Imagine that you partially fill a horizontal cylinder with a viscous fluid, like corn syrup or honey. If that cylinder is still, the fluid will simply pool along the bottom. On the opposite extreme, if you spin it very fast, that cylinder will become coated in an even layer of fluid that rotates along with the cylinder thanks to centrifugal force. Between those two extremes in rotational velocity, some interesting fluid behaviors occur. Start spinning the cylinder and some of the pooled fluid will be pulled up the sides, eventually forming a thicker film with a straight front along the bottom of the cylinder. Spin faster and that straight front starts to break down, forming sharper cusp-like waves known as shark teeth. (Image credit: S. Morris et al., source; research credit: S. Thoroddsen and L. Mahadevan)
Month: September 2016
Fog Over Marin
Fog rolls over the hills of Marin County in this long-exposure photograph by Lorenzo Montezemolo. One of the most beautiful aspects of fluid dynamics is the way the same patterns and forms show up across situations. The slow flow of fog over hills in moonlight can echo the blurring speed of rivers pouring over a rocky streambed. Despite the differences in speed, lengthscale, and fluid, the physics remain the same. (Photo credit: L. Montezemolo; via Colossal)
Shear Across the Water
This photo series shows the development of a Kelvin-Helmholtz instability. It’s formed when two layers of fluid move past one another at different speeds. In this case, the two fluids meet off the back of a flat plate (seen at the left of the top image) when fast-moving flow from the top of the plate encounters slower fluid beneath. Friction and shear between the fluid layers causes billows to rise up and form waves very similar to those on the ocean (wind across the water works the same way!). Those waves turn over into vortex-like spirals and keep mixing until they break down into turbulence. This pattern crops up pretty frequently, especially in clouds. (Image credit: G. Lawrence)
Droplet Bounce
Water droplets don’t always immediately disappear into a pool they’re dropped onto. If the droplet is small and doesn’t have much momentum, it will join the pool gradually through a process known as the coalescence cascade, seen here in high speed video. The droplet bounces off the surface, then settles. A thin layer of air is caught between it and the pool. Slowly the weight of the drop pushes that air out until there is contact between the drop and pool. Before the drop can merge completely, though, surface tension pinches it off, creating a smaller daughter droplet. Ripples caused by the merger help bounce the little droplet, which repeats the same process until the tiniest droplet merges completely. (Video credit: B. ter Huume)
Reader Question: Rudders
Reader le-mec writes:
My question involves “fenestrated rudders”, a Chinese invention that
involved cutting diamond-shaped holes in the rudders of ancient Chinese
sailing ships (known as Junks). According to several articles (on the
internet, ha ha), it reduces the amount of effort required to steer the
ship at higher speeds with “no loss of function”. All I can find is
anecdotal evidence and I’d like to know if these claims hold water or if
they’re just steering us in the wrong direction.First off:
Now, I’m no expert on ships or sailing, but let’s talk rudders. Ships use rudders for steering. The rudder is completely submerged and turning it deflects water and creates a side force that helps steer a boat. In essence, it’s an underwater wing that generates lift in the side-to-side direction. Modern rudders even have the same shape as airfoils. That’s clearly not the case with the rudders of Chinese junks, but flat plates are a lot easier to make.
There’s another key feature of the junk’s rudder, and that’s the way it’s mounted. The junk’s rudder attaches to the ship such that it rotates about its leading edge. This makes it an unbalanced rudder. More modern rudders are typically mounted so that they rotate around an axis that’s partway back on the rudder. This is called a balanced rudder; I’ve illustrated both below.
The advantage of the balanced rudder is that it’s easier to turn. You can see this for yourself without adding water into the equation. Imagine holding a big rectangular sheet. If you hold it by one edge and try to rotate it, you can do it, but it’s kind of difficult. If you instead hold it about a third of the way across, you’ll find rotating it easier. Once you have a fluid moving past, it will only magnify how hard it is to turn the rudder.
So the Chinese junks had rudders that were harder to handle (by later ship-building standards) to begin with. By putting holes in the rudder, they equalized the pressure on either face of the rudder. That does make it easier to steer, since the helmsman is no longer fighting pressure differences across the rudder, but it would also reduce steering efficiency. It’s likely, however, given the slow speed of the junks, large rudder area, and their low hydrodynamic efficiency to begin with, that any drop in efficiency was negligible compared to the reduction in force necessary to steer.
Since modern designs rely on foil shapes to generate pressure differences (and therefore side force) across the rudder, adding holes to them would be a bad idea. But back in the Song dynasty, the fenestrated rudder was major advance in nautical engineering!
(Image credits: Chinese junk ship model – Premier Ship Models; Joffrey applauding – HBO; Rudder diagram – N. Sharp)
“Catacomb of Veils”
Burning Man’s “Catacomb of Veils”, the largest sculpture burned in the 2016 event, produced a series of smoke tornadoes as it blazed. Like dust devils or fire tornadoes, these vortices are driven by hot, buoyant air rising – in this case, from the fire. As the surrounding air moves in toward the fire, any rotational motion, or vorticity, in the air is intensified due to conservation of angular momentum. That concentrates it into a vortex, which becomes visible when it picks up smoke. Simultaneously, the wind was blowing in a consistent direction, sending any new vortices generated marching downstream. You can watch even more vortices and some slow-motion footage of the burning in the full video by Mark Day. (Image credit: M. Day, source; submitted by Larry B)
Happy 50th, Star Trek!
Today’s post is largely brought to you by the fact that I have been sick the past four days and my fiance and I have been bingeing on Star Trek Voyager. At some point, we began wondering about the sequence from 0:30-0:49 in which Voyager flies through a nebula and leaves a wake of von Karman vortices. Would a starship really leave that kind of wake in a nebula?
My first question was whether the nebula could be treated as a continuous fluid instead of a collection of particles. This is part of the continuum assumption that allows physicists to treat fluid properties like density, temperature, and velocity as well-defined quantities at all points. The continuum assumption is acceptable in flows where the Knudsen number is small. The Knudsen number is the ratio of the mean free path length to a characteristic flow length, in this case, Voyager’s size. The mean free path length is the average distance a particle travels before colliding with another particle. Nebulae are much less dense than our atmosphere, so the mean free path length is larger (~ 2 cm by my calculation) but still much smaller than Voyager’s length of 344 m. So it is reasonable to treat the nebula as a fluid.
As long as the nebula is acting like a fluid, it’s not unreasonable to see alternating vortices shed from Voyager. But are the vortices we see realistic relative to Voyager’s size and speed? Physicists use the dimensionless Strouhal number to describe oscillatory flows and vortex shedding. It’s a ratio of the vortex shedding frequency times the characteristic length to the flow’s velocity. We already know Voyager’s size, so we just need an estimate of its velocity and the number of vortices shed per second. I visually estimated these as 500 m/s and 2.5 vortices/second, respectively. That gives a Strouhal number of 0.28, very close to the value of 0.2 typically measured in the wake of a cylinder, the classical case for a von Karman vortex street.
So far Voyager’s wake is looking quite reasonable indeed. But what about its speed relative to the nebula’s speed of sound? If Voyager is moving faster than the local speed of sound, we might still see vortex shedding in the wake, but there would also be a bow shock off the ship’s leading edge. To answer this question, we need to know Voyager’s Mach number, its speed relative to the local speed of sound. After some digging through papers on nebulae, I found an equation to estimate speed of sound in a nebula (Eq 9 of Jin and Sui 2010) using the specific gas constant and temperature. Because nebulae are primarily composed of hydrogen, I approximated the nebula’s gas constant with hydrogen’s value and chose a representative temperature of 500 K (also based on Jin and Sui 2010). This gave a local speed of sound of 940 m/s, and set Voyager’s Mach number at 0.53, inside the subsonic range and well away from any shock wave formation.
Of course, these are all rough estimates and back-of-the-envelope fluid dynamics calculations, but my end conclusion is that Voyager’s vortex shedding wake through the nebula is realistic after all! (Video credit: Paramount; topic also requested by heuste11)
Happy 50th anniversary, Star Trek! Some of my earliest memories of TV are of watching TNG with my parents. Star Trek taught me that curiosity and scientific inquiry were vital and valuable, and that anyone could grow up to be a scientist, engineer, and leader. Thank you for such an inspiring and hopeful vision for humanity’s future!
And, seriously, those von Karman vortices are awesome.
Hearing in Space
Everyone knows that, in space, no one can hear you scream. Sound is a wave that requires a medium to travel through, and if space is empty, there’s no medium to carry that sound. Except, as Mike from The Point Studios explains, empty is a relative term. Space is full of dust and gas and plasma, just not as full of that matter as we’re used to. Thus, the question of whether sound can travel through space turns into a matter of scale. If the scale–the wavelength–of a sound is much larger than the distance between molecules, then the sound can propagate. So there CAN be sound in space – it just has to have a very long wavelength and, thus, a very low frequency. Check out the video for the full story! (Video credit: The Point Studios)
Roll Cloud Over Chicago
A cold front passing through Chicago last week triggered a roll cloud, shown in the timelapse above. These clouds look like spinning horizontal tubes and form in areas where cool, sinking air displaces warmer, moist air to higher altitudes. The moist air is forced up along the cloud’s leading edge, causing it to cool and condense into cloud. Air on the trailing edge sinks downward again, warming and dissipating the cloud. The clouds are a visible form of soliton, or solitary wave, traveling through the atmosphere. They go by several other names, too, including Morning Glory clouds and arcus clouds. (Image credit: A. King; via Colossal)
Bioluminescent Shrimp
Trevor Williams and Jonathan Galione of Tdub Photo captured these beautiful images of bioluminescent shrimp along the Japanese coast. The duo collected the tiny shrimp and poured them over and near rocks to create the effect they wanted. With their blue light, the shrimp act like tracer particles in the water, and with long exposures, the photos track the movements of the shrimp and waves. Technically speaking, they trace out pathlines – the trajectory that a specific fluid (or shrimp) particle takes in a flow. It’s a lovely way of capturing the water’s dynamic motion in a still photo. (Image credit: Tdub Photo; via Colossal)
