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).