attractor in the phase space is found to be well approximated by a continuous set of solutions generated from the UPO through a one-parameter phase transformation.