This work examines the maintenance of geostrophic, long-lived vortices through absorption of inertial waves. Such flows occur in a uniformly rotating fluid. To provide context, we first review turbulent flows in two- and nonrotating three-dimensional systems. Three-dimensional turbulent flow is characterized by a direct energy cascade, when energy without losses is transferred down the chain from larger to smaller scales. When dissipation is not relevant, in addition to the energy, two-dimensional flow conserves enstrophy. This additional conservation law drastically differs the statistical properties of two-dimensional turbulence, making the energy cascade inverse. This means that the energy is transferred to the largest scales, that under certain conditions leads to the self-organization of large, long-lived vortices. Rotating flow, in a sense, combines properties of both two- and three-dimensional systems and introduces unique new characteristics. The geostrophic part of the rotating flow is uniform along the rotation axis and resembles the two-dimensional flow. Inertial wave constitutes the part of the flow which is inhomogeneous along the rotation axis. However, if the flow is too intensive, it restores into three-dimensional turbulence. In number experiments and numerical simulations, long-lived, or coherent geostrophic vortices are observed against a background of turbulent flow. Analysis of the numerical data shows that the vortices gain energy from the turbulence. Here we analytically consider a process of inertial wave absorption by an axially symmetric geostrophic flow. We show that a monochromatic wave does not exert any torque on the vortex flow in the inviscid limit until it is absorbed inside its critical layer. Among convergent waves, those only are absorbed, which carry angular momentum of the same sign as one's of the rotation in the vortex. Convergent waves with the opposite sign of angular momentum are just reflected from the vortex. The wave absorption is possible only if the vortex flow is characterized by fast enough angular velocity there. Based on the results, we provide qualitative picture of the phenomenon.

Sergei Vergeles was born in 1982. Entered Moscow Institute of Physics and Technology in 1999. He defended his PhD thesis on the topic “Rheological properties of a vesicular suspension” in 2008 under the supervision of Lebedev Vladimir Valentinovich at Landau Institute for Theoretical Physics. After that, he became a researcher in the Landau Institute and the main topics of his interest were fibre optics, surface waves interaction with near-surface flows, and turbulent flow of rotating fluid. In 2025, Sergei Vergeles has defended his doctoral dissertation on the topic “Generation of coherent flows by regular and chaotic sources”. He is a lecturer of the courses “Hydrodynamics” and “Electrodynamics of continuous media”.

I will present our recent works on (1) how cilia can coordinate with each other to beat in the form of the metachronal wave, and (2) how hydrodynamics can determine the physical responses of a multiflagellated microswimmer. With these theoretical attempts, we try to understand how complex living systems can function in fluids by utilizing simple physical rules.

Fanlong Meng is a professor at Institute of Theoretical Physics, Chinese Academy of Sciences. He received his bachelor's degree from University of Science and Technology of China in 2010 and his Ph.D. from Institute of Theoretical Physics, Chinese Academy of Sciences in 2015. From 2015 to 2019, he conducted postdoctoral research at the University of Cambridge, the University of Oxford, and the Max Planck Institute for Dynamics and Self-Organization. In December 2019, Fanlong Meng joined the Institute of Theoretical Physics, Chinese Academy of Sciences as an associate professor and then promoted to be a full professor. His current research focuses on theoretical studies in statistical physics and soft matter physics, including the nonequilibrium dynamics of active matter, rheological properties of polymer systems, etc. (http://lib.itp.ac.cn/html/meng).

We study the spatial dependence of pair correlation functions of velocity field components in a rotating turbulent fluid on a background of a coherent geostrophic vortex. The statistics of the turbulent pulsations are determined by their dynamics, which is the dynamics of inertial waves affected by the differential rotation in the vortex and a weak viscous damping. We are interested in distances which are larger than the scale of the wave forcing but smaller than the radius of the coherent vortex. We establish the anisotropy of the velocity field correlation function at the distances. All the diagonal elements of the correlation function decay logarithmically in the streamwise direction and power-like in radial direction and the direction along the rotation axis. This laws are independent of the details of the forcing correlation function that indicate “coherency” of the flow. On the contrary, the cross-correlation function of the radial-azimuth velocity components, which turns into the Reynolds stress for zero distance, demonstrates strong dependence on the forcing correlation function and decays quickly at distances larger than the forcing scale.

Leon L. Ogorodnikov, Sergey S. Vergeles. “Long-range spatial velocity statistics in a rotating coherent turbulent vortex”, Physical Review Fluids, vol. 10, p. 124702 (2025)

The search for conditions supporting degenerate steady states in nonequilibrium topological superconductors is important for advancing dissipative quantum engineering, a field that has attracted significant research attention over the past decade. In this study, we address this problem by investigating topological superconductors hosting unpaired Majorana modes under the influence of environmental dissipative fields. Within the Gorini-Kossakowski-Sudarshan-Lindblad framework and the third quantization formalism, we establish a correspondence between equilibrium Majorana zero modes and non-equilibrium kinetic zero modes. We further derive a simple algebraic relation between the numbers of these excitations expressed in terms of hybridization between the single-particle wavefunctions and linear dissipative fields. Based on these findings, we propose a practical recipes how to stabilize degenerate steady states in topological superconductors through controlled dissipation engineering. To demonstrate their applicability, we implement our general framework in the BDI-class Kitaev chain with long-range hopping and pairing terms — a system known to host a robust edge-localized Majorana modes.

Within the quantum field-theoretical approach describing the evolution of a quadratic Liouvillian in the basis of Keldysh contour coherent states, we investigate the spectral and transport properties of a dissipative superconducting system coupled to normal Fermi reservoirs. We derive a generalization of the Meir-Wingreen formula and Onsager matrix for a superconducting system subject to an arbitrary number of fermionic baths. Following Kirchhoff's rule, we obtain an expression describing the dissipation-induced loss current and formulate modified quantum kinetic equations. For wide-band contacts locally coupled to individual sites, we find that each contact reduces the degeneracy multiplicity of the non-equilibrium steady state by one. These results are numerically verified through several cases of the extended Kitaev model at symmetric points with a single contact. Furthermore, in the linear response regime at low temperatures, we demonstrate that (non-)degenerate non-equilibrium steady states correspond to (non-)quantized conductance peaks. Revisiting a paradigmatic problem of resonant transport in the Majorana mode of the Kitaev model we demonstrate that the dissipation accounts for the zero-bias peak suppression and its asymmetry.