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Related Experiment Video

Updated: Apr 12, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published on: February 22, 2018

Cascades in nonlocal turbulence.

Gregory Falkovich^1,2, Natalia Vladimirova³

¹Weizmann Institute of Science, Rehovot 76100, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 15, 2015

Summary

This summary is machine-generated.

We derived exact turbulence flux laws for the Gross-Pitaevskii model, confirming them with simulations. These laws, valid for any nonlinearity, reveal nonlocal wave interactions drive turbulence.

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Area of Science:

Physics
Fluid Dynamics
Quantum Mechanics

Background:

Developed turbulence in the 2D Gross-Pitaevskii model is crucial for understanding phenomena in atomic physics, optics, condensed matter, fluids, and plasma.
Weak-turbulence approximations fail to predict realistic local spectra and energy fluxes in turbulent systems.
Existing theoretical frameworks struggle with the complexities of inverse and direct cascades in this model.

Purpose of the Study:

To analytically derive exact flux constancy laws for developed turbulence in the 2D Gross-Pitaevskii model.
To validate these laws through direct numerical simulations.
To elucidate the underlying mechanisms responsible for maintaining constant energy fluxes in turbulent cascades.

Main Methods:

Analytical derivation of flux constancy laws using the fourth-order moment.
Confirmation of derived laws via direct numerical simulations of the 2D Gross-Pitaevskii equation.
Analysis of wave spectra (second-order moments) to understand equilibrium properties.

Main Results:

Exact flux constancy laws, analogous to Kolmogorov's laws, were derived and confirmed.
These laws are valid for any nonlinearity within the Gross-Pitaevskii model.
Nonlocal wave interactions were identified as the mechanism responsible for constant fluxes in both direct and inverse cascades.
Wave spectra were found to closely resemble slightly distorted thermal equilibrium.

Conclusions:

The derived flux laws provide a robust framework for understanding turbulence in the 2D Gross-Pitaevskii model.
Nonlocal interactions are essential for realizing realistic turbulent spectra and fluxes.
The findings offer new insights into the behavior of wave turbulence across various physical systems.