Seminar “Nonlinear waves”

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