Even on the scale of light-years, fluid dynamics plays a role in our universe. This photograph shows the Lagoon Nebula, where stars, gas, and dust are battling for supremacy. Jets from young stars push the dust left from supernova remnants into a chaotic patterns, and the high-energy particles streaming from the youthful stars illuminate interstellar gases, creating the nebula’s distinctive glow. This section of the nebula is about 50 light-years across, so every picture we capture is only the tiniest snapshot of the true scale of its turbulence. (Image credit: Z. Wu; via APOD)
Tag: nebula
Turbulence and Star Formation
Space, as I’ve discussed previously, is surprisingly full of matter, especially clouds of dust. And yet the rate of star formation we observe is bizarrely low; the Milky Way, for example, produces only about one solar mass worth of new stars every year. If gravity were the sole force driving star formation, we’d see far more stars forming. Recent research suggests that turbulence plays a major role in regulating the star formation process, both by countering gravity’s attempts to collapse gases into a proto-star and by creating supersonic shocks that drive material together to jump-start star formation. There seem to be other important ingredients as well: young stars tend to form jets that blow material back into the interstellar clouds they’re forming in, feeding the turbulent background. For more, check out Physics Today. (Image credit: ESA/NASA/Hubble/ESO, via APOD; research credit: C. Federrath)
The Bubble Nebula
This spectacular Hubble image shows the Bubble Nebula. The source of this nebula is the star seen toward the upper left side of the bubble. This massive, super-hot star has ceased to fuse hydrogen and is now fusing helium, powering its way to a likely end as a supernova. As it burns, the star emits a stellar wind of gas moving at over 6.4 million kilometers an hour. As the flow moves outward, it encounters colder dense gases that it pushes along as it expands; this is the blue bubble surface that we see. The asymmetry of the bubble with respect to its source star is caused by the variation in the surrounding gas’s density. The bubble’s front moves more slowly in areas with more gas, thus making the bubble appear lop-sided. (Image credit: NASA; via Gizmodo)
Is the Star Trek Voyager Opening Sequence Physically Realistic?
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)
