PHYSICAL REVIEW FLUIDS 5, 034604 (2020) Structure of coherent columnar vortices in three-dimensional rotating turbulent flow I. V. Kolokolov , 1, 2 L. L. Ogorodnikov, 2 and S. S. Vergeles 1, 2, * 1 Landau Institute for Theoretical Physics, Russian Academy of Sciences, 1-A Akademika Semenova av., 142432 Chernogolovka, Russia 2 National Research University Higher School of Economics, Faculty of Physics, Myasnitskaya 20, 101000 Moscow, Russia (Received 6 October 2019; accepted 20 February 2020; published 30 March 2020) It is known that the turbulence in a fast-rotating volume becomes effectively two- dimensional. The latter is characterized by an inverse energy cascade leading to the formation of coherent flow in finite systems. In a rotating three-dimensional vessel this flow has the form of columnar vortices. Here we develop an analytical theory describing interaction of the vortex with turbulent pulsations. This interaction results in energy transfer from small-scale eddies to the large-scale vortex. We derive the equation for the radial velocity profile of the vortex and solve it for the simplest boundary conditions. We indicate the domain of physical parameters where our theory works. DOI: 10.1103/PhysRevFluids.5.034604 I. INTRODUCTION Fluid flow at large Reynolds numbers is nonstationary and should be described within a statistical approach. The first successful theory was built by Kolmogorov for statistically isotropic three- dimensional (3D) developed turbulent flow. The theory established scaling laws based on direct energy cascade within inertial interval of scales; see Ref. [1]. Direct energy cascade implies that large eddies split into smaller eddies and so on. Two-dimensional (2D) turbulence, in contrast, is characterized by inverse energy cascade, when small eddies join together to form larger eddies [2]. Bounded 2D flow is of particular physical interest. If the bottom friction is small enough, the size of the largest eddies is limited by the size L of the cell, and large-scale coherent vortices are formed [3,4]. The kinetic energy dissipation due to the bottom friction inside a coherent vortex is compensated by direct energy transfer from small-scale eddies to the vortex in this case, in contrast to the local in scales energy cascade, which is in unbounded systems. The relatively small amplitude of fluctuations compared with the coherent component of the flow allows one to build an analytical theory of the vortices structure [5,6]. The theoretical predictions were recently experimentally verified for the first time [7]. The 2D flow is usually a simplified model of 3D flow that has a suppressed third velocity component. The suppression can be forced for geometric reasons when the third direction is restricted by a scale that is smaller than the scale of the lateral flow (see, e.g., numerical simulations [8] and [9,10], where coherent vortices were observed). For instance, this concerns experiments with excitation of turbulence in thin fluid layers [7,11]. The theory developed for the 2D case can be applied almost directly. The suppression of the third velocity component can be caused by rotation and thus is not associated with geometrical factors [12]. The Taylor-Proudman theorem states that the velocity of the fluid becomes constant along the rotation axis at low Rossby numbers due to * Corresponding author: ssver@itp.ac.ru 2469-990X/2020/5(3)/034604(11) 034604-1 ©2020 American Physical Society