10.1103/PhysRevLett.125.104501
https://zenodo.org/records/4009824
oai:zenodo.org:4009824
Gregory Falkovich, Michal Shavit
Michal Shavit
Gregory Falkovich
Singular measures and information capacity of turbulent cascades
Zenodo
2020
Atmospheric science Capillary waves Dissipative dynamics Fluctuations & noise Geophysical fluid dynamics Geophysics Hydrodynamic waves Interfacial flows Nonequilibrium & irreversible thermodynamics Nonequilibrium statistical mechanics Plasma waves Renormalization group Sound waves Stochastic processes Turbulence Weak turbulence Quantum Information Particles & Fields Statistical Physics Interdisciplinary Physics Fluid Dynamics Nonlinear Dynamics
2020-08-31
eng
Creative Commons Attribution 4.0 International
How weak is the weak turbulence? Here, we analyze turbulence of weakly interacting waves using the tools of information theory. It offers a unique perspective for comparing thermal equilibrium and turbulence. The mutual information between modes is stationary and small in thermal equilibrium, yet it is shown here to grow with time for weak turbulence in a finite box. We trace this growth to the concentration of probability on the resonance surfaces, which can go all the way to a singular measure. The surprising conclusion is that no matter how small is the nonlinearity and how close to Gaussian is the statistics of any single amplitude, a stationary phase-space measure is far from Gaussian, as manifested by a large relative entropy. This is a rare piece of good news for turbulence modeling: the resolved scales carry significant information about the unresolved scales. The mutual information between large and small scales is the information capacity of turbulent cascade, setting the limit on the representation of subgrid scales in turbulence modeling.
European Commission
10.13039/501100000780
823937
Hydrodynamical approach to light turbulence