ICTS

The one-dimensional ($1D$) Galerkin-truncated Burgers equation, with both dissipation and noise terms included, is studied using spectral methods. When the truncation-scale Reynolds number $R_{\rm min}$ is varied, from very small values to order $1$ values, the scale-dependent correlation time $\tau(k)$ is shown to follow the expected crossover from the short-distance $\tau(k) \sim k^{-2}$ Edwards-Wilkinson scaling to the universal long-distance Kardar-Parisi-Zhang scaling $\tau(k) \sim k^{-3/2}$. In the inviscid limit: $R_{\rm min}\to \infty$, we show that the system displays {\it another} crossover to the Galerkin-truncated inviscid-Burgers regime that admits thermalised solutions with $\tau(k) \sim k^{-1}$. The scaling form of the time-correlation functions are shown to follow the known analytical laws and the skewness and excess kurtosis of the interface increments distributions are characterised.

There are challenges in the field theory of hydrodynamic turbulence. For example, whether renormalised viscosity of two-dimensional turbulence is negative or positive? Does turbulent energy flux get suppressed with the increase of space dimension? Earlier, Fournier and Frisch [Phys. Rev. A, 17, 747, 1978] performed field-theoretic and eddy-damped quasi-normal Markovian calculation of d-dimensional turbulence and showed that the energy cascade changes sign from negative to positive at d = dc ≈ 2.06. In this paper, we revisit d-dimensional turbulence and perform recursive renormalization and energy transfer calculations. We employ Craya-Herring basis that provides separate renormalized viscosities and energy transfers for its two components. We test the stability of nonequilibrium energy spectrum and equilibrium spectrum . We also investigate how the energy cascade rate is suppressed with the increase of space dimension.

I demonstrate that black hole dynamics simplifies - without trivializing - in the limit in which the number of spacetime dimensions D in which the black holes live is taken to infinity. In the strict large D limit and under certain conditions I show the equations that govern black hole dynamics reduce to the equations describing the dynamics of a non gravitational membrane propagating in an unperturbed spacetime (e.g. flat space). In the stationary limit black hole thermodynamics maps to membrane thermodynamics, which we formulate in a precise manner. We also demonstrate that the large D black hole membrane agrees with the fluid gravity map in the appropriate regime.

I will describe an attempt to describe turbulence using the methods of quantum field theory. We consider waves that interact via four-wave scattering (such as sea waves, plasma waves, spin waves, and many others). By summing the series of the most UV-divergent terms in the perturbation theory, we show that the true dimensionless coupling is different from the naive estimate, and find that the effective interaction either decays or grows explosively with the cascade extent, depending on the sign of the new coupling. The explosive growth possibly signals the appearance of a multi-wave bound state (solitons, shocks, cusps) similar to confinement in quantum chromodynamics.
We find that IR divergence in the effective coupling could be responsible for an anomalous scaling in wave turbulence.

I will discuss progress in generating and analysing steady state turbulent flow via holography

TBA

We have found an infinite dimensional manifold of exact solutions of the Navier-Stokes loop equation for the Wilson loop in decaying Turbulence in arbitrary dimension $d >2$. This solution family is equivalent to a fractal curve in complex space $\mathbb C^d$ with random steps parametrized by $N\to \infty$ Ising variables $\sigma_i=\pm 1$, in addition to a rational number $\frac{p}{q}$ and an integer winding number $r$, related by $\sum \sigma_i = q r$. The energy dissipation rate grows as $\nu/\mu^2$ in the continuum limit when chemical potential $\mu \rightarrow 0$, leading to anomalous dissipation at $\mu \propto \sqrt{\nu} \to 0$. The same method is used to compute the local vorticity distribution. The small perturbation of the fixed manifold satisfies the linear equation we solved in a general form. This perturbation decays as $t^{-\lambda}$, with a continuous spectrum of indexes $\lambda$ in the local limit $\mu \to 0$.

Mesoscale convection comprises buoyancy-driven turbulence at an intermediate range of scales. These processes are typically characterized by regular convection cell patterns and can be found in atmospheric flows or stellar interiors. We will discuss possible dynamical origins of these patterns, the related turbulent transport of heat and momentum, and data-driven approaches for the modeling of unresolved scales in these systems. The related numerical simulation studies start from Rayleigh-Bénard systems and are extended to non-Boussinesq cases.

We investigate the spectral properties of buoyancy-driven bubbly flows. Using high-resolution numerical simulations and phenomenology of homogeneous turbulence, we identify the relevant energy transfer mechanisms. We find (a) at a high enough Galilei number (ratio of the buoyancy to viscous forces) the velocity power spectrum shows the Kolmogorov scaling for the range of scales between the bubble diameter and the dissipation scale. (b) For scales smaller than the dissipation scale, the physics of pseudo-turbulence is recovered.

I will describe our recent efforts to generalize the effective field theories for thermal systems (especially the effective field theory of hydrodynamics) to nonequilibrium matter, including active solids and fluids. Our approach is organized around a generalized time-reversal transformation, which can provide strong constraints on the effective field theory that seem to go beyond the standard Landau paradigm, even at leading non-trivial order. Our approach will be illustrated using three examples: (1) active solids and fluids; (2) kinematically-constrained "fracton" hydrodynamic universality classes, with and without microscopic time-reversal symmetry; (3) a new universality class of "flocking spins" on a lattice, which seems to have qualitatively distinct behavior than the conventional theory of "Malthusian" flocking birds in active matter.

Quantum hydrodynamics and turbulence is an important research topic in low temperature physics. Quantum condensed systems such as superfluid helium and atomic Bose-Einstein condensates (BECs) have order parameters. Thus hydrodynamics and turbulence of these systems are severely restricted by the order parameters and quantum mechanics. The typical example is quantized vortex; any rotational motion of superfluid is sustained only by quantized vortices. Quantum hydrodynamics and turbulence [1] have been long studied in superfluid helium since 1950’s[2], and recently in atomic Bose-Einstein condensates (BECs) too [3]. In this presentation, I would review the characteristics and motivation of this field and discuss the recent novel topics.

1. Fully coupled two-fluid dynamics in superfluid 4He
Hydrodynamics of superfluid 4He is well described by the two-fluid model. The most characteristic phenomenon of the two-fluid model is thermal counterflow, which has been studied for more than a half century. However, the three-dimensional coupled dynamic of the two-fluid model is seldom addressed. The recent visualization experiments show that the profile of the normal fluid flow is seriously modified by the development of superfluid turbulence [4] and anisotropic velocity fluctuation in the laminar normal fluid [5]. We performed numerically the three-dimensional coupled dynamics of the two-fluid mode, l and found the serious change of the profile of the normal fluid flow [6] and the anisotropic velocity fluctuation [7].

2. Hydrodynamics and turbulence of atomic BECs
Most experiments of atomic BECs have been performed for systems trapped by a harmonic potential. The recent realization of the box potential has made this system more attractive. Navon et al. observed the clear statistical law of quantum turbulence in a BEC trapped by a box potential [8] and the cascade flux sustaining the turbulence [9]. It is known that the restoration of symmetries is one of the most fascinating properties of classical turbulence [10]. This phenomenon is reported in Ref. 8. We performed the simulation of the Gross-Pitaevskii model and found the particle distribution in momentum space became isotropic as the turbulence develops [11].

[1] C. F. Barenghi, L. Skrbek, K. R. Sreenivasan, Quantum Turbulence (Cambridge Univ. Press) (2023): 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] J. T. Tough, Superfluid turbulence, in Prog. in Low Temp. Phys., edited by D. F. Brewer (North-Holland, Amsterdam,1982), Vol. 8, Chap. 3.
[3] M. C. Tsatsos, P. E. S. Tavares, A. Cidrim, A. R. Fritsch, M. A. Caracanhas, F. E. A. dos Santos, C. F. Barenghi, V. S. Bagnato,Phys. Rep., 622 (2016) 1.
[4] A. Marakov, J. Gao, W. Guo, S.W. Van Sciver, G. G. Ihas,, D. N. McKinsey, and W. F. Vinen, Phys. Rev. B 91, 094503 (2015).
[5] B. Mastracci, S. Bao, W. Guo, and W. F. Vinen, Phys. Rev. Fluids 4, 083305 (2019).
[6] S. Yui, M. Tsubota, H. Kobayashi, Phys. Rev. Lett. 120, 155301 (2018).
[7] S. Yui, H. Kobayashi, M. Tsubota, W. Guo, Phys. Rev. Lett. 124, 155301 (2020).
[8] N. Navon, A. L. Gaunt, R. P. Smith, Z. Hadzibabic, Nature 539, 72 (2016).
[9] N. Navon, C. Eigen, J. Zhang, R. Lopes, A. L. Gaunt, K. Fujimoto, M. Tsubota, R. P. Smith and Z. Hadzibabic, Science 366, 1267 (2019).
[10] U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press) 1995.
[11] Y. Sano, N. Navon, M. Tsubota, EPL140, 66002 (2022).

One of the most impressive phenomena in atmospheric flows is the organization of turbulent convective motions into large-scale structures. Turbulence theory has proposed an inverse cascade in two-dimensional flows as the mechanism behind this process, but its applicability to realistic atmospheric and oceanic flows remains heavily debated. In this talk I will discuss recent advances in our understanding of three-dimensional flows under specific geometrical constraints, the possibility of phase transitions giving rise to spontaneous self-organization even when these flows remain three-dimensional, and present direct numerical simulations with unprecedented spatial resolution that support the development of a bi-directional cascade of energy for parameters comparable to that of the Earth’s atmosphere.

Heavy particles in turbulent flow are expected to centrifuge out of vortical regions and agglomerate in strain regions. We show that in a rotating system, particles can permanently reside in the vicinity of vortices. In addition, the clustering is extreme, into low-dimensional objects such as fixed points, limit cycles or chaotic orbits. We will discuss the Basset history force, and how it changes the dynamics.

Fluid turbulence is a major unsolved problem of physics exhibiting an emergent complex structure from simple rules. We will briefly review the problem and discuss three avenues towards its solution: field theory, gravity, and deep learning.