Transition from dissipative to conservative dynamics in equations of hydrodynamics

Abstract

We show, by using direct numerical simulations and theory, how, by increasing the order of dissipativity ($\alpha$) in equations of hydrodynamics, there is a transition from a dissipative to a conservative system. This remarkable result, already conjectured for the asymptotic case $\alpha \to \infty$ [U. Frisch et al., Phys. Rev. Lett. {\bf 101}, 144501 (2008)], is now shown to be true for any large, but finite, value of $\alpha$ greater than a crossover value ${\alpha }_{\mathrm{crossover}}$. We thus provide a self-consistent picture of how dissipative systems, under certain conditions, start behaving like conservative systems and hence elucidate the subtle connection between equilibrium statistical mechanics and out-of-equilibrium turbulent flows.

arXiv comment12 pages, 4 figures

References in corpus (18)

• Burgers Turbulence
• Hyperviscosity, Galerkin truncation and bottlenecks in turbulence
• Effective Dissipation and Turbulence in Spectrally Truncated Euler Flows
• Bottleneck crossover between classical and quantum superfluid turbulence
• Bottleneck effect in three-dimensional turbulence simulations
• Cascades, thermalization and eddy viscosity in helical Galerkin truncated Euler flows
• Non-local interactions in hydrodynamic turbulence at high Reynolds numbers: the slow emergence of scaling laws
• Energy Flux and Bottleneck Effect in Turbulence
• Turbulence in non-integer dimensions by fractal Fourier decimation
• Energy cascade with small-scales thermalization, counterflow metastability and anomalous velocity of vortex rings in Fourier-truncated Gross-Pitaevskii equation
• Resonance phenomenon for the Galerkin-truncated Burgers and Euler equations
• Cascade time-scales for energy and helicity in homogeneous isotropic turbulence
• Turbulence in the two-dimensional Fourier-truncated Gross-Pitaevskii equation
• Dispersive bottleneck delaying thermalization of turbulent Bose-Einstein Condensates
• Quasi-Gaussian Statistics of Hydrodynamic Turbulence in 3/4+εdimensions
• Real-space Manifestations of Bottlenecks in Turbulence Spectra
• Numerical Solutions of the Isotropic 3-Wave Kinetic Equation
• Alfvén waves and ideal two-dimensional Galerkin truncated magnetohydrodynamics

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• The Onset of Thermalisation in Finite-Dimensional Equations of Hydrodynamics: Insights from the Burgers Equation
• Insights from a pseudospectral study of a potentially singular solution of the three-dimensional axisymmetric incompressible Euler equation
• On the thermalization of the three-dimensional, incompressible, Galerkin-truncated Euler equation
• Lagrangian Irreversibility and Eulerian Dissipation in Fully-Developed Turbulence
• Revisiting the SABRA Model: Statics and Dynamics
• Adaptive solution of initial value problems by a dynamical Galerkin scheme
• Fractional hyperviscosity induced growth of bottlenecks in energy spectrum of Burgers equation solutions
• Optimal response to non-equilibrium disturbances under truncated Burgers-Hopf dynamics
• Analytic structure of solutions of the one-dimensional Burgers equation with modified dissipation
• The Galerkin-truncated Burgers equation: Crossover from inviscid-thermalised to Kardar-Parisi-Zhang scaling