Fuck Yeah Fluid Dynamics

Celebrating the physics of all that flows. Ask a question, submit a post idea or send an email. You can also follow FYFD on Twitter and Google+. FYFD is written by Nicole Sharp, PhD.

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Posts tagged "rotating flow"

UCLA Spinlab has another great video demonstrating the effects of rotation on a fluid. In a non-rotating fluid, flow over an obstacle is typically three-dimensional, with flow moving over as well as around the object. But in a steadily rotating fluid, as shown in the latter half of the video, the flow only moves around the obstacle, not over it. This non-intuitive behavior is part of the Taylor-Proudman theorem, which shows that flow around an obstacle in a rapidly rotating fluid will be two-dimensional and confined to planes perpendicular to the axis of rotation. (For the mathematically-inclined, Wikipedia does have a short derivation.) This 2D flow creates what are called Taylor columns over the obstacle. The Taylor column is like an imaginary extension of the original obstacle, turning the puck into a tall cylinder, and it’s real enough to flow, which diverts around it as though the column were there. (Video credit: UCLA Spinlab)

Rotation can cause non-intuitive effects in fluid dynamical systems. UCLA Spinlab’s newest video tackles the problem using four demonstrations. The first two deal with droplets released in air, first in a non-rotating environment and then in a rotating one. As one would expect, in a non-rotating environment, droplets fall through the tank in a straight line. When rotating, though, the droplets follow a deflected, straight-line path due to centrifugal effects. This is the same as the way passengers in a car feel like they’re being thrown to the outside of a turn on a curvy road. When the experiment is repeated with a tank of water instead of air, the results are different. The densities of the creamer and water are much closer to one another, so the droplet falls much slower than before. The tank now rotates faster than time it takes the drop to fall. This smaller timescale means that the droplet experiences more acceleration from Coriolis forces than centrifugal forces in the rotating tank of water. Thus, instead of being thrown outward, the drop now forms a column aligned with the axis of rotation. (Video credit: UCLA Spinlab; submitted by Jon B.)

Nature is full of surprising behaviors. If one imagines putting a bucket of water on a rotating plate and spinning it, one would expect the water’s free surface to take on a curved, axially symmetric shape. The photos above are from a similar experiment, but instead of the entire container rotating, only the bottom plate spins. Surprisingly, the water’s surface does not remain symmetric around the axis of rotation. Instead, the water forms stable polygon shapes that rotate slower than the spinning plate. As the plate’s rotation speed increases, the number of corners in the polygon increases. Shapes up to a hexagon were observed in the experiment. Photos of the set-up and more experimental results are available, as is the original research paper. Symmetry breaking and polygons can also be found in hydraulic jumps and bumpsliquid sheets, and planetary polar vortices. (Photo credit: T. Jansson et al.; research paper)

Vortices appear in scales both large and small, from your shower and the flap of an insect’s wing to cyclones and massive storms on other planets. Especially with these large-scale vortices, it can be difficult to understand the factors that affect their trajectories and intensities over time. Here researchers have studied the vortices produced on a heated half bubble for clues as to their long-term behavior. Heating the base of the bubble creates large thermal plumes which rise and generate large vortices, like the one seen above, on the bubble’s surface. Researchers observed the behavior of the vortices with and without rotation of the bubble. They found that rotating bubbles favored vortices near the polar latitudes of the bubble, just as planets like the Earth and Saturn have long-lived polar vortices. They also found that the intensification of both bubble vortices and hurricanes was reasonably captured by a single time constant, which may lead to better predictions of storm behaviors. Their latest paper is freely available here. (Image credit: H. Kellay et al.; research credit: T. Meuel et al.; via io9)

If you’ve ever watched a swirling vortex disappear down the drain of your bathtub and wondered what was happening, you’ll appreciate these images. This dye visualization shows a one-celled bathtub vortex, created by rotating a cylindrical tank of water until all points have equal vorticity before opening a drain in the bottom of the tank. A recirculating pump feeds water back in to keep the total fluid mass constant. Once a steady vortex is established, green dye is released from the top plate of the tank and yellow dye from the bottom. The green dye quickly marks the core of the vortex. Ekman layers—similar to the boundary layers of non-rotating flows—form along the top and bottom surfaces, and the yellow dye is drawn upward in a region of upwelling driven by Ekman pumping. (Photo credit: Y. Chen et al.)

Just a reminder for those at Texas A&M University: I will be giving a talk today Wednesday, October 2nd entitled “The Beauty of the Flow” as part of the Applied Mathematics Undergraduate Seminar series at 17:45 in BLOC 164. 

If you have any leftover hard-boiled eggs, you can recreate this bit of fluid dynamical fun. Spin the egg through a puddle of milk, and you’ll find that the egg draws liquid up from the puddle and flights it out in a series of jets. As the egg spins, it drags the milk it touches with it. Points closer to the egg’s equator have a higher velocity because they travel a larger distance with each rotation. This variation in velocities creates a favorable pressure gradient that draws milk up the sides of the egg as it spins, creating a simple pump. To see the effect in action check out this Science Friday video or the BYU Splash Lab’s Easter-themed video. (Photo credit: BYU Splash Lab)

With the Oscars just over, it seems like a good time for some movie-trailer-style fluid dynamics. This video shows a rotating water tank from the perspective of a camera rotating with the tank at 10 rpm. Initially, the tank and its contents are at rest. When the tank begins spinning, the fluid inside responds. Pink potassium permanganate crystals at the bottom of the tank show fluid motion as they dissolve, and food coloring is spread on the water’s surface to show motion there. Fluid near the edge of the tank reaches the tank’s rotational velocity fastest, due to friction with the wall, while fluid near the center of the tank takes longer to spin up to speed. This creates the spiral-galaxy-like shape in the dye. Eventually viscosity will transmit the effects of the wall’s motion even into the center of the tank. (Video credit: UCLA Spinlab)

In large-scale geophysical flows, rotation and density gradients often play major roles in the structures that form. Here the UCLA SPINLab demonstrates how large, essentially flat vortices—pancake vortices—form in rotating, stratified fluids. The stratification, in this case, is due to the density difference between salt water and fresh water; salt water is denser and therefore less buoyant, so it sinks toward the bottom of the tank. Note how the pancake vortex only forms when the fluid is both stratified and rotating.  If it lacks one of the two, the structures will be very different. (Video credit: O. Aubert et al./SPINLab UCLA)

In fluid dynamics, we like to classify flows as laminar—smooth and orderly—or turbulent—chaotic and seemingly random—but rarely is any given flow one or the other. Many flows start out laminar and then transition to turbulence. Often this is due to the introduction of a tiny perturbation which grows due to the flow’s instability and ultimately provokes transition. An instability can typically take more than one form in a given flow, based on the characteristic lengths, velocities, etc. of the flow, and we classify these as instability modes. In the case of the vertical rotating viscous liquid jet shown above, the rotation rate separates one mode (n) from another.  As the mode and rotation rate increase, the shape assumed by the rotating liquid becomes more complicated. Within each of these columns, though, we can also observe the transition process. Key features are labeled in the still photograph of the n=4 mode shown below. Initially, the column is smooth and uniform, then small vertical striations appear, developing into sheets that wrap around the jet. But this shape is also unstable and a secondary instability forms on the liquid rim, which causes the formation of droplets that stretch outward on ligaments. Ultimately, these droplets will overcome the surface tension holding them to the jet and the flow will atomize. (Video and photo credits: J. P. Kubitschek and P. D. Weidman)

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A viscous fluid inside a horizontally rotating circular cylinder forms a shark-tooth-like pattern along the fluid’s free surface. This is one of several patterns observed depending on the fluid’s viscosity and surface tension and the rotational rate of the cylinder. (Photo credit: S. Thoroddsen and L. Mahadevan; for more, see Thoroddsen and Mahadevan 1996 and 1997)