Session LP: Couette Flow

Bi-Stable Turbulent Spherical Couette

We study the turbulent shear flow between differentially rotating concentric spheres of radius ratio $\eta = r_{\mathrm{i}}/r_{\mathrm{o}} = 0.35$ in the University of Maryland three meter spherical Couette device. We impart rapid overall rotation and reach a region of parameter space of Ekman number $ \nu/\Omega_{\mathrm{o}}(r_{\mathrm{o}}-r_{\mathrm{i}})^2$ of $10^{-6} [Preview Abstract]

Turbulent Taylor-Couette flow between independently rotating cylinders

We present experimental studies of the turbulent flow of water between independently rotating cylinders. The Taylor-Couette system is capable of both strong turbulence $(Re>10^6)$ and rapid rotation $(\mbox{Ek}<10^{-7})$. The torque required to drive the inner cylinder is precisely measured as a function of the two angular velocities \textit{$\Omega $}$_{i}$ and \textit{$\Omega $}$_{o}$. Of particular interest are three distinct regions of the (\textit{$\Omega $}$_{i}$, \textit{$\Omega $}$_{o})$ parameter space defined by the inner and outer boundaries having equal: ($i)$ angular velocities (solid-body rotation), (\textit{ii}) azimuthal velocities and (\textit{iii}) angular momenta (Rayleigh criterion) with the outer boundary stationary line (\textit{$\Omega $}$_{o }$= 0) serving as the final bound. We supplement the global torque measurements with local wall shear stress measurements as a means of detecting Coriolis-restored, linear inertial modes. We model the system as being composed of two interacting, turbulent boundary layers. There are several open questions that we hope to be able to answer: (1) Are there conditions under which angular momentum will flow uphill? (2) What quantity (angular velocity, azimuthal velocity, or angular momentum) does the system most effectively ``mix,'' and does that depend upon system parameters.   

Precession in a laboratory model of the Earth's core

The Earth's rotation axis precesses with a period of 25800 years, caused mainly by the combined torques of the sun and the moon acting on the slight equatorial bulge of the planet. Without precession (or convection), a viscous core will come to rotate as a solid body with the mantle. The fluid core responds to the precessional forcing and the resulting motion can in principle power the geodynamo. There have been several attempts, both theoretical and experimental, to unveil the role of precession in the motion of the fluid core. A three meter diameter spherical-Couette system with a 1m inner sphere is the most recent and largest experimental model of the Earth's core. The experiment provides data at parameter ranges much closer to the Earth's compared to what was possible before either experimentally or numerically. Experimental data from this system evidencing precessional forcing will be presented and compared to theoretical predictions.   

Spin-up and Spin-down in a Spherical Annulus

We present experimental studies of turbulent fluid flow in a spherical annulus with approximate radius ratio 1/3 that is spun up and spun down. One experimental apparatus uses water as the working fluid, and provides localized measurements of velocity, wall shear, and pressure. The other experimental apparatus has sodium as the working fluid, and uses magnetic field measurements to extract information about the global flow within the device. The geometry of the experiments makes these studies potentially applicable to geophysical and astrophysical bodies. In particular, Mercury is known to have an at least partially fluid core, and during its orbit its rotation rate increases and decreases periodically. Preliminary results of spin-down indicate a transfer of energy to the so-called spin-over mode as the turbulence decays after the outer and inner spheres have been brought to a stop.   

Incipient spots in plane Couette flow

We investigate by direct numerical simulations the transition from laminar to turbulent plane Couette flow in long and wide domains. Previous studies in small domains have established that the boundary between laminar and turbulent is formed by the stable manifold of a persistent structure, called the edge state. Because of the small size of the domain and its periodic continuation in downstream and spanwise directions, this edge state was infinitely extended. Using an adaptation of the edge state tracking algorithm to larger domains we could detect edge states that are localized in the spanwise, in the downstream or in both directions. The structures are dominated by downstream vortices, and they are found to be exponentially localized in the downstream direction, and faster than exponentially in the spanwise direction. The structures serve as nuclei for the formation of spots and provide estimates for optimal widths and intensities. They evolve towards space filling turbulence by first increasing in energy content then by spreading in the surrounding laminar regions.   

Spatially localized solutions and homoclinic snaking in plane Couette flow

We examine a new class of spatially localized solutions to plane Couette flow, first discovered by Schneider, Marinc, and Eckhardt. Under continuation in Reynolds number the equilibrium and traveling-wave solutions exhibit a sequence of saddle-node bifurcations strikingly similar to the ``homoclinic snaking'' phenomenon observed in simpler PDE systems such as the Swift-Hohenberg equation. These localized solutions originate from bifurcations off the spatially periodic equilibria discovered by Nagata and others and retain their physical structure, demonstrating the relevance of exact periodic solutions to turbulent flows in spatially extended domains.   

Twente Turbulent Taylor-Couette

A newly constructed turbulent Taylor-Couette (TC) system consists of two independently rotating cylinders of 0.93 m in length and the inner and maximum outer radii are respectively 0.20 m and 0.28 m. The maximum rotation rates are 1200 RPM for the inner cylinder and 600 RPM for the outer cylinder. With the working fluid held at a constant temperature within at least 0.1 degree Celsius the setup allows for precisely controlled measurements. The maximum Reynolds number that can be achieved with inner cylinder rotation only, is estimated to be around 2x10$^{6}$. This allows for measurements well into the turbulent regime. The system is designed not only for single-phase flow studies, but also for two-phase flow research like bubbly drag reduction. The clear acrylic outer cylinder and several view ports in the top and bottom plate allow for optical measurement techniques such as LDA, PIV and PTV. Instead of only measuring global quantities like drag, temperature and pressure, the system is also equipped with a multitude of sensors for measuring local quantities. Combining the detailed localized information from inside of the gap with the global quantities, provides a way to study the mechanisms of bubbly drag reduction.   

Drag and lift forces on a counter-rotating cylinder in rotating shear flow

We experimentally investigated the motion of a heavy cylinder in a drum filled with water, and rotating about a horizontal axis. The cylinder either co-rotates or counter-rotates with the rotating drum. The flow field around the cylinder, both for co-rotation and counter-rotation situations, was measured with Particle Image Velocimetry in order to investigate the different flow mechanism. For the counter-rotation situation, the cylinder freely rotates without contact with the wall of the drum, due to the lift force acting on it. The drag and lift coefficients, on the freely counter-rotating cylinder, were measured in a wide range of Reynolds numbers 2,500 $<$ Re $<$ 25,000 and dimensionless rotation rates 0.0 $< \quad \alpha $ $<$ 1.2. We found that the drag coefficient is consistent with previous measurements on a cylinder in a uniform flow. However, a significant enhancement of the lift coefficient is observed in the present measurements. We expect the enhancement of the lift force is caused by the combined effects of rotation of the cylinder and the vicinity of a wall.