An Equation of State for Turbulence in the Gross-Pitaevskii model

Abstract

We report the numerical observation of a far-from-equilibrium equation of state (EOS) in the Gross-Pitaevskii model. We first show that the momentum distribution of the turbulent cascade is well described by wave-turbulent kinetic theory in the appropriate limits. Calculating the energy and particle fluxes ${\Pi }_{\epsilon }(k)$ and ${\Pi }_N(k)$, we show that the turbulent state possesses the hallmarks of a direct energy cascade. Building on this, we show that the GP model encodes a universal EOS in the form of a relationship between the turbulent cascade's momentum distribution amplitude $n_0$ and the energy flux $\epsilon$ in the steady state. We find that in our regime of `mixed' turbulence - where both vortices and waves play a significant role - $n_0\propto {\epsilon }^{0.67(2)}$, a result that is not captured by any existing theory of turbulence but that agrees with a recent experimental measurement for large energy fluxes. Finally, we find that the concept of quasi-static thermodynamic processes between equilibrium states extends to far-from-equilibrium steady states.

Main text: 4 pages, 4 figures; End Matter: 2 pages, 3 figures; Supplementary information: 4 pages, 4 figures

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Cited by in corpus (1)

• Generation of wave turbulence in dipolar gases driven across their phase transitions