Workshop
``Turbulence of all kinds''
April 25 (Thu)-26 (Fri), 2019 @ Umeda Satellite, Osaka City U.
Oleg Evnin (Chulalongkorn University, Bangkok) part 1: Weakly nonlinear dynamics in AdS and BEC
Makoto Tsubota (OCU &NITEP): Hydrodynamics and turbulence in quantum fluids
Takaaki Ishii (Kyoto U): Turbulence on strings in AdS spacetime
Chihiro Matsuoka (OCU): Vortex sheet dynamics in magnetohydrodynamic turbulence
Oleg Evnin (Chulalongkorn University, Bangkok) part 2: Resonant systems, classical and quantum, integrable and chaotic
Michikazu Kobayashi (Kyoto U): Transition between turbulence and steady flow in quantum fluid
Akihiro Ishibashi (Kindai): Turbulence, instability, and singularities in general relativity
Title: Weakly nonlinear dynamics in AdS and BEC
Abstract:
I'll review the weakly nonlinear energy transfer in Anti-de Sitter spacetimes that is conjectured to lead to a turbulent instability, supported by strong numerical evidence. In particular, the resonant approximation, which I will review, plays a key role in simplifying the weakly nonlinear dynamics on the relevant timescales. All of this has a completely elementary but slighly surprising connection to dynamics of Bose-Einstein condensates in harmonic traps, a common subject of terrestrial condensed matter experiments, since the relevant PDEs arise by taking a non-relativistic limit of dynamics in Anti-de Sitter spacetimes.
Title: Hydrodynamics and turbulence in quantum fluids
Abstract:
Quantum hydrodynamics and turbulence have been studied in superfluid helium and cold atoms. In this talk, I would discuss the basics of these issues and the recent interesting topics. The main contents are as follows.
1. Basics of quantum hydrodynamics [1]
2. What is turbulence? What is quantum turbulence?
3. Counterflow turbulence in superfluid helium [2]
4. Synthetic dissipation and cascade fluxes in turbulence [3,4]
[1] M. Tsubota, M. Kobayashi, H. Takeuchi, Phys. Rep. 522, 191 (2013).; M. Tsubota, K. Fujimoto, S. Yui, J. Low Temp. Phys. 188, 119 (2017).
[2] S. Yui, M. Tsubota, H. Kobayashi, Phys. Rev. Lett. 120, 155301 (2018)
[3] N. Navon et al., Nature 539, 72 (2016).
[4] N. Navon, C. Eigen, J. Zhang, R. Lopes, A. L. Gaunt, K. Fujimoto, M. Tsubota, R. P. Smith and Z. Hadzibabic, arXiv:1807..07564.
Title: Turbulence on strings in AdS spacetime
Abstract:
The rise of the AdS/CFT duality, discovered in string theory, brought about strong motivations to study nonlinear dynamics of classical Nambu-Goto strings in AdS spacetime. I will talk about a turbulent phenomenon in this context, that in nonlinear perturbations on the classical open string in AdS spacetime. The energy cascade transferring the energy to higher modes is observed, resulting in cusp formation on the string, while in this case the power law exponent is nonuniversal. I will also discuss the relation of the string's embedding in the geometry and the strength of the turbulence and comment on the integrability of the strings in AdS.
Title: Vortex sheet dynamics in magnetohydrodynamic turbulence
Abstract:
A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. This model well describes the extraordinary magnetic field amplification in supernova remnants (SNR's). Numerical solutions provide the roll-up of the interface, exponential growth of the magnetic field, and its saturation and oscillation.
Title: Resonant systems, classical and quantum, integrable and chaotic
Abstract:
Resonant systems, classical and quantum, integrable and chaotic resonant systems emerge as weakly nonlinear approximations to long-time dynamics of highly resonant PDEs (such as those emerging in AdS spacetimes and for Bose-Einstein condensates in harmonic potentials). This class of Hamiltonian systems is very rich, containing thoroughly studied integrable representatives, partially integrable cases for which specific fully nonlinear solutions are known, as well as cases exhibiting strong turbulent behaviors according to numerical evidence. Resonant systems become strikingly simple when quantized, to the extent that the quantum version can illuminate the classical dynamics. In particular, the statistics of the quantum energy levels, which is easy to analyze, is a powerful indicator distinguishing generic resonant systems from those displaying enhanced symmetry structures.
Title: Transition between turbulence and steady flow in quantum fluid
Abstract:
Quantum turbulence in quantum fluid features a spatially and dynamically complicated structure of quantized vortices with quantized circulation. In the case of quantum fluid, we can easily separate laminar and turbulent states as a system with or without vortices. Defining the vortex density as the “order parameter of turbulence”, we find that the laminar-turbulent transition can be regarded as the non-equilibrium phase transition belonging to the temporally-directed percolation universality class. The key concept is that vortices has a finite energy barrier to be nucleated and cannot be re-nucleated after their extinction.
Title: Turbulence, instability, and singularities in general relativity
Abstract:
In the first part, I shall provide a brief overview of turbulent instabilities known to occur in closed systems in general relativity such as asymptotically AdS spacetimes. Such an instability indicates the formation of a black hole and/or occurrence of singularities even starting from arbitrarily small initial disturbances. In the second part, I shall discuss possible fate of turbulent instabilities, and type of singularity theorems in asymptotically AdS spacetimes with or without the strong gravity/trapped set condition.
Organizers: H. Itoyama, T. Oota and M. Tsubota (Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP))