The next session of academician V.E. Zakharov seminar “Nonlinear Waves” will be
held on Wednesday, January 27th at 15:30, at https://bbb2.itp.ac.ru/b/ale-wkj-mvm
“Fibonacci turbulence”
Gregory Falkovich
Weizmann Institute of Science
Abstract: Never is the difference between thermal equilibrium and turbulence so dramatic, as when a quadratic invariant makes the equilibrium statistics exactly Gaussian with independently fluctuating modes. That happens in two very different yet deeply connected classes of systems: incompressible hydrodynamics and resonantly interacting waves. This work presents the first case of a detailed information-theoretic analysis of turbulence in such strongly interacting systems. The analysis elucidates the fundamental roles of space and time in setting the cascade direction and the changes of the statistics along it. We introduce a beautifully simple yet rich family of discrete models with neighboring triplet interactions and show that it has families of quadratic conservation laws defined by the Fibonacci numbers. Depending on the single model parameter, three types of turbulence were found: single direct cascade, double cascade, and the first ever case of a single inverse cascade. We describe quantitatively how deviation from thermal equilibrium all the way to turbulent cascades makes statistics increasingly non-Gaussian and find the self-similar form of the one-mode probability distribution. We reveal where the information (entropy deficit) is encoded and disentangle the communication channels between modes, as quantified by the mutual information in pairs and the interaction information inside triplets.
Questions to Andrei Pushkarev, dr.push@gmail.com, +7 (909) 949-96-13
E.A. Kuznetsov, A.N. Pushkarev
Organizers
Date |
Speaker | Title | |
27.01.2020 |
Gregory Falkovich | Fibonacci turbulence | |
20.01.2021 | Sergei K. Turitsyn | Intermediate asymptotics in nonlinear systems and coexistence of coherent structures and linear waves | |
13.01.2021 | S. Nazarenko | Self-similar evolution in wave turbulence and non-equilibrium | |
14-15.12.2020 | 24 speakers | Joint seminar “Nonlinear Waves” with Scientific Council “Nonlinear Dynamics” RAS “Nonlinear Session – 20″ | |
02.12.2020 | A. Kamchatnov | Optico-mechanical analogy and number of solitons | |
25.11.2020 | V.Sirota | Stationary scaling in small-scale turbulent dynamo problem | |
18.11.2020 | M.Onorato | Thermalization and anomalous correlators in the Fermi-Pasta-Ulam-Tsingou chain | |
11.11.2020 | E.Kochurin | Numerical Simulation of Collinear Capillary-Wave Turbulence | |
28.10.2020 | Y.Stepanyants | The asymptotic approach to the description of two-dimensional soliton patterns | |
21.10.2020 | K.Zybin | No feedback is possible in small-scale turbulent magnetic field | |
14.10.2020 | S.Vergeles | Steady axial magnetic field maintained in a columnar vortex in a rotating turbulent conducting fluid | |
07.10.2020 | A.Slunyaev | Direct numerical simulation of 3D rogue waves | |
30.09.2020 | A.Gelash | Solitonic model of the condensate | |
23.09.2020 | R.Mullyadzhanov | Solitons in a box-shaped wavefield with noise: perturbation theory and statistics | |
16.09.2020 | P.Lushnikov | Motion of singularities in fluid dynamics | |
09.09.2020 | V.E.Zakharov | Are the equations of deep water with the free surface integrable? | |
17.06.2020 | E.Pelinovsky | Bottom Pressure under Waves in Shallow Waters | |
10.06.2020 | N.Ussembayev | On some new results in the Hamiltonian theory of weakly nonlinear surface waves | |
03.06.2020 | V.Gordin | Wind in the boundary layer of the Earth’s atmosphere. Observations and a generalized Ekman-Akkerblom model. The complex coefficient of the turbulent exchange is more adequate | |
27.05.2020 | D.Agafontsev | Adiabatically growing integrable turbulence | |
20.05.2020 | A.Minakov | Long-time asymptotics for the modified Korteweg-de Vries equation with step-like initial data | |
13.05.2020 | S. Badulin | Theory of wave turbulence for satellite altimetry: wave dynamics and climatology remote sensing of sea state | |
29.04.2020 | V. Geogjaev | Quadruplet form of Hasselmann equation | |
22.04.2020 | A. Pushkarev | Nonlinear Wind Waves Generation in Straits: Laser-Like and Self-Similar Regimes | |
15.04.2020 | D. Kachulin | Soliton turbulence in approximate and exact models for deep water waves | |
08.04.2020 | E. Kuznetsov | Compressible structures in two-dimensional hydrodynamic systems | |
01.04.2020 | A. Dyachenko | Multiple Soliton Interactions on the Surface of Deep Water | |
25.03.2020 | I. Sibgatullin | Linear and nonlinear wave attractors in stratified or rotating fluids | |
18.03.2020 | E. Mikhailov | Propagation of nonlinear waves in problems of magnetic field generation in the dynamo theory | |
11.03.2020 | A. Gelash | Synchronized breather interactions | |
04.03.2020 | E. Prosviryakov | Exact solutions of the Navier-Stokes equations for describing large-scale flows of the oceans and amplification of Stokes waves in a liquid | |
19.02.2020 | V. Zakharov | Chain solitons in KP-1 equation |