# Emergent isotropy of a wave-turbulent cascade in the Gross-Pitaevskii model

Yuto Sano (Osaka City University) talks about “Emergent isotropy of a wave-turbulent cascade in the Gross-Pitaevskii model”.

Turbulence is an ubiquitous phenomenon in nonlinear science and one of its remarkably emergent features is the statistical restoration of symmetries. Weak flows are typically sensitive to boundary conditions - even far from the boundaries - and often break various symmetries (associated with the direction of the flow, for instance). On the other hand, at large fluid velocities, such broken symmetries are usually restored, in a statistical sense, at small length scales [1]. Quantum turbulence has recently attracted interest as a way to better understand turbulence, and ultracold quantum gases have been a platform for many different studies of the turbulence, owing to its high controllability. In this talk, we report the problem of the restoration of isotropic symmetry in the Gross-Pitaevskii model [2]. This work is motivated by a set of recent experiments that studied turbulence of Bose gases in a cylindrical box trap [3,4]. These papers reported the emergence of a statistically isotropic power-law momentum distribution [3] and turbulent cascade [4] under a strongly anisotropic forcing, but a more detailed characterization of the emergence of isotropy was lacking. Therefore, we numerically investigate the development of turbulence and the emergence of isotropy by introducing a new measure of anisotropy. We indeed find that the anisotropy is strongly suppressed in the turbulent inertial range and that its steady-state value is robust with respect to the amplitude of the forcing. We find, quite surprisingly, that the anisotropy does not appear to behave self-similarly with time, unlike the momentum distribution in the inertial range.

[1] Frisch U., Turbulence: the legacy of A. N. Kolmogorov (Cambridge University Press) 1995.

[2] Sano Y., Navon N., and Tsubota M., arXiv:220908973.

[3] Navon N., Gaunt A. L., Smith R. P., and Hadzibabic Z., Nature, 539 (2016) 72–75.

[4] Navon N., Eigen C., Zhang J., Lopes R., Gaunt A. L., Fujimoto K., Tsubota M., Smith R. P., and Hadzibabic Z., Science, 366 (2019) 382–385.