One-dimensional "turbulence" in a discrete lattice

Area of Science:

• Nonlinear dynamics
• Fluid mechanics
• Statistical physics

Background:

• The von Karman flow is a key model for turbulence.
• Understanding energy transfer and scaling in nonlinear systems is crucial.

Purpose of the Study:

• To investigate a discrete analog of von Karman flow.
• To characterize energy density and dissipation in a nonlinear lattice.
• To compare system dynamics to fluid turbulence and inertial systems.

Main Methods:

• Simulating a 1D lattice of anharmonic oscillators with damping.
• Analyzing energy density in real and Fourier space.
• Examining probability distributions of velocity increments and dissipated power.

Main Results:

• At low excitation, a stable power-law energy spectrum emerges, indicative of interacting scales.
• At high excitation, discrete breathers dominate, leading to an exponential energy spectrum.
• Velocity increment distributions mimic experimental turbulence, described by nonextensive thermodynamics.
• Dissipated power exhibits non-Gaussian fluctuations, characteristic of inertial systems.

Conclusions:

• The discrete analog captures key features of fluid turbulence, including scaling laws and non-Gaussian statistics.
• Discrete breathers play a role analogous to vortices in fluid dynamics.
• The system's behavior provides insights into inertial systems and nonlinear energy transfer.