Energy spectra and fluxes of turbulent rotating Bose-Einstein condensates in two dimensions

TL;DR

This study explores the energy spectra and fluxes in turbulent rotating 2D Bose-Einstein condensates, revealing different scaling laws and energy cascades depending on initial conditions and rotation parameters.

Contribution

It provides new insights into the energy cascade behavior and scaling laws in 2D turbulent BECs under rotation, highlighting the influence of initial vortex configurations and rotation frequency.

Findings

Kolmogorov-like $k^{-5/3}$ scaling observed in non-vortex initial states

Vinen $k^{-1}$ scaling appears transiently with vortex lattices

Positive energy fluxes indicate a forward cascade of kinetic energy

Abstract

We investigate the scaling of the energy cascade in a harmonically trapped, turbulent, rotating Bose-Einstein condensate (BEC) in two dimensions. We achieve turbulence by injecting a localized perturbation into the condensate and gradually increasing its rotation frequency from an initial value to a maximum. The main characteristics of the resulting turbulent state depend on the initial conditions, rotation frequency, and ramp-up time. We analyze the energy and the fluxes of kinetic energy by considering initial profiles without vortices and with vortex lattices. In the case without initial vortices, we find the presence of Kolmogorov-like scaling ($k^{-5/3}$) of the incompressible kinetic energy in the inertial range. However, with initial vortex lattices, the energy spectrum follows Vinen scaling ($k^{-1}$) at transient iterations. For cases with high rotating frequencies, Kolmogorov-like scaling emerges at longer durations. We observe positive kinetic energy fluxes with both initial states across all final frequencies, indicating a forward cascade of incompressible and compressible kinetic energy.