mean-free-path

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.

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I love Crowley’s amazement at humanity’s potential (and creativity) for both good and evil, because Crowley made it happen

Crowley gave humanity free will and through it the ability for sublime good and pure evil. He gave humanity infinite choice and then fell in love with them for what they did with it.

(This demon will be the death of me)

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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 sizeThe 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)

Mean Free Path by Ben Lerner

In an unconscious effort to unify my voice

I swallow gum. An old man weeps in the airport

Over a missed connection. The color of money is

Night-vision green. Ari removes the bobby pins

I remove the punctuation. Our freezer is empty

Save for vodka and film. Leave the beautiful

Questions unanswered. There are six pages left 

Of our youth and I would rather swallow my tongue 

Than waste them on description.

[By any measure]

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

*          *          *
Ben Lerner, “[By any measure]” from Mean Free Path (Copper Canyon Press, 2010). Copyright ©2010 by Ben Lerner.

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.