Goes With The Flow (Until It Doesn't)

#conversationswithgrant #turbulence

"Alright, Nix, it's time for the million dollar question!" Grant announced.

"42?" Nix offered dryly.

Grant blinked, thrown off. "Eh?"

"You know, life, the universe and everything?" She shrugged lightly, eyes laughing.

Grant rolled his eyes. "Funny. No, I mean, literally a million dollars. Millennium Prize Problems, set up back in 2000, offers a nice $1M to whoever first solves the seven big problems in maths. The one we," He said, gesturing between himself and Nix, "are talking about today is turbulence. Because, really, to hell with ULEZ." He muttered darkly under his breath as he lifted his mug to take a sip.

"Oh? The, uh, rough patches in an airplane flight are, what, 'unsolved'?" Nix asked, bemused.

Grant choked, spitting the mouthful of tea back into the mug, sputtering. "Rough patches?!" He cackled hoarsely. "Ha! No, see, that's just the first thing you think of when I say turbulence, yeah, but it applies to a hell of a lot more. Like weather, or, ya know, how to build a skyscraper without the wind tearing it apart."

Nix nodded slowly. "Um. So what is turbulence, exactly?"

"Yeah, that's part of the whole problem. There still ain't one definition for it, well, in mathematical terms, anyway. The general idea of turbulence is the complex chaotic motion of a fluid."

“Fluid?” Nix queried.

“Eh, not liquid, more anything that flows.” Grant explained.

"Water, then, and air, and, what, sand?”

“Technically, yes.” Grant nodded.

“Sooo... what, we can't predict it?" Nix frowned at him.

Grant snapped his fingers and pointed at her, grinning madly. "Exactly! Rumour has it Heisenberg said that he’d ask God two questions: Why quantum mechanics? And why turbulence? And he thought God would be able to answer the first.”

Nix snickered. “Okay, then, I get the point that this is a pretty big problem.”

“There is no way to predict how fast a normal, smooth flow - called laminar - turns into the spinning whirlpools of chaos. Ya know, outside of very exact conditions that have been tested and recorded. Frankly, until Spalding we had no idea of how matter and mass was going around in, say, an explosion. All we can do is assume based on past experiences, predicting or understanding the minutiae of how it’s happening has been an ongoing problem for, eh, centuries, really. Plenty of attempts, mind you, just no 'one size fits all' solution. " Grant raved.

"What would this ‘one solution fits all’ equation/formula look like then?" Nix asked, head titling.

"Well, to put it in perspective, fluid dynamics doesn't even come close." Grant waved a hand.

"..." Nix watched him with a silent, pitying smile.

“Right, well, to ‘solve’ the problem of turbulence, you would need an equation that could accurately predict how the fluid would move under any set of conditions. We should technically be able to do this, it’s just Newtons laws again, but, well. As soon as you interrupt the nice, even flow from a Navier-Stokes equation, you get chaotic motion, turbulence. There’s…. A wide range of ways turbulence flows act in time and space. Ever seen smoke coming off of a candle? Or even waves breaking on a beach.”

“Yeaah… I kind of see what you mean with the waves, but, Navier-Stokes?”

“Oh, that’s how to apply Newton’s first law of motion to simple fluids. Um, water, air, and so on. Doesn’t like paint or blood. Or any disturbances to the flow. Anyway! Point is, this should be solvable! We know what’s going on! Seriously, there’s proper structure to the chaos, ya know, like the giant spot of Jupiter’s storm, or our own hurricanes. We’re just… missing something.” Grant deflated with a great sigh, pouting down at the table.

Nix grinned at him. “Alright, cheer up. So there’s method in the madness. Then the problem isn’t so much the… ‘fluid’, but all the thousands of little factors around it? If I understand that right?”

“Oh, right!” He perked up. “I forgot the non-linear bit.”

Nix blinked slowly.

“Look, linear or non-linear is about how the equation works, ya know? Basic Quantum Mechanics is linear, like Schrodinger’s equation. You add up simple solutions to get to the complicated solution. Now, the big BIG problem for turbulence is that fluid dynamics is not linear. It just ain’t possible to find a solution by adding up smaller bits of Navier-Stokes. And some of the other equations don’t add friction, so only apply to things like honey, and… I lost you. Where’d I lose you?”

“Round about when you started ranting about fluid dynamics.” Nix said dryly.

Grant drooped. "... We didn'a go over fluid dynamics, did we?"

"No. No, you didn't. We can get back to that later - or a very brief overview of it, because, let's be honest, it sounds horrendously complicated. More importantly, how the hell are we building horrifically tall skyscrapers and flying planes if we don't understand turbulence?"

“CFD!” Grant announced cheerfully. “Computational fluid dynamics. We can’t solve it mathematically, yet, but we needed some kind of handle on it. Which is where modelling comes in.”

"Modelling.” Nix echoed blankly.

“Modelling.” Grant stated emphatically. “Modelling of everything. Airplanes, pipelines, weather systems. Computer’s are a giant help and a driving force, but even a modern state-of-the-art super computer would crash ‘n burn without help.”

“Slowing it down just a tad,” Nix commented wryly, “I assume you mean the either 2D or 3D grids?”

Grant nodded. “Yeah, that’s the stuff. Each point of the grid is a tiny bit of water fluid or scenario you’re trying out. But, see, you could model a plane wing, right, and try to estimate how turbulence will behave over the top of it, but that still leaves thousands of grid points that’re just.. empty. No turbulence, nothing going on.”

“Uhuh…” Nix motioned him to go on.

“But if a computer is still putting equal amounts of work into every single grid point, that’s a lot of time getting wasted.”

“Ahh.” Nix uttered in sudden understanding. “I get it.”

“So, the clever bit they came up with is to kind of stretch the grid. But bigger, or more prioritised, points where we know the turbulence is going to be, and less important points further away. ‘Adaptive Mesh Refinement’. Which isn’t to say it’s not still computer-intense. It just won’t melt the poor machine. You follow?”

“Yeah. Makes sense. But, hm, doesn’t all this modelling basically mean… we do know how turbulence works?” Nix suggested hesitantly.

“Eh, no.” Grant scratched his jaw. “See, the models rely on all the past data we got. We know how and where the chaos is gonna happen, and a fair bit why. The big problem is the when. The computer’s not there to solve it, it doesn’t work like that. What it can do, is statistics. What’s the probability of this flow turning turbulent at this point and this speed? Probabilities. It’s just running through all the possible permutations of events/behaviours so we can have some forward planning, see?”

Nix made a face. “So, say, a bumblebee should still technically not be able to fly according to physics?” She said, amused.

Grant barked a laugh. “Yeah, pretty much. Obviously they can fly, but the how is still up in the air.” He paused, then snickered to himself. “Heh. Up in the air, Nix!”

She rolled her eyes. “Has anyone got any closer to solving turbulence, then?”

“Good question. Hm. So far as I know, no. Something came up back in 2020, a new approach… gimme a minute.” He trailed off, brow furrowed as he swiped at his phone.

“Right, okay, these three managed to prove Batchelor’s law by using randomization and mixing paint…” He muttered.

“… I really hope you don’t expect me to understand any of that.” Nix said flatly.

“What?” Grant startled, glancing up. “No, I’m just interested in the proofs… just gimme a sec..” He trailed off, eyes darting over the screen.

“Huh.” He said finally. “So that’s why…”

Nix reached over to poke his wrist. “Care to share?”

“Right, sorry. So, these three figured out a proof of Batchelor’s law. Which is kinda the strongest handle on turbulence we’ve had… ever.”

“Which means… what, exactly? Normal English, please.” Nix pleaded.

Grant chuckles. “It shows that turbulence actually conforms to a pretty simple law. Batchelor predicted that patterns in moving liquids followed an exact order, almost universally. Batchelor’s law is about randomness, and turbulence is so chaotic that it’s practically random. Sets up a new way to model turbulence, ya see?”

“But it is still unsolved.” She smirked at Grant. “If there’s a million dollars waiting around, do you fancy taking a shot at it?” She teased, lifting her mug up.

“Hell no.” Grant leaned back, waving his hands in the air. “Absolutely not. There’s other bits I can get into – I mean, some people think the whole turbulence problem might actually go back to quantum – but it ain’t for me. There’s been mathematicians who dedicate their whole lives to trying to fix this. Let them have at it.” He declared.

“What brought this up, anyway?” Nix asked, setting her mug down.

“What? Oh, my boss was fuming about ULEZ yesterday, and since the new zone is gonna hit me, too... ” He shrugged.

“The low emission zone?” Nix stared at him, baffled. “What does that have to do with turbulence?”

“… weather patterns? Distribution of pollution? Come on, Nix, I know you were listening, turn you’re brain on.” Grant said exasperated.

She leaned back, tapping the mug absently as she thought. “The weather forecast is basically modelling of turbulence, right?” She glanced swiftly at Grant, continuing at his nod. “But if we can’t reliably predict it, then… well, I suppose we have no idea of where air-borne pollution is going to end up.” She frowned. “Which is horrifying on more than one level.”

Grant grimaced. “Yeah. I mean, we can test air quality, so we know, like, which London borough is really really bad and which isn’t, but that’s after the fact. We can assume that the air currents will probably follow the same pattern and keep dumping more pollution in the already bad areas. But we cannot mathematically predict it.”

“Kind of brings it home, doesn’t it.” Nix mused. “It’s one thing to talk about bumblebees or airplanes, but air pollution is something everyone is affected by.”

“’S why Sam, my manager, ya know, was ranting about the new ultra-low emission zones.” Grant said sagely. “Why are they bothering to expand the zones when we don’t know how the pollution’s going to go? Course, that’s mostly cause his car’s gonna get hit by the new tariffs, but, he’s gotta point.”

"That's fair, I suppose,, but I'm pretty sure they have some idea of how pollution is effecting those zones." Nix commented wryly. "Still, it's nice to know that's there's more mysteries to the universe than the fact we might all be holographic."

Grant rolled his eyes at her. "You're just not going to let that go, are ya?"

Nix shrugged, smirking lightly.

"Course, I haven't mentioned that up above twenty-thousand feet, there is no turbulence at all, so…” Grant added on in-sotto.

“Wait. What?!"

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