TY - JOUR

T1 - Testing wave turbulence theory for the Gross-Pitaevskii system

AU - Zhu, Ying

AU - Semisalov, Boris

AU - Krstulovic, Giorgio

AU - Nazarenko, Sergey

N1 - Funding Information: This work is funded by the Simons Foundation Collaboration grant Wave Turbulence (Award ID 651471). Part of this work was granted access to the high-performance computing facilities under GENCI (Grand Equipement National de Calcul Intensif) A0102A12494 (IDRIS and CINES), the OPAL infrastructure from Université Côte d'Azur, supported by the French government, through the UCAJEDI Investments in the Future project managed by the National Research Agency (ANR) under Reference No. ANR-15-IDEX-01, and the SIGAMM infrastructure hosted by Observatoire de la Côte d'Azur and supported by the Provence-Alpes Côte d'Azur region. Publisher Copyright: © 2022 American Physical Society.

PY - 2022/7

Y1 - 2022/7

N2 - We test the predictions of the theory of weak wave turbulence by performing numerical simulations of the Gross-Pitaevskii equation (GPE) and the associated wave-kinetic equation (WKE). We consider an initial state localized in Fourier space, and we confront the solutions of the WKE obtained numerically with GPE data for both the wave-action spectrum and the probability density functions (PDFs) of the Fourier mode intensities. We find that the temporal evolution of the GPE data is accurately predicted by the WKE, with no adjustable parameters, for about two nonlinear kinetic times. Qualitative agreement between the GPE and the WKE persists also for longer times with some quantitative deviations that may be attributed to the combination of a breakdown of the theoretical assumptions underlying the WKE as well as numerical issues. Furthermore, we study how the wave statistics evolves toward Gaussianity in a timescale of the order of the kinetic time. The excellent agreement between direct numerical simulations of the GPE and the WKE provides a solid foundation to the theory of weak wave turbulence.

AB - We test the predictions of the theory of weak wave turbulence by performing numerical simulations of the Gross-Pitaevskii equation (GPE) and the associated wave-kinetic equation (WKE). We consider an initial state localized in Fourier space, and we confront the solutions of the WKE obtained numerically with GPE data for both the wave-action spectrum and the probability density functions (PDFs) of the Fourier mode intensities. We find that the temporal evolution of the GPE data is accurately predicted by the WKE, with no adjustable parameters, for about two nonlinear kinetic times. Qualitative agreement between the GPE and the WKE persists also for longer times with some quantitative deviations that may be attributed to the combination of a breakdown of the theoretical assumptions underlying the WKE as well as numerical issues. Furthermore, we study how the wave statistics evolves toward Gaussianity in a timescale of the order of the kinetic time. The excellent agreement between direct numerical simulations of the GPE and the WKE provides a solid foundation to the theory of weak wave turbulence.

UR - http://www.scopus.com/inward/record.url?scp=85134893925&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.106.014205

DO - 10.1103/PhysRevE.106.014205

M3 - Article

C2 - 35974496

AN - SCOPUS:85134893925

VL - 106

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 1

M1 - 014205

ER -