I What if I made you hear this as music But not how you mean that. The slow beam Opened me up. Walls walked through me Life resonant waves. I thought that maybe If you aren’t too busy, we could spend our lives Parting in stations, promising to write War and Peace, this time with feeling As bullets leave their luminous traces across Wait, I wasn’t finished. I was going to say Breakwaters echo long lines of cloud α Renunciation seales. Exhibits shade Imperceptibly into gift shops. The death of a friend Opens me up. Suddenly the weather Is written by Tolstoy, whose hands were giant Resonant waves. It’s hard not to take When your eye is at the vertex of a cone Autumn personally. My past becomes Of lines extending to each leaf Citable in all its moments: parting, rain
II There must be an easer way to do this I mean without writing, without echoes Arising from focusing surface, which should Should have been broken by structures Hung from the apex in hope of deflecting In the hope of hearing the deflection of music As music. There must be a way to speak At a canted angle of a enabling failures The little collisions, the path of decay α But before it was used by the blind, it was used By soldiers who couldn’t light their lamps Without drawing fire from across the lake Embossed symbols enable us to read Our orders silently in total dark In total war, the front is continuous Night writing, from which descends Night vision green. What if I made you Hear this with your hands.
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)
By any measure, it was endless winter. Emulsions with Then circled the lake like This is it. This April will be Inadequate sensitivity to green. I rose early, erased for an hour Silk-brush and ax I’d like to think I’m a different person latent image fading
around the edges and ears Overall a tighter face now. Is it so hard for you to understand From the drop-down menu In a cluster of eight poems, I selected sleep, but could not I decided to change everything Composed entirely of stills or fade into the trees
but could not remember the dream save for one brief shot of a woman opening her eyes Ari, pick up. I’m a different person In a perfect world, this would be April, or an associated concept Green to the touch several feet away
I admire the hell out of Ben Lerner, if that’s possible. He recently forayed into prose, and not just prose poems, but a novel: Leaving the Atocha Station. I like it but still think he should stick to poetry, which is some of the best that poets are writing today.