On the excitation of inertial modes in an experimental spherical Couette flow

Spherical Couette flow (flow between concentric rotating spheres) is one of flows under consideration for the laboratory magnetic dynamos. Recent experiments have shown that such flows may excite Coriolis restored inertial modes. The present work aims to better understand the properties of the observed modes and the nature of their excitation. Using numerical solutions describing forced inertial modes of a uniformly rotating fluid inside a spherical shell, we first identify the observed oscillations of the Couette flow with non-axisymmetric, retrograde, equatorially anti-symmetric inertial modes, confirming first attempts using a full sphere model. Although the model has no differential rotation, identification is possible because a large fraction of the fluid in a spherical Couette flow rotates rigidly. From the observed sequence of the excited modes appearing when the inner sphere is slowed down by step, we identify a critical Rossby number associated with a given mode and below which it is excited. The matching between this critical number and the one derived from the phase velocity of the numerically computed modes shows that these modes are excited by an instability likely driven by the critical layer that develops in the shear layer staying along the tangent cylinder of the inner sphere.Comment: 11 pages, 17 figure

Bubbly Turbulent Drag Reduction Is a Boundary Layer Effect

In turbulent Taylor-Couette flow, the injection of bubbles reduces the overall drag. On the other hand, rough walls enhance the overall drag. In this work, we inject bubbles into turbulent Taylor-Couette flow with rough walls (with a Reynolds number up to 4×105), finding an enhancement of the dimensionless drag as compared to the case without bubbles. The dimensional drag is unchanged. As in the rough-wall case no smooth boundary layers can develop, the results demonstrate that bubbly drag reduction is a pure boundary layer effec

The Twente turbulent Taylor-Couette (T3C) facility: Strongly turbulent (multiphase) flow between two independently rotating cylinders

A new turbulent Taylor-Couette system consisting of two independently rotating cylinders has been constructed. The gap between the cylinders has a height of 0.927 m, an inner radius of 0.200 m, and a variable outer radius (from 0.279 to 0.220 m). The maximum angular rotation rates of the inner and outer cylinder are 20 and 10 Hz, respectively, resulting in Reynolds numbers up to 3.4 x 10^6 with water as working fluid. With this Taylor-Couette system, the parameter space (Re_i, Re_o, {\eta}) extends to (2.0 x 10^6, {\pm}1.4 x 10^6, 0.716-0.909). The system is equipped with bubble injectors, temperature control, skin-friction drag sensors, and several local sensors for studying turbulent single-phase and two-phase flows. Inner cylinder load cells detect skin-friction drag via torque measurements. The clear acrylic outer cylinder allows the dynamics of the liquid flow and the dispersed phase (bubbles, particles, fibers, etc.) inside the gap to be investigated with specialized local sensors and nonintrusive optical imaging techniques. The system allows study of both Taylor-Couette flow in a high-Reynolds-number regime, and the mechanisms behind skin-friction drag alterations due to bubble injection, polymer injection, and surface hydrophobicity and roughness.Comment: 13 pages, 14 figure

Dynamics of a piecewise smooth map with singularity

Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a map. We show that though such maps in general fall in the category of piecewise smooth maps, the mechanisms of bifurcations are quite different from those in other piecewise smooth maps. We obtain the conditions of occurrence of infinite states, and show that periodic orbits containing such states are superstable. We observe period-adding cascade in this system, and obtain the scaling law of the successive periodic windows.Comment: 10 pages, 6 figures, composed in Latex2

Azimuthal velocity profiles in Rayleigh-stable Taylor-Couette flow and implied axial angular momentum transport

We present azimuthal velocity profiles measured in a Taylor-Couette apparatus, which has been used as a model of stellar and planetary accretion disks. The apparatus has a cylinder radius ratio of $\eta = 0.716$, an aspect-ratio of $\Gamma = 11.74$, and the plates closing the cylinders in the axial direction are attached to the outer cylinder. We investigate angular momentum transport and Ekman pumping in the Rayleigh-stable regime. The regime is linearly stable and is characterized by radially increasing specific angular momentum. We present several Rayleigh-stable profiles for shear Reynolds numbers $Re_S \sim O(10^5) \,$, both for $\Omega_i > \Omega_o > 0$ (quasi-Keplerian regime) and $\Omega_o > \Omega_i > 0$ (sub-rotating regime) where $\Omega_{i,o}$ is the inner/outer cylinder rotation rate. None of the velocity profiles matches the non-vortical laminar Taylor-Couette profile. The deviation from that profile increased as solid-body rotation is approached at fixed $Re_S$. Flow super-rotation, an angular velocity greater than that of both cylinders, is observed in the sub-rotating regime. The velocity profiles give lower bounds for the torques required to rotate the inner cylinder that were larger than the torques for the case of laminar Taylor-Couette flow. The quasi-Keplerian profiles are composed of a well mixed inner region, having approximately constant angular momentum, connected to an outer region in solid-body rotation with the outer cylinder and attached axial boundaries. These regions suggest that the angular momentum is transported axially to the axial boundaries. Therefore, Taylor-Couette flow with closing plates attached to the outer cylinder is an imperfect model for accretion disk flows, especially with regard to their stability.Comment: 22 pages, 10 figures, 2 tables, under consideration for publication in Journal of Fluid Mechanics (JFM

Boolean Chaos

We observe deterministic chaos in a simple network of electronic logic gates that are not regulated by a clocking signal. The resulting power spectrum is ultra-wide-band, extending from dc to beyond 2 GHz. The observed behavior is reproduced qualitatively using an autonomously updating Boolean model with signal propagation times that depend on the recent history of the gates and filtering of pulses of short duration, whose presence is confirmed experimentally. Electronic Boolean chaos may find application as an ultra-wide-band source of radio wavesComment: 10 pages and 4 figur