Nervous dog hiding in alley with police car sirens, fireworks, and crowd unrest

How Loud Can It Get?

On By rolcottIn Astronomy: Planetary Science, Physics: Waves, UncategorizedLeave a comment

Mr Richard Feder stumbles into Cal’s Coffee Shop with his hands over his ears. “Holy Pete, those fireworks were loud! They pulled out all the stops with that finale. BAM! BaBANG! BAMBAMBAM!! I’m still jazzed, see, I’m shaking. My dog back home’s hiding under the bed.”

Cal shoves a mug at him. “Try some of this.”

“Smells like a bakery. What is it?”

“It’s called chai. Just some spices and decaf tea. Supposed to be calming.”

<sips> “Hmm. … Yeah, seems to be working. Still can’t get over the impossible noise level, though. Had to be hundreds of decibels.”

I’m over here nursing my usual cup of mud. “Several hundred decibels can’t happen on Earth.”

“Hey, I was right there, I heard it, I felt it!”

“What you felt wasn’t sound, and it’s not measured in decibels.”

“Sounded like sound.”

<sketching on Old Reliable> “Sound is a continuous wave of out‑and‑in pressure changes, like the orange line here. The variation is what matters — push and pull, the waves average out to atmospheric pressure. What you felt was a shock front, a quick pulse of high pressure, all outward like the red line. OK, you felt a bunch of shock fronts, but not the regular waves that decibels care about.”

“What’s the green line about? It’s regular.”

“That stands as a baseline for comparisons. I’ve marked its high‑low range as pref. Most people doing sound measurements set pref to the smallest pressure swing that most people can hear, about 2×10-10 atmospheres—”

“That’s pretty small.”

“Indeed, but you’ve got to start somewhere. If you whisper to a partner at exactly that sound wave level, p=pref, the p/pref ratio is 1.0. That’s zero on the bel scale. Sounds from rustling leaves have a p/pref ratio about ten times larger. We give that a two‑bel rating. Every factor of ten above that rates an additional two bels. A busy nightclub could easily have a p/pref ratio near 105, ten bels, a hundred thousand times more pressure swing than your quiet whisper.”

“What’s that got to do with decibels?”

“They’re for rating sound waves that are between ten‑factors. ‘Deci-‘ means one‑tenth so there’s ten decibels per bel. The noise police would assess that ten‑bel nightclub at 100 decibels. If you sit right next to the loudspeakers where the sound pressure is 120 decibels, the extra 20 decibels pummel your eardrums with an extra ten times the pressure swing. Which is why people suffer short-term hearing loss at that intensity.”

“Uhhh… so 300 decibels from those fireworks would be a 1015 ratio which is a lot but why do you say it’s impossible?”

“That’s what the blue ‘Over‑driven’ line is about. Suppose you give an alarm siren a continuously growing power feed. As the siren’s power increases, it emits pressure peaks that push out more strongly and valleys that pull in more strongly. When the valley’s part of p eventually grows to atmospheric pressure patm, the sound’s pressure valleys try to drop below zero, which they can’t because zero is is a vacuum. Further output power beyond that level only goes to the outward pressure phase. The siren isn’t making a sound any more, it’s making push pulses. Maximum loudness happens when the p/pref ratio nears patm/pref. On Earth, patm/pref is 5×109. If you do the math, that’s 194 decibels. You just can’t make a sound any louder than that, no matter how you modify the siren.”

“You said ‘on Earth’ twice, like the limit’s different on other planets?”

“Sure. The same formula applies to any body with a solid surface and an atmosphere. The Solar System has only three planets and one moon that qualify. Here, I’ll tell Old Reliable to run the numbers for those. … How about that? Earth’s ‘loudest possible sound’ almost exactly matches the one for Saturn’s moon Titan. Mars is 40 decibels quieter than we are, but Venus is 40 decibels louder.”

“Dogs got sensitive ears. I bet they’d like it on Mars. They’d probably invent a different bel scale, though.”

Nervous dog hiding in alley with police car sirens, fireworks, and crowd unrest

~ Rich Olcott

Dodeca to The Rescue

On By rolcottIn Cosmology, General: Fun Stuff, Physics: Black Holes and Relativity, UncategorizedLeave a comment

Days are getting warmer, so my walk around the park’s lake is at dawn. I’m enjoying the view when my phone blares out <bomPAH-dadadadaDEEdah>. Of course, the caller‑ID display shows 710‑555‑1701. “Good morning, Ms Baird. Surprised to hear from you again so soon. How is Project Lonesome coming along?”

“It’s been saved, thanks to your knowledge of antique Physics.”

“Antique??!?”

“Lenz’s Law was already nearly 200 years old in your time, Mr Moire, and I’m another 200 years on. Our engineers have to learn exponentially more than yours do. Things get lost in the welter so we missed the magnetic squirt‑out stumbling block. Anyway, armed with your hint I was able raise the issue early enough in the design phase that we could adjust.”

“Repulsion between opposed magnetic fields is pretty basic Physics. How will your people get around that?”

“By going from ten anti‑matter factory sites to twelve.”

“Huh? Your original design had ten current‑carrying tractor/pressor beams arrayed around the equator of Planetoid Road. That was a problem because currents in the beams would induce their own magnetic fields. The combined field would be perpendicular to the equator. Lenz’s Law says induced fields are in opposition to the black hole’s external field. Field‑field pressure would squeeze Road right out of the system. Twelve beams around the equator would make an even stronger magnetic dipole. How would that solve the problem?”

“It wouldn’t, but that’s not the configuration we’re looking at. Do you know what a dodecahedron is?”

“One of the Platonic solids — twelve identical pentagonal faces, lots of symmetry.”

“Right. So we’re going to center each AM factory in its own face of a dodecahedron plotted onto Road’s surface.”

“Ah, the symmetry’s nearly spherical so the induced fields won’t combine as a dipole. Cute.”

“It’s better than that, Mr Moire. The currents are pulsed, remember, and we didn’t expect to have all the factories running full‑out all the time. By varying individual pulse rates or even shutting down one or two factories we can control the strength and direction of our combined magnetic field. We can tweak that vector relative to the black hole’s field lines as needed to stabilize our position. We could even steer the planetoid around the system if we have to. All with zero fuel expenditure. Wins all around!”

“What about the spaceport?”

“Spaceport?”

“You’re making a lot of AM product here, and you’re going to need to ship it out to wherever Star Fleet needs it. That means Road will need a port and docking facilities and everything that goes with that. I had assumed that’d be at one of the poles. Zero rotational speed up there would would make for easy landings and take‑offs. But the new configuration would have the worldlet tumbling arbitrarily. No fixed poles. Where will you put the docks? For that matter, how else could you build and staff the factories in the first place?”

“That we did think about. Not even the original design included on‑planetoid docking. Landing a ship at either magnetic field convergence point would have been too risky. That’s why we were originally going to site all the AM factories at the equator. Putting them somewhere else is no problem because each factory will be assembled in space. Space tugs can drop it into any position and then flit away. Every AM factory will be fully automated, including the robots that will repair whatever needs repairing, so no staffing required.”

“But how will you get the AM away from the planetoid?”

“The usual way. The AM will be magnetically suspended in massive gamma bixonate cannisters transmitted by industrial‑scale transporters. The bixonate blocks the black hole’s field. Transporter range is limited near Lonesome’s steep gravity well, but we can orbit a transshipment facility close enough to be useful but far enough to be safe.”

“What if a transporter malfunctions? You wouldn’t want AM spraying around the transshipment deck.”

“Reception transporters for AM cargoes work from the outside in so the cannister’s integrity is complete before the AM signal exits the buffer.”

“I sense a promotion in your future.”

~ Rich Olcott

  • Thanks to Alex and Xander for keeping me on‑topic.

The Polar Peril

On By rolcottIn Cosmology, General: Fun Stuff, Physics: Black Holes and Relativity, UncategorizedLeave a comment

This park bench is perfectly situated for watching the summer solstice sun setting across the lake. I’m enjoying the view when <bomPAH-dadadadaDEEdah> blares from my phone. Number 710‑555‑1701 on the caller‑ID display evokes memories of a sultry stare and pointed ears…. “Good evening, Ms Baird. What’s new in the 23rd century?”

“Not much that I can tell you about, considering the Prime Directive. We’re taking a second shot at Project Lonesome. You may recall we’d identified an isolated black hole we called Lonesome. We were going to use two orbiting planetoids, Pine and Road, to generate electricity from its spinning electromagnetic field. Star Fleet’s anti‑matter synthesizers need that power.”

“Yes, I remember. Three‑body gravitational instability cost you Pine and your rank. Have you recovered the rank?”

“I’m only up to Lieutenant Commander so far, but part of the deal was that I’m back on Invigilator for a second shot at Lonesome. This time we’ve simplified the design. We had to, we only have Road to work with.”

“If I recall correctly, the idea was that the rotating field would induce electrical currents within conducting tractor beams strung between Pine and Road. How are you going to do that with only one orbiter? Relativity would be a challenge if you string something down to Lonesome.”

“We’re not stupid, Mr Moire, and we’re quite familiar with Relativity’s effects. I’ll give you an example your science is ready for. General Relativity says that time runs more slowly the deeper you go into a gravity well, yes?”

“Indeed. Our GPS time‑signal calibrations include an Einstein correction for reduced Earth gravity at satellite height. We have a movie, Interstellar, where gravitational time dilation was a major plot element.”

“A classic film. Even now we watch it occasionally. Consider this: on its own timeline, a star within its gravity well is younger than remote measurements say it is. The more massive the star, the greater the difference between experienced and apparent age.”

“Ooo, nice.”

“Counteracting gravitational discrepancies was a major challenge when we were developing transporter technology. Physics just doesn’t like teleporting a material object between different timescales, even through subspace. We finally gave up on that approach. What worked was transcribing the object into a subspace signal between pattern buffers. In the receiving environment we rebuild from the buffered signal and amorphous matter. Sometimes roundabout is the best path.”

“I’m with Bones on that—”

“Who?”

“Doctor Leonard McCoy.”

“Never heard of him. Must have been before my time.”

“Anyway, he’ll refuse to use transporters, convinced they’ll spray his atoms all over the Universe.”

“Way, way before my time, then. These days they’re as safe as your airplanes. Safer.”

“So what’s the new design?”

“The plan is to site ten plants around Road‘s equator. Each plant will have a free‑standing AM production facility teamed with two conductive tractor/pressor beams locked onto a floating plate of gamma‑phase bixonate. I’m allowed to give you those details because it’ll be a century before you’ll have bixonate production technology, much less gamma restructuring capability.”

“Why the special material?”

“At the nanoscale level, gamma bixonate’s surface is an array of corner‑cube mirrors that perfectly reflect electron waves back to their source. Meanwhile, the jagged edges between nano‑cubelets topologically obstruct local coherent magnetic fields. The combination is key to my Project Lonesome architecture. The power production cycle starts with injecting pulses of spin‑up electrons into one beam’s center where they’re trapped and streamed upwards. The black hole’s rotating magnetic field accelerates the electrons until they hit the bixonate nano‑cubelets that reflect them down the other beam. The reflection operation also flips the electron spin state so now the field accelerates them downward towards the factory’s energy receptors.”

“Double the acceleration effect.”

“Mm‑hm. We expect to achieve energies in the high exa‑electronvolt range, about a billion times what your CERN instrument can do. That’s plenty for AM synthesis.”

“One question.”

“Yes?”

“Have your engineers considered Lenz’ Law? Your immense electric currents will generate their own magnetic fields in opposition to the black hole’s. The induced fields will squirt Lone right out of the system.”

A sudden shocked pause, then the connection drops.

~ Rich Olcott

  • Thanks to Xander for a deeper Time question.

By Her Bootstraps

On By rolcottIn General: Fun Stuff, Physics: Einstein, UncategorizedLeave a comment

A rainy day and business is slow. Vinnie and I are playing cards in my office. He lays down a queen of hearts and gets a distant look in his eye. “I wonder where she is now. Or when.”

That ‘or when’ phrase told me who he’s thinking about — Anne, with her white satin attire and molten‑silver voice. “I’m always wondering about that, Vinnie, but it’s hard to apply the word ‘now’ to a time‑traveler. She’s visited so many time periods. When you say ‘now’ you’re covering a lot of separated moments from our perspective, even if there’s only one continuous series from hers.”

“Good point, Sy. I still have trouble believing she’s real and not some figment of your imagination. Yeah, Eddie and Cathleen and Susan and me, we’ve all met her. But like Cal said the other day, it looks like she breaks some pretty fundamental rules. Conservation of Energy, for one.”

“How do you figure that?”

“Stands to reason. Einstein says mass is energy, right?”

“Mm-hm.”

“Anne has mass, right?”

“Mm-hm.”

“So the Universe is moving along, one second per second as usual, with however much total energy it’s got. Suddenly Anne appears when there wasn’t an Anne before. That’s a burst of energy that wasn’t in the Universe up to then. Later on, when she feels like it, she pops out to some other time or Universe and her mass‑energy disappears. Where’s the Conservation?”

“I can think of two possibilities. First, maybe Anne is a virtual particle. According to Heisenberg’s Uncertainty Principle, virtual particles are always popping into and out of existence even in empty space. In this application, ‘uncertainty’ is the difference between ‘there’ and ‘not there.‘ How long a virtual particle lasts depends on how much energy it packs — sneaky little ones can hang around for a while, big ones generally check out quickly. Stephen Hawking said that black holes evaporate by eating the anti‑particle partners of virtual particle pairs created at the Event Horizon.”

“Put numbers to that.”

<poking at Old Reliable’s keypad> “Let’s see… I have no idea how much she weighs, say it’s about 50 kilograms. For an object with that mass, the minimum expected lifetime would be about 10‑53 second. Anne’s lifetime is enormously longer than that, thank goodness, so we can probably rule out the virtual particle option. On the other hand, maybe Anne somehow keeps a separate set of books. Maybe she conserves her own personal mass‑energy which doesn’t count in whatever Universe she’s visiting. As a physicist I’m not willing to guess how she’d do that.”

“I like the second one. Makes sense, sorta. But Cal came up with another difficulty, though.”

“Which is?”

“Chains of cause and effect. You’ve said keeping the links in the right order was a big part of Einstein’s Relativity theory.”

“That’s true. Any observer should see a distant cause precede its effect no matter the observer’s speed relative to the event locations. That imperative means that the Universe has Lorentz symmetry which is the basis for Special Relativity. That’s a fundamental.”

“Right. So what blocks time‑traveling Anne from looping back to cause or uncause something? Killing off Hitler while he was still painting houses, for instance, or getting Columbus to schedule his trip a little later into hurricane season. Anyone else in the Universe would see Anne’s effect happening before she went back to do that.”

<fffshwwwPOP!!> A molten‑silver voice behind me. “Easy answer, Vinnie. And no, I’m not in Sy’s imagination, see?”

“Whoa! Talk about timing. Hi, Anne. You look way too good for Sy’s imagination. What’s your easy answer?”

“Pure self-interest. Ever read Heinlein’s story, By His Bootstraps? My timeline is so twisted back and forth I don’t have any idea where I started from. Sometimes I meet myself and I don’t know whether I’m coming or going. We never know what to say to each other. If I were to change anything, anywhere or anywhen, it’d probably get in the way of my being me. My strict rule is, ‘Always an observer, never a participant.‘ It’s worked so far.”

~ Rich Olcott

  • Thanks to Alex for getting me started on this topic.

Airborne Amazons

On By rolcottIn Astronomy: Planetary Science, UncategorizedLeave a comment

Vinnie blows into Cal’s place dripping wet. “Man, it’s coming down out there! This monsoon’s trying to drown us.”

“No monsoon, Vinnie, this rain’s from an atmospheric river.”

“Monsoon, river, what’s the difference, I’m soaked, Cathleen!”

“Cal, Vinnie needs a warm‑up mug, quick!”

“Comin’ right up. Here you go, Vinnie. Cathleen, I’ve always used ‘monsoon’ for rain like this. What’s wrong with that?”

“Because a proper monsoon is seasonal; the year’s too early for monsoon season around here.”

“Didn’t realize we had a monsoon season. I just figure if it’s not snowing and it’s not steaming we got rain.”

“Not funny, Vinnie. Our local weather deserves better from you. We have lots of sunny days even during our July‑September monsoon season.”

“Why pick on those particular months?”

“Temperature and wind patterns. Sy would push the ‘because’ all the way down to heat capacity difference. Per unit area, a one‑centimeter layer of rock has about ¾ the heat capacity of the same thickness of still water. Convective water circulation magnifies the difference by ten.”

“So?”

“So a given amount of energy will raise the temperature of a rock expanse almost 13 times as many degrees as it would the same ocean area. On the other hand, night‑time energy radiation cools rock by almost 13 degrees where the ocean would cool by one. Compared to the ocean, land surface gets hotter in the daytime, cools off more at night.”

“So?”

“So Summer sunlight heats land area more than its neighboring ocean. Air over warm land expands and rises, making room for water‑laden air from the relatively cool ocean cover. That air warms and rises, too, but as it rises it cools again. The water vapor condenses and rain falls. Come Autumn, land temperature drops more than ocean surface temperature does. That reverses the air’s general circulation and shuts off the rain. End of monsoon season.”

“It works that way all over the world?”

“Most everywhere except Antarctica. Apparently it stays so cold there all year around that the back‑and‑forth rocking never gets a chance to develop.”

“Doesn’t seem to have anything to do with the Coriolis Effect.”

“Most of the movement is roughly perpendicular to the local coastlines, but Coriolis gets into play farther away from the coast. The North American monsoon, for instance, comes up from the Gulf of California and trends northeast across the mountain states into Kansas and Oklahoma.”

Water vapor, afternoon of August 22, 2018. Dry air is orange.
Image from Albuquerque, NM National Weather Service

“That strong west‑to‑east trend looks like some weather maps I’ve used flown by. Is that an atmospheric river?”

“Similar, Vinnie, but no. Atmospheric rivers are a completely separate phenomenon from monsoons — different physical settings, different behavior. They’re both fueled by warm oceanic water vapor but that’s about it. Monsoons are seasonal, last for months, and hover over particular regions; atmospheric rivers are perennial, generally live for only a few days, and wander around. We’ve known about monsoons for millennia, but it wasn’t until 1992 that scientists had satellite data to support the rivers notion.”

“How can they be perennial and only last for days?”

“I meant that individual rivers come and go but the northern and southern hemispheres generally have about four each throughout the year. Rivers thousands of kilometers long, hundreds of kilometers wide, carrying as much water as the Amazon. Together they’re responsible for transporting 80‑90% of the tropical moisture that crosses the mid‑latitudes each year.”

“That’s a lot of water hanging over our heads. How could people have just missed them all those years?”

Vinnie has a calculating look. “A million square kilometers. How tall are these things?”

“Can’t give you a firm answer. Probably a kilometer or two but that’s a guess. The satellite sensors register total water mass from orbit down to ground. The numbers peak around 60 millimeters of H₂O per square centimeter. Spread along a one‑kilometer height that’s 60 g/m³ maximum; figure a 30‑gram average.”

“It’s just moist air, then, not liquid water. Cal, your breath’s more humid than that. A million cubic kilometers of 30‑gram 1‑meter cubes packs a lot of grams. I’m sure I’ve flown right through those things without noticing them.”

~ Rich Olcott

The Coriolis Mandala

On By rolcottIn Astronomy: Planetary Science, Physics: Newton and Gravity, UncategorizedLeave a comment

“Cathleen, this Coriolis Effect‘s rule is so easy. The force always twists you to the right no matter which way you travel. Going north, you swerve eastward; going south you swerve westward, always to the right. But what about the in‑betweens? What if I’m going east or west? Does the force just go away?”

“Of course not, Cal, but it mutates. Mind you, the rules you quoted only apply in Earth’s northern hemisphere. If you’re south of the Equator they go the other direction. Anyway, the northbound and southbound cases everybody writes about are the simplest to describe. You might be surprised how it varies across all the compass points separating them.” <pulling another image up on her tablet> “Here’s a chart I did for my class.”

“Whoa, that’s complicated.”

“Let me break it down for you. The circles around the outside represent different travel orientations — north’s at the top, then northeast to its left, directly east at the three-o’clock position, and so on. The brown arrows point to the corresponding direction. They’re all the same length to imply equal travel speed because why not.”

“Southbound’s at the bottom, just like on a map, right?”

“Right. Now, the blue arrow in a circle shows the relative Coriolis force experienced by an object traveling in that circle’s direction. See how the leftward force falls off from full‑strength if you’re northbound, to 70% if you’re going northeast, so zero for eastbound motion.”

“I’ll take your word for the 70%, but yeah, that’s what the picture shows. Wait, right after you turn the corner from east to south that blue arrow flips like the rule says.”

“It’s not like there’s a big toggle switch somewhere. If you’re going a little bit north of due east, there’s just a little bit of east‑pushing Coriolis; drive just a little bit south of due east there’s just a little bit of west‑pushing Coriolis. Build a Coriolis swerve‑meter. Swivel it all around the compass. It’ll show peak force when pointed north or south. The force smoothly fades away through zero, grows to a peak in the other direction, fades away, then re‑grows as you come back full circle.”

“So that’s what the pink and green disks are about, huh? Strong to fade‑away east both sides in the top half, strong to fade‑away west in the south?”

“You’ve got it.”

“What’s the red and blue stuff about then?”

“Re‑think the picture to 3‑D. Visualize each of those circles as a sphere. The thin black arrows are x‑y‑z pointers coming out from the sphere’s center. Can you see that?”

“The arrows coming out an angle, that’s like coming out of the screen?”

“Mm‑hm. Suppose you’re driving straight east in a vehicle that doesn’t care about gravity. What would happen?”

“Heh‑heh‑heh, lift‑off!”

“Exactly. It’s not centrifugal force, technically, but the Coriolis Effect’s equation establishes a trade‑off between Coriolis acting horizontally and a centrifuge‑like sibling acting vertically. Both sibs act to increase or decrease an object’s effective inertia depending on the object’s direction of motion relative to Earth’s rotation. The vertical component strengthens as the horizontal component weakens and vice‑versa.”

“The vertical one is the tubes coming out?”

“Yes, that’s what those are about. Long tubes in the diagram indicate high relative strength, short tubes signify weaker intensity, which is why the northbound and southbound spheres don’t have any tubes at all.” <grins> “Sy would appreciate my color choices.”

“I don’t get the joke.”

“Over there on the left side, the vertical component is upward, towards us. If a star’s coming towards its spectrum is shifted to shorter wavelengths, bluer than it it were standing still. No surprise, we call that a blue shift. Being an astronomer, I made those tubes blue‑ish.”

“I suppose the right side has red tubes because the vertical component pushes down when you’re westbound?”

“You broke the code, Cal. Red‑shifted stars are flying away from us. I’m being careful here — the red tubes don’t represent a true centripetal force. There’s no pushing and the effect doesn’t depend on distance from the rotation axis. But it makes a westbound truck act a bit like the road’s coming up to meet it.”

~ Rich Olcott

The Winds of Change

On By rolcottIn Astronomy: Planetary Science, Physics: Waves, Uncategorized1 Comment

“You said that so careful, Cathleen.”

“What that was that, Cal?”

“When you said those blue donuts in your diagram could be Earth’s equivalent to Jupiter’s brown bands. Why not the white zones, too?”

“Because Earth has a much better analog for the white zones. Juno‘s observations showed us Jupiter’s white zones floating a hundred or more kilometers above the brown stuff.”

“We don’t have that much room, do we?”

“Nowhere near. Our clouds and weather stay inside the troposphere, mostly less than a dozen kilometers up. Inside that shell, though, similar dynamics may apply.” <scribbling on her tablet> “Here’s a grossly oversimplified sketch.”

After an image by Kaidor, lic. under CC A-SA 3.0

“White frosting on the donuts?”

“Winds, Cal, not frosting, though they are cold. Think of each blue donut as a conveyor belt transporting air between warm and cold regions. The arrows reflect separate lower‑level and upper‑level wind regimes. What happens up at 60°N?”

“That’s actually a ring, right, goes all around the planet up there? I see two lower‑level conveyor belt donuts dumping at the same meridian — stuff’s gonna pile up over the ring unless the upper‑level parts move it out fast enough.”

“They do, mostly, during each hemisphere’s Summer. Winter’s another matter. The lower‑level conveyors are more sensitive to surface conditions than their upper‑level partners; seasonal surface condition changes affect the dump/clear balance. Wind speed’s driven by density difference; cold winter air is denser than summer air, even in the Arctic. Typical wintertime lower‑level polar cell transport dumps more air into that convergence than the upper‑level mechanism can sweep away.”

“So it piles up, like I said. Just sits there, I bet.”

“It might if the Earth weren’t rotating. That dense air acts to lift lighter air coming in from the South—”

“I know! Coriolis in action! The lighter southern air gets into the upper level first and it’s already turning to the east so it kicks that white cylinder into going east, too. Except it’s a ring.”

“It’s a continuous process so getting there first doesn’t count. But yes, eastward momentum from lighter southern air is the dominant influence that speeds the polar jet stream’s winds on their way, 200 kilometers/hour or more.”

“Whoa, that ‘polar jet stream’ phrase just sunk in. I keep hearing the weather guy talking about how the polar jet stream brings down the cold.”

“That’s like saying robins bring the springtime. The warm/cold front’s established by the balance between cold’s centrifugal force, heat’s poleward momentum and Coriolis twisting everything to the right. The jet stream just rides the back of the front. To my mind, it’s more accurate to say that the cold brings down the polar jet.”

“Cart before the horse.”

“Mm-hm. Remember I said that diagram is a gross simplification. One of the simplifications was to localize the stream at 60°N. Here’s a slightly less gross simplification. That ‘ring’ isn’t circular, it ranges more-or-less regularly between 60° and 45° in a nice pattern.”

“The crinkly circle looks like a coffee grinder part. So the cold just slides down that jet from Greenland to Europe.”

“Um, no. Weather doesn’t travel along the streams and the waves aren’t locked in place. The whole structure rotates eastward. Carl‑Gustaf Rossby discovered that, which is why it’s called a Rossby wave. Rossby was an early pioneer in atmospheric physics; his group’s weather predictions help decide World War II. Anyway, even Rossby waves are simplifications.”

“How much more unsimple can it be?”

“Much more. This idealized sketch shows how things might settle down under stable conditions. Conditions are rarely stable, especially now that global warming is upsetting the apple cart. The polar land areas are warming up the most, which means the polar cell’s outbound air currents are weaker and patchier than they used to be.”

“So the warm air masses can punch up closer to the poles like Summertime. Big deal.”

“Very big. Amplify the Rossby wave beyond a certain point, distortions create vortex cascades inside the peaks — the structure goes chaotic. Cold air leaks out past the warm air, like for this horrible early May snowstorm we’re getting.”

“Global warming causes cold air leaks. How about that?”

~ Rich Olcott

Belts And Zones

On By rolcottIn Astronomy: Planetary Science, Chemistry, Physics: Newton and Gravity, UncategorizedLeave a comment

“This cold-brew latte concoction — good choice, Cal. Thanks.”

“You’re welcome, Cathleen. Sounded like it’d fit your mood. Hey, Sy’s latitude racetracks got me wondering. Do Jupiter’s stripes follow the same pattern?”

“The ‘racetracks’ exist, sort of, but they’re a very small part of a very complicated picture. Jupiter’s belts and zones are each wider than Earth. Maybe half an Earth‑width deep, too. That’s just a small fraction of Jupiter’s fluid interior. A grand arena for a host of dueling pseudo‑forces.”

“Lotsa ways for winds to work, then.”

“Indeed. Ferocious drafts everywhere, up, down and sideways. Water in all its forms is a major weather driver here on Earth. Jupiter has water, too, in multiple forms acting at multiple atmospheric levels. It also has ammonia, sulfides, phosphines, tholins, hydrocarbons, a potpourri of chemicals flavoring its hydrogen and helium. Ammonia has gas/liquid and liquid/solid transitions like water does but they happen at their own temperatures and pressures. Jupiter’s white zones are mostly ammonia ice floating a couple hundred kilometers above its brown belts of ammonium sulfides and tholins. We’re still learning about how the planet’s complicated ammonia‑sulfides system works. Compared to Jupiter, Earth’s atmosphere is a kid’s toy.”

Earth’s landmasses in natural colors.
Image by Daniel R Strebe, licensed under CC A-SA 3.0

“Earth’s a lot smaller, for sure. Do we have belts and zones?”

“Oh, yes. You’ve seen evidence for them on a world map, but maybe you haven’t noticed it.” <pulls up an image on her tablet> “All those deserts stretching across low latitudes north and south of the forested Equator and below the boreal forests. Pretty distinctive pattern, right?”

“How about that? My astronomy magazines carry photos from Chile’s waterless Atacama observatories all the time. I’ve never connected those with the Australian outback or Namibia’s desert. All at the same level, aren’t they? And the Sahara’s tan blotch goes all the way east to the Gobi and matches northern Mexico and USA’s high plains on the other side. The green areas must get all the water that the deserts don’t. How does that square with your vapor‑ice water pump theory?”

“Sideways, actually. I don’t claim that molecules evaporating near the Equator make it all the way to an ice sheet in a single pass. The heat energy does, eventually, but the molecules get waylaid by the Coriolis force. That’s where the racetracks come in. I can’t do better than this graphic. Each of those flattened blue ovals is a slice through an air‑mass donut that dominates its latitude range.”

Earth’s atmospheric circulation patterns
After an image by Kaidor, lic. under CC A-SA 3.0

“That third‑down donut pretty much covers the Sahara. Is that why it’s dry?”

“It’s a big part of the reason, but you’re way ahead of me. Look at the colored arrows inside that donut’s slice on the right. Why do they point where they do?”

“Well, we’re hottest at the Equator. Hot air rises which is why the red arrow goes up. We said rising air over the ocean carries evaporated water with it, right, which the grey arrow will drop close by as the Earth spins eastward. That’s why the Equator’s got the forest. How’m I doin’?”

“Just fine. How about the yellow and orange arrows?”

“Um, the yellow’s colliding with the next donut north so it’s gotta go down?”

“There’s more to it than that. The air up high gets chilled which makes it more dense. That’s the major reason it descends. When it gets down to ground level, though, how much water does it hold?”

“Not much, ’cause it rained out over the Equator’s forests. The orange arrow’s gonna be thirsty so it’ll pick up more water sweeping over the ocean.”

“But what if it sweeps over land?”

“Ah‑hah. It’ll suck the land dry and THAT’s why the Sahara is where it is.”

“Right. Now, those black arrows over the same cell…?”

“Northbound twisting to the right — that’s Coriolis in action. The gray arrow up top must skew eastward. By the rules, the southbound orange arrow at sea level skews west. Hey, that’s those white‑arrow trade winds. Cool.”

“Those blue donuts could be Earth’s version of Jupiter’s brown belts.”

~ Rich Olcott

Tropical beach with palm trees next to icy polar region with glaciers.

The Big Water Pump

On By rolcottIn Astronomy: Planetary Science, Physics: Newton and Gravity, UncategorizedLeave a comment

“Springtime! Could you make me a lilac latte, Cal?”

“Maybe if I left out the coffee, Cathleen. Lilac’s too delicate to stand up to coffee’s punch. How about a cold brew of light roast? I just made a batch. Plenty of caffeine in there, not too much intensity and you can imagine the flowery part.”

“I’ll have that, and a lemon scone, please.”

“Here you go, fresh from the filter. Hey, you sure lit a fire under Sy. He’s done a whole string of posts about Coriolois Effects.”

“Tsk, Cal, the scientist’s name was Coriolis. I’m not surprised there’s been multiple posts — the same pseudo‑force shows up in many ways.”

“Pseudo‑force?”

<looks around> “Good, Sy’s not here. He’d talk our ears off about inertial frames. My quick answer from a planet scientist perspective is that real forces are the ones that make things happen in systems where everything’s moving in straight lines at a steady pace.”

“Like on a pool table?”

“Mm-hm. You can generally make good predictions on systems like that, which is how pool sharks make their money. But if part of the system is accelerating in some way, maybe it’s rotating, you’ve got two choices for predicting how the system will behave. The hard way is to calculate each individual component’s motion in a single coordinate system using just the real forces. The easier way is to group components that have a common acceleration. Pick a convenient group to serve as your base subsystem. Define another subsystem for the components that all have the same acceleration relative to the first subsystem and so on. Then you pretend a pseudo‑force drives the interactions between your subsystems.”

“Like Earth and our Moon make a subsystem ’cause they orbit the Sun together and you said rotation’s a kind of acceleration. The pseudo‑force is centrifugal, fighting against the Sun’s gravity to keep Earth’s subsystem in orbit!”

“I love it when that kind of connection‑making happens in my classroom. Thank you, Cal.”

“You’re welcome. So your subsystems are what Sy calls frames?”

“Pretty much. Skipping some technical caveats, that’s the idea. When I think about atmosphere dynamics, I could try to calculate the planet’s whole atmosphere as an incredibly messy collection of atoms. I prefer to think of the Earth as a subsystem hosting some number of air mass subsystems, all embedded in the Universe system. The Universe enforces straight‑line inertia and the Earth adds rotational acceleration but the air masses are constrained to the planet’s spherical geometry. The Coriolis pseudo‑force summarizes all three effects. The calculation’s still messy, but it’s a lot more manageable. And then there’s water.”

“Water?”

“The piston that drives the climate. Water molecules are small so they move easily through the atmosphere. The important thing is, they’re good at transporting heat energy.”

“How’s that? They’d be the same temperature as everything else.”

“Temperature doesn’t always measure energy. Water molecules like to hold onto other water molecules. It takes energy to get them apart. When they get back together, the energy’s released so it’s like the freed‑up molecules store heat energy. In solid water, every molecule is locked into position. Melting a given mass of water amounts to breaking those locks. The liquid mass at freezing temperature contains more energy than the ice did. When liquid water evaporates, the gas contains even more energy, because the molecules can roam even more freely. Visualize a bucket of water someplace warm.”

“A Hawai’ian beach.”

“That bucketful absorbs heat energy as it evaporates, cooling the Pacific Ocean. Winds sweep up the gas and carry it north to the Arctic where it freezes. In the process it warms the ice cap by giving up its liquid‑to‑gas heat and also its solid‑to‑liquid heat. Water’s two active phase transitions make it a far more efficient heat transporter than dry air alone.”

“One bucket’s teeny in the ocean, though.”

“Multiply that by gazillions. We have gigatons of surface water. The evaporate/freeze/melt process cycles as the icecaps degrade, continuously acting to moderate Earth’s temperature differences. If Earth were dry, the gradient would be far steeper. Thermal gradients drive air movement. A dry Earth’s extreme temperature discrepancies would generate permanent gale‑force winds towards the poles.”

~ Rich Olcott

Atmospheric Jiu-jitsu

On By rolcottIn Astronomy: Planetary Science, Physics: Newton and Gravity, UncategorizedLeave a comment

A gorgeous early Spring day for a walk by the lake — blue sky, air just the right side of crisp, trees showing their young green leaves, geese goosily paddling around. As I pass the park bench I hear a familiar voice. “Hello, Mr Moire.”

“Morning, Walt. It’s been a while. What do your people want to know about now?”

“We’ve been reading your series of posts about the Coriolis Effect. You have masses of air pushing each other around, you have pendulums twisting about, and you have objects flying weird orbits around latitudes instead of the planet’s center. Which is the real Effect?”

“All three.”

“They’re so different. How can all three be right?”

“Knowing something of your interests, I can think of another Coriolis application will help clarify the connection. How do you steer an old‑fashioned artillery shell?”

“You don’t, you aim it.” <His eyes are looking inward.> “Those old howitzers, you traverse to the target’s coordinates, set the elevation for the distance and your munitions and whatever your barrel’s still good for, load ‘er up, let ‘er rip and wait for the forward observer to tell you how to adjust.”

“No correction for the Earth turning west‑to‑east beneath the shell’s trajectory?”

“No need. Inside a max 10‑mile range, the artillery, target and shell all share the same initial eastward vector. Windage and temperature inversions are more of a problem than Coriolis forces. That’s where judgement, feedback and reload speed come in.”

“Now stand that up against a cruise missile.”

“Very different situation. With cannons, all the propulsion happens at the start. That’s why they call it ballistic. Cruise missiles have an extended boost phase, maybe more than one, so they can do in‑flight steering. On the other hand, range is hundreds of miles or more so you do need to figure in relative easting.”

“And the easting correction takes power, right?”

“Of course.”

“From the missile’s point of view, that power goes to counteract the Coriolis force pushing it off‑course. You don’t see it from the ground but the missile does. Clearer now?”

“Give me a minute.” <sketches on his notepad> “Okay, counteracting attempt to deflect course — got it. Hmm, a pendulum’s even simpler, because it’s not trying to keep in sync with the Earth’s rotation. No forces in play crosswise to the swing plane so it can maintain orientation relative to the Universe. To museum visitors it looks like something’s twisting, but it’s us doing the moving. The air masses, though … forces are in play with that one.”

“It’s always important to keep track of who’s doing what to whom. That system has four distinct frames of reference: the Earth, a moving air mass, the air mass it collides with, and the Universe.”

“The Universe?”

“Sets the stage for Newton’s First Law, about conservation of linear momentum. Say there’s an air mass hovering over Dallas, latitude 30° north. Relative to the Earth it’s stationary, but relative to the Sun and the rest of the Universe it has an eastward vector clocking 1450 km/hour. Now suppose that mass moves north relative to the Earth.”

“But there’s already an airmass taking up space there, say in Manitoba. There’ll be a collision, northbound momentum against Manitoban inertia.”

“Here’s where Coriolis gets into the game. Manitoba may have zero motion relative to Earth, but Manitoba and its air mass are also moving eastward relative to the Universe. Manitoba’s speed is slower than Dallas’ but it’s not zero. Manitoba’s momentum deflects the Dallas mass into an even more easterly vector.”

“You’re saying that Coriolis plays jiu‑jitsu with the atmosphere.”

“I wouldn’t have come up with that interpretation, but it’s reasonable.”

“What about the weird orbits?”

“Not really orbits, more like equilibrium bands. The concept comes from the theoretical notion that every latitude along a meridian has a natural equilibrium speed where air pressure balances other forces. The bands would be parallel circles around the globe except for geography and transient disturbances. Dallas’ 1450‑km/h number was an example. If you exceed your local natural speed, centrifugal force moves you towards the Equator; if you’re a slowpoke, you’re shoved towards the nearest pole. Real weather’s more complicated.”

“Everything’s always more complicated.”

~ Rich Olcott