TY - JOUR
T1 - Cascades in nonlocal turbulence
AU - Falkovich, Gregory
AU - Vladimirova, Natalia
N1 - Part of this work was done during a visit to the Kavli Institute for Theoretical Physics, UCSB, supported by Grant No. NSF PHY11-25915. N.V. was supported in part by NSF Grant No. DMS-1412140. Simulations were performed at the Center for Advanced Research Computing, UNM, and the Texas Advanced Computing Center using the Extreme Science and Engineering Discovery Environment, which was supported by NSF Grant No. ACI-1053575. The work of G.F. was supported by grants of the Bi-National Science Foundation, Minerva Foundation with funding from the German Ministry for Education and Research and by Russian Science Foundation Projects No. 14-22-00259 and No. 14-50-00150 (for the development of the analytical theory and writing the paper).
PY - 2015/4/29
Y1 - 2015/4/29
N2 - We consider developed turbulence in the two-dimensional Gross-Pitaevskii model, which describes wide classes of phenomena from atomic and optical physics to condensed matter, fluids, and plasma. The well-known difficulty of the problem is that the hypothetical local spectra of both inverse and direct cascades in the weak-turbulence approximation carry fluxes that are either zero or have the wrong sign; Such spectra cannot be realized. We analytically derive the exact flux constancy laws (analogs of Kolmogorov's 4/5 law for incompressible fluid turbulence), expressed via the fourth-order moment and valid for any nonlinearity. We confirm the flux laws in direct numerical simulations. We show that a constant flux is realized by a nonlocal wave interaction in both the direct and inverse cascades. Wave spectra (second-order moments) are close to slightly (logarithmically) distorted thermal equilibrium in both cascades.
AB - We consider developed turbulence in the two-dimensional Gross-Pitaevskii model, which describes wide classes of phenomena from atomic and optical physics to condensed matter, fluids, and plasma. The well-known difficulty of the problem is that the hypothetical local spectra of both inverse and direct cascades in the weak-turbulence approximation carry fluxes that are either zero or have the wrong sign; Such spectra cannot be realized. We analytically derive the exact flux constancy laws (analogs of Kolmogorov's 4/5 law for incompressible fluid turbulence), expressed via the fourth-order moment and valid for any nonlinearity. We confirm the flux laws in direct numerical simulations. We show that a constant flux is realized by a nonlocal wave interaction in both the direct and inverse cascades. Wave spectra (second-order moments) are close to slightly (logarithmically) distorted thermal equilibrium in both cascades.
UR - http://www.scopus.com/inward/record.url?scp=84929176071&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.91.041201
DO - 10.1103/PhysRevE.91.041201
M3 - مقالة
SN - 1539-3755
VL - 91
JO - Physical Review E
JF - Physical Review E
IS - 4
M1 - 041201
ER -