Related Experiment Video
Updated: Jul 5, 2025

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
Published on: February 13, 2018
Self-similar evolution of wave turbulence in Gross-Pitaevskii system
Ying Zhu1, Boris Semisalov2,3,4, Giorgio Krstulovic2
1Université Côte d'Azur, CNRS, Institut de Physique de Nice (INPHYNI), 17 rue Julien Lauprêtre 06200 Nice, France.
Abstract:
We study the universal nonstationary evolution of wave turbulence (WT) in Bose-Einstein condensates (BECs). Their temporal evolution can exhibit different kinds of self-similar behavior corresponding to a large-time asymptotic of the system or to a finite-time blowup. We identify self-similar regimes in BECs by numerically simulating the forced and unforced Gross-Pitaevskii equation (GPE) and the associated wave kinetic equation (WKE) for the direct and inverse cascades, respectively. In both the GPE and the WKE simulations for the direct cascade, we observe the first-kind self-similarity that is fully determined by energy conservation. For the inverse cascade evolution, we verify the existence of a self-similar evolution of the second kind describing self-accelerating dynamics of the spectrum leading to blowup at the zero mode (condensate) at a finite time. We believe that the universal self-similar spectra found in the present paper are as important and relevant for understanding the BEC turbulence in past and future experiments as the commonly studied stationary Kolmogorov-Zakharov (KZ) spectra.
Related Concept Videos
Euler's Equations of Motion
Laminar and Turbulent Flow
Propagation of Waves
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
Turbulent Flow
Navier–Stokes Equations
Deriving the Speed of Sound in a Liquid
The speed of sound in fluids can be derived by considering a mechanical wave...

