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Estimates vary as to what the total kinetic energy of Earth's Wind is, and how much could be sustainably extracted to power civilization. Complex estimation is required, especially as to when and where kinetic energy of Wind is extracted. Wind Energy Extraction is also a geoengineering factor, with the possibility of controlling climate, for better or worse, and even reversing harmful climate change.

This Topic is not confined to relatively limited conventional Wind Energy at the surface, but includes the vast potential for Airborne Wind Energy (AWE) Extraction up to the Tropopause (~10km high). The scope of discussion is both geophysical and technological, reasoning about Wind top-down, from largest to smallest scale.

Here is the classic starting reference in AWE, at Global Scale-

Archer, C. L., and K. Caldeira, 2009: Global assessment of high-altitude wind power. Energies,2(2), 307–319, doi: 10.3390/en20200307

## Comments

Starting numbers for civilizational-scale power load- 10TW of wind would be a huge game-changer. 20TW would pretty power the world at current demand. 30TW would be a sort of New Golden Age of Abundance, where we might decide to power utopian projects, like rewild Earth, spread out across the Solar System, whatever...

`Starting numbers for civilizational-scale power load- 10TW of wind would be a huge game-changer. 20TW would pretty power the world at current demand. 30TW would be a sort of New Golden Age of Abundance, where we might decide to power utopian projects, like rewild Earth, spread out across the Solar System, whatever...`

At the upper end of Planetary Wind Power estimates, there are thousands of TW just over our heads, begging to be tapped. However, there are skeptics as well, and academic debate raged a decade ago, that still simmers; but consensus is that there are a few nice TW at least, and ongoing reanalysis suggests the hyperabundance view is correct, but the environmental impacts must be carefully understood.

Here is the classic skeptic side-

https://www.mpg.de/4689869/high_wind_low_energy

Can't wait for PaulP to weigh in...

`At the upper end of Planetary Wind Power estimates, there are thousands of TW just over our heads, begging to be tapped. However, there are skeptics as well, and academic debate raged a decade ago, that still simmers; but consensus is that there are a few nice TW at least, and ongoing reanalysis suggests the hyperabundance view is correct, but the environmental impacts must be carefully understood. Here is the classic skeptic side- https://www.mpg.de/4689869/high_wind_low_energy Can't wait for PaulP to weigh in...`

Misc. Planetary Scale Wind Harvesting Impacts-

Large Wind Plants, conventional and AWES, create a rain shadow downwind while enhancing rain upwind, much as hills and mountains do.

Steering the major Westerly Jet Streams, while also harvesting kinetic energy, might reverse accelerated Polar Warming.

Cyclonic Weather systems, including hurricanes, could be steered by AWES formations. Under Chaotic Sensitivity to Initial Conditions, large weather systems could be controlled by small early inputs (Chaos Control).

Moisture at high altitude that would otherwise overfly continents could be harvested to water continental arid zones. AWE moisture by-catch on the Lee-side of continents has less negative impact.

Condensate Trails created by AWES would be cooling by day, but warming by night. AWES can adjust altitude to modulate this planetary albedo factor.

Again, AWES tech is both an energy source and geoengineering means. Energy provides the economic basis for geoengineered climate-change mitigation that might otherwise go unfunded.

`Misc. Planetary Scale Wind Harvesting Impacts- - Large Wind Plants, conventional and AWES, create a rain shadow downwind while enhancing rain upwind, much as hills and mountains do. - Steering the major Westerly Jet Streams, while also harvesting kinetic energy, might reverse accelerated Polar Warming. - Cyclonic Weather systems, including hurricanes, could be steered by AWES formations. Under Chaotic Sensitivity to Initial Conditions, large weather systems could be controlled by small early inputs (Chaos Control). - Moisture at high altitude that would otherwise overfly continents could be harvested to water continental arid zones. AWE moisture by-catch on the Lee-side of continents has less negative impact. - Condensate Trails created by AWES would be cooling by day, but warming by night. AWES can adjust altitude to modulate this planetary albedo factor. - Again, AWES tech is both an energy source and geoengineering means. Energy provides the economic basis for geoengineered climate-change mitigation that might otherwise go unfunded.`

The stochastic nature of wind has never been fully characterized to an analytical level. I took all the data from the wind farms near the Columbia River in Oregon and charted them to match the expected maximum entropy model.

This is taken from Mathematical Geoenergy and is essentially a starting point to gauge how well constant power can be extracted from an intermittent source

`The stochastic nature of wind has never been fully characterized to an analytical level. I took all the data from the wind farms near the Columbia River in Oregon and charted them to match the expected maximum entropy model. ![](https://imagizer.imageshack.com/img924/6219/sfwpsA.png) ![](https://imagizer.imageshack.com/img923/2271/0bPquL.png) This is taken from Mathematical Geoenergy and is essentially a starting point to gauge how well constant power can be extracted from an intermittent source`

As the source above suggests, given global wind speed average and frontal area of wind, then total Wind Power is easy to calculate.

At what lower scale is Wind no longer Wind? Is Brownian Motion Wind? Brownian molecular-scale velocities are quite high, but the path lengths are short. Lets suppose meter-scale (human-scale) turbulence to be our effective lower bound. We are considering only Planetary Wind inherently ordered to match our probable harvesting technology (from AWE at extreme-scale down to small personal devices), as Prigoginian Dissipative Systems. How much of that is there?

Here's a calculation, if someone would do the honor- Calculate the volume of the atmospheric Wind Field to 10km high, and the Wind Power in it as the cube of 10m/sec times a frontal area defined inside the Wind Field volume, like longitudinal vertical planes every 1m to 1000km, for a range of regeneration times. My head is starting to hurt. Calculating instantaneous Energy might be easiest, simply calculate Planetary Wind-Mass Kinetic-Energy at 10m/sec.

The issue of Wind Entropy is fascinating, but ontologically vague. If Information equals Thermodynamic Energy, under Shannon Equivalence, and Entropy encodes more Information than Order, then we are talking about Energy of Entropy. A Entropic System can settle into an Time-Symmetric Inverse Boltzmann Distribution, recovering Order. These are fine mind-boggling chestnuts, but the simple question here need not invoke Entropy too broadly.

What makes this Green Mathematics is applied (engineered) sustainability. Pure science ranges from opaque to transparent, but is not Green as such. We seek a mathematical peek at how the Holocene Extinction bottoms-out (cockroaches?), or if a New Golden Age is nigh. Bets, anyone?

`As the source above suggests, given global wind speed average and frontal area of wind, then total Wind Power is easy to calculate. At what lower scale is Wind no longer Wind? Is Brownian Motion Wind? Brownian molecular-scale velocities are quite high, but the path lengths are short. Lets suppose meter-scale (human-scale) turbulence to be our effective lower bound. We are considering only Planetary Wind inherently ordered to match our probable harvesting technology (from AWE at extreme-scale down to small personal devices), as Prigoginian Dissipative Systems. How much of that is there? Here's a calculation, if someone would do the honor- Calculate the volume of the atmospheric Wind Field to 10km high, and the Wind Power in it as the cube of 10m/sec times a frontal area defined inside the Wind Field volume, like longitudinal vertical planes every 1m to 1000km, for a range of regeneration times. My head is starting to hurt. Calculating instantaneous Energy might be easiest, simply calculate Planetary Wind-Mass Kinetic-Energy at 10m/sec. The issue of Wind Entropy is fascinating, but ontologically vague. If Information equals Thermodynamic Energy, under Shannon Equivalence, and Entropy encodes more Information than Order, then we are talking about Energy of Entropy. A Entropic System can settle into an Time-Symmetric Inverse Boltzmann Distribution, recovering Order. These are fine mind-boggling chestnuts, but the simple question here need not invoke Entropy too broadly. What makes this Green Mathematics is applied (engineered) sustainability. Pure science ranges from opaque to transparent, but is not Green as such. We seek a mathematical peek at how the Holocene Extinction bottoms-out (cockroaches?), or if a New Golden Age is nigh. Bets, anyone?`

We recently created an ontological classification system for environmental modeling. This is a white paper, with wind on p.50

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.465.2731&rep=rep1&type=pdf

Our massive report is here: https://www.researchgate.net/publication/283579370_C2M2L_Final_Report

It's all interesting, but FYI if I work on an ontology project again, I'm not going to start from scratch.

`> "The issue of Wind Entropy is fascinating, but ontologically vague." We recently created an ontological classification system for environmental modeling. This is a white paper, with wind on p.50 http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.465.2731&rep=rep1&type=pdf Our massive report is here: https://www.researchgate.net/publication/283579370_C2M2L_Final_Report It's all interesting, but FYI if I work on an ontology project again, I'm not going to start from scratch.`

Wind Ontology in recent years has been approached from two fresh angles, Analogue QM, and Linguistics. Its still a very open subject, like thermodynamic QM itself.

Paul, It would be great if you (or Prof. Baez) could peek at Planck's Constant, which is wrongly dimensionalized by being tied to atomic-scale quantum-of-action. If quantum-of-action is allowed to be non-dimensional, QM is recoverable at all scales, including ENSO-QBO, all the way to Cosmic scale. A wave is a wave is a wave (function). That's ontology.

As Modern Physics has become all Hydrodynamic Field-Theory and (quasi) particles merely effective approximations, the cracks in Copenhagen QM have been patched over again and again. Now there are many Classical extensions and the "Classical Limit" has dissipated. This two-way identity opens up ready use of elegant "Analogue" QM math for macroscopic problems like Wind Fields.

Here is an atmospheric-scale QM Analogue of Tunneling-

https://en.wikipedia.org/wiki/List_of_Atlantic–Pacific_crossover_hurricanes

Walking Drop Dynamics are recognized macroscopic Quantum Analogues-

http://math.mit.edu/~bush/?page_id=484

`Wind Ontology in recent years has been approached from two fresh angles, Analogue QM, and Linguistics. Its still a very open subject, like thermodynamic QM itself. Paul, It would be great if you (or Prof. Baez) could peek at Planck's Constant, which is wrongly dimensionalized by being tied to atomic-scale quantum-of-action. If quantum-of-action is allowed to be non-dimensional, QM is recoverable at all scales, including ENSO-QBO, all the way to Cosmic scale. A wave is a wave is a wave (function). That's ontology. As Modern Physics has become all Hydrodynamic Field-Theory and (quasi) particles merely effective approximations, the cracks in Copenhagen QM have been patched over again and again. Now there are many Classical extensions and the "Classical Limit" has dissipated. This two-way identity opens up ready use of elegant "Analogue" QM math for macroscopic problems like Wind Fields. Here is an atmospheric-scale QM Analogue of Tunneling- https://en.wikipedia.org/wiki/List_of_Atlantic%E2%80%93Pacific_crossover_hurricanes Walking Drop Dynamics are recognized macroscopic Quantum Analogues- http://math.mit.edu/~bush/?page_id=484`

But there are waves and there are waves. Apart from their difference in scale, quantum waves and ENSO waves are of fundamentally different types - quantum wave-functions consisting of complex-valued probability amplitudes, versus classical, determinate ENSO waves. How is there more than an analogy between QM and ENSO waves?

`But there are waves and there are waves. Apart from their difference in scale, quantum waves and ENSO waves are of fundamentally different types - quantum wave-functions consisting of complex-valued probability amplitudes, versus classical, determinate ENSO waves. How is there more than an analogy between QM and ENSO waves?`

There's obviously no wall in the atmosphere above the Panama Canal that needs to be tunneled through.

`> Here is an atmospheric-scale QM Analogue of Tunneling- > https://en.wikipedia.org/wiki/List_of_Atlantic–Pacific_crossover_hurricanes There's obviously no wall in the atmosphere above the Panama Canal that needs to be tunneled through.`

There's this paper "Topological origin of equatorial waves"

https://science.sciencemag.org/content/358/6366/1075

https://physicsworld.com/a/do-topological-waves-occur-in-the-oceans/

Related, just published in Physical Review Letters

https://arxiv.org/abs/2002.10607 "Non-Newtonian Topological Mechanical Metamaterials Using Feedback Control"

`> How is there more than an analogy between QM and ENSO waves? There's this paper "Topological origin of equatorial waves" https://science.sciencemag.org/content/358/6366/1075 >That unity reaches beyond materials science, according to Pierre Delplace and Antoine Venaille of the École Normal Supérieure de Lyon in France, working with Brad Marston of Brown University in Rhode Island. They say that two types of long-recognized wavelike flow in the atmosphere and oceans, called Kelvin and Yanai waves, also have a topological origin, which is mathematically analogous to the surface-conducting states of topological insulators. > This equivalence shows up in the mathematics of the problem, the researchers say. In condensed-matter physics, electron states are described by the wavelike Schrödinger equation. Orbits are created by the fact that an applied magnetic field breaks time-reversal symmetry: the solutions to the Schrödinger equation change when time t is replaced by –t. The surface electron flows then arise from a breakdown of translational symmetry that occurs at the surface. >Coriolis force > All these features, say Delplace and colleagues, are mimicked in the wave equations for flows in the atmosphere and oceans, where the Coriolis force – an effective force due to the Earth’s rotation that displaces flows to the right and left in the northern and southern hemispheres, respectively – plays the role of a magnetic field. These equations produce waves trapped close to the equator, always compelled to travel eastward, which are known as equatorial Kelvin and mixed Rossby-gravity (Yanai) waves. > Other such waves also exist, such as the long-period pure Rossby waves, but these are not “topologically protected” in the same way. Kelvin and Rossby waves can act as precursors to the quasi-periodic ocean-atmosphere oscillation called the El Niño Southern Oscillation, which produces significant climatic effects such as drought or high rainfall in some equatorial regions. https://physicsworld.com/a/do-topological-waves-occur-in-the-oceans/ --- Related, just published in Physical Review Letters https://arxiv.org/abs/2002.10607 "Non-Newtonian Topological Mechanical Metamaterials Using Feedback Control" > "we focus on the quantum Haldane model, which is a two-band system with directional complex coupling terms, **violating Newton's third law** "`

DaveT asked: "How is there more than an analogy between QM and ENSO waves?"

Between Planck's original Black Body Radiation QM case, there is only coarse analogy with ENSO. With Bush's walking-drop example of Analogue QM (broadly part of QM2.0) there is a macroscopic identity emergent.

A 100m wavelength radio wave is a fully QM "particle" (photon), but QM is still commonly taught as "microscopic only". By social convention, to avoid confusion with "quantum quackery", physicists carefully refer to "quantum analogues".

Scientific Analogy is not trivial, but a core principal. By Analogy, ENSO truly is a QM quasi-particle creation-annihilation process, for those who find the comparison insightful. QM principles are applied and accepted in many macroscopic fields, like crowd and traffic analysis, geology, cosmology, etc. Meteorology is just one more branch of science suited to modern wave function math.

PaulP wrote: "There's obviously no wall in the atmosphere above the Panama Canal that needs to be tunneled through."

In this Tunneling Analogy the analogous barrier is the land-bridge, as Hurricanes are created and sustained over warm water. In Physics, there is "no wall", solid as such, just >0 probabilities that quasi-particles can pass thru on-average effective boundaries.

=========

Its often claimed, "everything is QM", but also often still disputed; as if Newton's Physics was more "real". In fact, Classical Physics is easily extended to recover QM, and vica-versa, so that a wave truly is a wave is a wave.

`DaveT asked: "How is there more than an analogy between QM and ENSO waves?" Between Planck's original Black Body Radiation QM case, there is only coarse analogy with ENSO. With Bush's walking-drop example of Analogue QM (broadly part of QM2.0) there is a macroscopic identity emergent. A 100m wavelength radio wave is a fully QM "particle" (photon), but QM is still commonly taught as "microscopic only". By social convention, to avoid confusion with "quantum quackery", physicists carefully refer to "quantum analogues". Scientific Analogy is not trivial, but a core principal. By Analogy, ENSO truly is a QM quasi-particle creation-annihilation process, for those who find the comparison insightful. QM principles are applied and accepted in many macroscopic fields, like crowd and traffic analysis, geology, cosmology, etc. Meteorology is just one more branch of science suited to modern wave function math. PaulP wrote: "There's obviously no wall in the atmosphere above the Panama Canal that needs to be tunneled through." In this Tunneling Analogy the analogous barrier is the land-bridge, as Hurricanes are created and sustained over warm water. In Physics, there is "no wall", solid as such, just >0 probabilities that quasi-particles can pass thru on-average effective boundaries. ========= Its often claimed, "everything is QM", but also often still disputed; as if Newton's Physics was more "real". In fact, Classical Physics is easily extended to recover QM, and vica-versa, so that a wave truly is a wave is a wave.`

To simplify the problem of characterizing Global Atmospheric Dynamics mathematically, Planck's Natural Unit criteria is helpful. Its simple Integer Math, of counting Whole Numbers of things like Days, Years, Rossby Waves, Hurricanes, and so forth. Yes, there are borderline cases, like not-quite hurricanes, and Rossby Packets, but many detail uncertainties tend to cancel out and/or not critically determine correctness of a broad model. With prudent caution, we are free to model a wave packet as a particle, to enable computation, and employ other such abstractions, like effective Field Theories. Analogues allow us to use mathematical tools from wherever they are found. This heuristic practice in engineering is "case-based" reasoning from "similarity cases".

Taking the geophysical abstraction to an extreme, we can consider the Atmosphere as a single quasi-particle, and the Earth as an interacting quasi-particle. We can quantify these masses and their bulk relative motion to estimate their shared kinetic energy. At the other end of the ladder-of-abstraction we can locate data-points, like the readings of meteorological stations. If one starts from the huge raw data-sets, seeking to reach the top-most abstraction levels, its easy to get lost, and not see the "big picture". Science works from both ends, top-down and bottom-up.

Whether we can resolve the Climate Change Crisis with Wind Energy starts as a top-down question. The answer may be bottom-up, like whether humans can behaviorally reduce their carbon footprints to 5% of present levels (as estimated by Union of Concerned Scientists members in '90s). The risk is that the answer is "No", that folks either will not change so radically, or an authoritarian Green Fascism might prevail. Top-down GeoEngineering is another possibility, with its own risks of abuse. Perhaps its too Utopian to hope for a "magic bullet" intervention, but maybe there is such possibility.

We may just muddle through the Holocene Extinction like we are the Covid Pandemic, as an all-of-the-above scenario. In that case, planetary-scale wind energy application could still be critical. We have to learn all we can about the atmosphere, but that is not enough; we actually have to try to apply that knowledge, as the essence of the Green Math quest. Entertaining debate about Atmospheric QM Analogues and Ancient Wind Folklore is part of Green Math due-diligence, not a-priori sterile. Green Math aims beyond "shut-up and calculate".

`To simplify the problem of characterizing Global Atmospheric Dynamics mathematically, Planck's Natural Unit criteria is helpful. Its simple Integer Math, of counting Whole Numbers of things like Days, Years, Rossby Waves, Hurricanes, and so forth. Yes, there are borderline cases, like not-quite hurricanes, and Rossby Packets, but many detail uncertainties tend to cancel out and/or not critically determine correctness of a broad model. With prudent caution, we are free to model a wave packet as a particle, to enable computation, and employ other such abstractions, like effective Field Theories. Analogues allow us to use mathematical tools from wherever they are found. This heuristic practice in engineering is "case-based" reasoning from "similarity cases". Taking the geophysical abstraction to an extreme, we can consider the Atmosphere as a single quasi-particle, and the Earth as an interacting quasi-particle. We can quantify these masses and their bulk relative motion to estimate their shared kinetic energy. At the other end of the ladder-of-abstraction we can locate data-points, like the readings of meteorological stations. If one starts from the huge raw data-sets, seeking to reach the top-most abstraction levels, its easy to get lost, and not see the "big picture". Science works from both ends, top-down and bottom-up. Whether we can resolve the Climate Change Crisis with Wind Energy starts as a top-down question. The answer may be bottom-up, like whether humans can behaviorally reduce their carbon footprints to 5% of present levels (as estimated by Union of Concerned Scientists members in '90s). The risk is that the answer is "No", that folks either will not change so radically, or an authoritarian Green Fascism might prevail. Top-down GeoEngineering is another possibility, with its own risks of abuse. Perhaps its too Utopian to hope for a "magic bullet" intervention, but maybe there is such possibility. We may just muddle through the Holocene Extinction like we are the Covid Pandemic, as an all-of-the-above scenario. In that case, planetary-scale wind energy application could still be critical. We have to learn all we can about the atmosphere, but that is not enough; we actually have to try to apply that knowledge, as the essence of the Green Math quest. Entertaining debate about Atmospheric QM Analogues and Ancient Wind Folklore is part of Green Math due-diligence, not a-priori sterile. Green Math aims beyond "shut-up and calculate".`

A few notes regarding Airborne Wind Energy from bottom-up direction. Some repetition of key points in other posts and topics will occur.

A kite anchored to Earth expresses Newton's First Law, of an opposite and equal reaction between Atmospheric Motion and Planetary Motion. Newton himself was an avid kiter, and the history of kite physics is a rich topic. Etzler foresaw the world could be kite powered almost 200 years ago.

In our time the Power Kite emerged as a steerable decelerator technology in NASA Gemini and Apollo Programs, and aerospace engineers soon applied it to new sports like paragliding and kitesurfing. These in fact have already displaced some portion of fueled sports (ski-lifts and water-ski boats).

Power Kites scale beyond any other aviation class, and have the highest power-to-mass, without fuel. The practical single soft-kite scaling limit is about 1000m2. Such a unit-kite can produce about 10MW of wind power. Topologically ordered unit-kite networks will reach GW-rated scale.

Aggregated Kite Power can directly drive by cableway the largest GW-rated utility generators. Existing Power Plants can in principle be converted to Kite Hybrids, with no fuel needed when wind is blowing.

There is a lot of interesting mathematical engineering science to a kite. A power kite is a thermodynamic heat-engine, when considered as such. The compression side of a wing is a hotter gas volume than the low pressure cooler side. In a "steady state", one may consider a working wing as a frozen wave system (surfer POV). Kite Chaos Physics identification started with [van Veem, 1997].

The Mass Scaling Exponent of a single-skin kite is Quadratic, but high L/D kiteplanes resembling gliders have a Cubic Mass Scaling Exponent. Therefore, while a kiteplane may have a far higher L/D, it does not scale as well as a soft kite. Superior figures-of-merit for soft kites are higher-power-to-mass and lower-Levelized-Cost-of-Energy (LCOE).

The current hot frontier of kite tech is Network Topologies (if anyone wants to join the global scholar email circle). A kite network is a sort of topological Boojum. Kite Network Operations are studied for their topological stabilities, and dependencies like Topological Surgeries. Subscale prototypes are designed and flown. Exascale Multi-Physics Multi-Solver Sims are being architected by a US DOE (NREL) affiliated circle. The combined CFD and structural-dynamics super-computing challenge is obviously math-intensive. The atmospheric dynamics alone is a vast aspect.

AWE is an emergent Green Math Wonderland.

`A few notes regarding Airborne Wind Energy from bottom-up direction. Some repetition of key points in other posts and topics will occur. A kite anchored to Earth expresses Newton's First Law, of an opposite and equal reaction between Atmospheric Motion and Planetary Motion. Newton himself was an avid kiter, and the history of kite physics is a rich topic. Etzler foresaw the world could be kite powered almost 200 years ago. In our time the Power Kite emerged as a steerable decelerator technology in NASA Gemini and Apollo Programs, and aerospace engineers soon applied it to new sports like paragliding and kitesurfing. These in fact have already displaced some portion of fueled sports (ski-lifts and water-ski boats). Power Kites scale beyond any other aviation class, and have the highest power-to-mass, without fuel. The practical single soft-kite scaling limit is about 1000m2. Such a unit-kite can produce about 10MW of wind power. Topologically ordered unit-kite networks will reach GW-rated scale. Aggregated Kite Power can directly drive by cableway the largest GW-rated utility generators. Existing Power Plants can in principle be converted to Kite Hybrids, with no fuel needed when wind is blowing. There is a lot of interesting mathematical engineering science to a kite. A power kite is a thermodynamic heat-engine, when considered as such. The compression side of a wing is a hotter gas volume than the low pressure cooler side. In a "steady state", one may consider a working wing as a frozen wave system (surfer POV). Kite Chaos Physics identification started with [van Veem, 1997]. The Mass Scaling Exponent of a single-skin kite is Quadratic, but high L/D kiteplanes resembling gliders have a Cubic Mass Scaling Exponent. Therefore, while a kiteplane may have a far higher L/D, it does not scale as well as a soft kite. Superior figures-of-merit for soft kites are higher-power-to-mass and lower-Levelized-Cost-of-Energy (LCOE). The current hot frontier of kite tech is Network Topologies (if anyone wants to join the global scholar email circle). A kite network is a sort of topological Boojum. Kite Network Operations are studied for their topological stabilities, and dependencies like Topological Surgeries. Subscale prototypes are designed and flown. Exascale Multi-Physics Multi-Solver Sims are being architected by a US DOE (NREL) affiliated circle. The combined CFD and structural-dynamics super-computing challenge is obviously math-intensive. The atmospheric dynamics alone is a vast aspect. AWE is an emergent Green Math Wonderland.`

Since Planck, the concept of a standing wave and a quantum state have been tied together. The major climate indices such as ENSO, IOD, QBO, etc are characterized by their standing-wave wavenumber, which is the number of wavelengths that will fit around the circumference of the earth. All these wavenumbers are non-zero except for QBO which has a wavenumber of 0. ENSO and IOD are essentially dipole standing waves that stretch across the Pacific and Indian ocean respectively. The QBO has a wavenumber of 0 because it encircles the earth uniformly at any one time and shows a collective motion that is either all easterly or all westerly. Outside of these indices, the collective motion breaks up into travelling waves such as the MJO and meandering waves that show less of a pattern.

This video shows the transition into standing waves of varying wavenumbers based on a stimulating frequency. You can see that one frequency almost creates a perfect wavenumber 0 formation.

https://youtu.be/AKIEbhChHbQ

Fluids are more a collective motion rather than quasiparticles, even though quasiparticles as described elsewhere

"are not elementary particles, but are instead collective excitations of many electrons in solid devices"https://www.nature.com/articles/d41586-020-01988-0

`> "we can consider the Atmosphere as a single quasi-particle, and the Earth as an interacting quasi-particle." Since Planck, the concept of a standing wave and a quantum state have been tied together. The major climate indices such as ENSO, IOD, QBO, etc are characterized by their standing-wave wavenumber, which is the number of wavelengths that will fit around the circumference of the earth. All these wavenumbers are non-zero except for QBO which has a wavenumber of 0. ENSO and IOD are essentially dipole standing waves that stretch across the Pacific and Indian ocean respectively. The QBO has a wavenumber of 0 because it encircles the earth uniformly at any one time and shows a collective motion that is either all easterly or all westerly. Outside of these indices, the collective motion breaks up into travelling waves such as the MJO and meandering waves that show less of a pattern. This video shows the transition into standing waves of varying wavenumbers based on a stimulating frequency. You can see that one frequency almost creates a perfect wavenumber 0 formation. https://youtu.be/AKIEbhChHbQ Fluids are more a collective motion rather than quasiparticles, even though quasiparticles as described elsewhere *"are not elementary particles, but are instead collective excitations of many electrons in solid devices"* https://www.nature.com/articles/d41586-020-01988-0`

Paul,

You provided a good reference above showing the increasing utility of analog QM to atmospheric geophysics.

https://science.sciencemag.org/content/358/6366/1075

Quasi-particles are collective excitations of any sort in Condensed Matter to which a Particle analogy is applied. Newton's Point-Mass Assumption for planetary objects is a prototypical case.

Since [Tamm 1938], a defined class of collective excitation are Phonons; Quanta of acoustic and mechanical energy. Under modern Quantum Field Theory, all QM fields are fluid ("hydrodynamic"). Many kinds of waves, jets, and vortices are effectively classed as Phonons. Collective mechanical atmospheric motions are Phonons.

Generally in chaotic geophysics we consider seething Phonon Wave Packets, with sub-waves continuously created and annihilated within an "envelope". Thus ENSO is not one quasi-particle, but a sequence of Phonons created and annihilated in its bounds. We can identify the periodic appearance of the vast warm water mass in the Western Pacific as a primary Phonon involved.

Chladni Plate vibrations are a good starting model for specific atmospheric effects, like coherent geometric patterns seen at Saturn's Poles. Oobleck Physics take oscillatory driving into Chaos, the suggestion being that periodic forcing creates hard to predict outcomes in a complex space-

https://www.youtube.com/watch?v=X77P_2S5w7A

QBO wave-number is properly two non-zero angular wavenumbers (for easterly and westerly motions, respectively) relative to Earth Frame. Precession, terrain, Coriolis, sunspot cycles, ENSO, and other variables, cause calculable QBO wavenumber variation.

AO and AAO most closely approximate wavenumber zero, as zonal (symmetric) flows.

`Paul, You provided a good reference above showing the increasing utility of analog QM to atmospheric geophysics. https://science.sciencemag.org/content/358/6366/1075 Quasi-particles are collective excitations of any sort in Condensed Matter to which a Particle analogy is applied. Newton's Point-Mass Assumption for planetary objects is a prototypical case. Since [Tamm 1938], a defined class of collective excitation are Phonons; Quanta of acoustic and mechanical energy. Under modern Quantum Field Theory, all QM fields are fluid ("hydrodynamic"). Many kinds of waves, jets, and vortices are effectively classed as Phonons. Collective mechanical atmospheric motions are Phonons. Generally in chaotic geophysics we consider seething Phonon Wave Packets, with sub-waves continuously created and annihilated within an "envelope". Thus ENSO is not one quasi-particle, but a sequence of Phonons created and annihilated in its bounds. We can identify the periodic appearance of the vast warm water mass in the Western Pacific as a primary Phonon involved. Chladni Plate vibrations are a good starting model for specific atmospheric effects, like coherent geometric patterns seen at Saturn's Poles. Oobleck Physics take oscillatory driving into Chaos, the suggestion being that periodic forcing creates hard to predict outcomes in a complex space- https://www.youtube.com/watch?v=X77P_2S5w7A QBO wave-number is properly two non-zero angular wavenumbers (for easterly and westerly motions, respectively) relative to Earth Frame. Precession, terrain, Coriolis, sunspot cycles, ENSO, and other variables, cause calculable QBO wavenumber variation. AO and AAO most closely approximate wavenumber zero, as zonal (symmetric) flows.`

Atmospheric dynamics are often conspicuously Non-Newtonian, with complex quasi-oobleck Deborah Number rheology. Being substantially Phonon-based, Sonic Relativity is a significant aspect.

Consider Power Kites in this context. A wind tunnel or water flume can be regarded as a hydrodynamic phonon Quasiparticle Accelerator. Natural Wind is analogous to Cosmic Rays, as a ubiquitous research particle source. A toy kite is therefore a workable experimental physics apparatus anyone can get their hands on. As a rather unique phase of condensed matter, it can be called "Kitematter".

A kite interacts with wind flow in complex ways. Its a dissipative system, a thermodynamic "heat engine" with hot (bottom) and cold (top) fields. The complex far field is in fact determining, and the kite itself is just a small topological defect in it. The kite's wake is a complex train of phonon debris, of shed vortices analogous to the particle wreckage particle accelerators like CERN create. Each step of the way, the phonon creation and annihilation sequence can be Feynman Diagrammed. The key phonon sequence of "green" interest is along the kite line.

Kite line hums with internal phonons as it sheds its own wake. When line is tense, sonic c can range beyond 50km/sec. Fly a kite high, sight along the line, and pluck it to see a pulse traveling faster than c in air. When the line is nearly slack, see waves moving less than 30m/sec. This is how easily sonic relativity is observed. Kite Control and Stability derivatives are highly dependent on sonic relativity.

Fly a kite high, sight along the line to sample wind field turbulence, seen as various bumps coming and going. Typically, there will be a bulk hodographic twist to kite orientation, known as an Ekmann Spiral, a Coriolis Effect.

In smooth minimal wind, a kite can seem "pasted to the sky", its zero-point energy level. Close observation reveals minute "dancing" oscillations in six dimensions (3 angular and 3 translational). With more wind, the kite begins to dance more energetically, and these free-energy sweeping motions can be harvested. Yaw and roll combine in a characteristic Lissajous lemniscate path, circular symmetry broken by gravity, the well known figure-of-eight (Dutch Roll), the most energetic dimensions.

Passive cybernetic embodied "edge-of-chaos" Control Theory explaining inherent emergent kite motions is conceptually advanced. Energy and control sensing-actuation information superposes and flows both ways. A kite can sustain flight in calm by pumping input from the ground. Spoiler-alert: Kite Network Topological Stability is optimal. Active Digital Control is best relegated to exception-handling.

Obviously kites are first class mathematical physics teaching aids. Its no coincidence that so many historical mathematical physicists have had close association with kites, and the science continues to unfold [Physics World, Feb, 2020].

What concerns us here is not just analytical kite curiosities as such, but the practical fact that the vast kinetic energy of upper wind may transfer by power kite networks to the ground, as towing force on kite lines, and how this force can turn the largest generator shafts. This may be the most important applied ("green") Mathematical Physics Azimuth Forum has considered.

`Atmospheric dynamics are often conspicuously Non-Newtonian, with complex quasi-oobleck Deborah Number rheology. Being substantially Phonon-based, Sonic Relativity is a significant aspect. Consider Power Kites in this context. A wind tunnel or water flume can be regarded as a hydrodynamic phonon Quasiparticle Accelerator. Natural Wind is analogous to Cosmic Rays, as a ubiquitous research particle source. A toy kite is therefore a workable experimental physics apparatus anyone can get their hands on. As a rather unique phase of condensed matter, it can be called "Kitematter". A kite interacts with wind flow in complex ways. Its a dissipative system, a thermodynamic "heat engine" with hot (bottom) and cold (top) fields. The complex far field is in fact determining, and the kite itself is just a small topological defect in it. The kite's wake is a complex train of phonon debris, of shed vortices analogous to the particle wreckage particle accelerators like CERN create. Each step of the way, the phonon creation and annihilation sequence can be Feynman Diagrammed. The key phonon sequence of "green" interest is along the kite line. Kite line hums with internal phonons as it sheds its own wake. When line is tense, sonic c can range beyond 50km/sec. Fly a kite high, sight along the line, and pluck it to see a pulse traveling faster than c in air. When the line is nearly slack, see waves moving less than 30m/sec. This is how easily sonic relativity is observed. Kite Control and Stability derivatives are highly dependent on sonic relativity. Fly a kite high, sight along the line to sample wind field turbulence, seen as various bumps coming and going. Typically, there will be a bulk hodographic twist to kite orientation, known as an Ekmann Spiral, a Coriolis Effect. In smooth minimal wind, a kite can seem "pasted to the sky", its zero-point energy level. Close observation reveals minute "dancing" oscillations in six dimensions (3 angular and 3 translational). With more wind, the kite begins to dance more energetically, and these free-energy sweeping motions can be harvested. Yaw and roll combine in a characteristic Lissajous lemniscate path, circular symmetry broken by gravity, the well known figure-of-eight (Dutch Roll), the most energetic dimensions. Passive cybernetic embodied "edge-of-chaos" Control Theory explaining inherent emergent kite motions is conceptually advanced. Energy and control sensing-actuation information superposes and flows both ways. A kite can sustain flight in calm by pumping input from the ground. Spoiler-alert: Kite Network Topological Stability is optimal. Active Digital Control is best relegated to exception-handling. Obviously kites are first class mathematical physics teaching aids. Its no coincidence that so many historical mathematical physicists have had close association with kites, and the science continues to unfold [Physics World, Feb, 2020]. What concerns us here is not just analytical kite curiosities as such, but the practical fact that the vast kinetic energy of upper wind may transfer by power kite networks to the ground, as towing force on kite lines, and how this force can turn the largest generator shafts. This may be the most important applied ("green") Mathematical Physics Azimuth Forum has considered.`

Moving on to the Materials Science of "polymerizing the sky" with kite networks, to sustainably harvest abundant kinetic energy of upper wind. A barrel of oil made into power kites can offset hundreds of barrels that might otherwise be burned for energy.

The key power soft-kite utility parameter is strength or power-to-mass. One material stands out, Ultra High Molecular Weight Polyethylene (UHMWPE), about 10x stronger than steel by mass. Ethylene is the non-toxic waxy coating many plants use to conserve moisture. Under heat and high pressure, the ethylene hydrocarbon monomer is extended into parallel crystals >100k units long, the carbon atoms double-bonded, and crosslinked by hydrogen bonds. Short of graphene tubes, with triple bonded carbon, UHMWPE is the best engineering fiber since Nylon.

UHMWPE is a liquid-crystal (it will creep), but its Debye temperature is comparable to diamond, so its physics are native QM, not just analogous, over a large scale-invariant spectrum. The speed-of-sound in tensioned UHMWPE can reach 50km/sec, similar to diamond. Elsewhere I have cited an example of a ship hawser towing a ship by a ship with a power of work of 10MW, yet remains cool to the touch. This sort of wonderful phonon physics frozen-wave power super-conductance has hardly been seriously studied, "hidden in plain sight". A few related physics concepts exist, like second-sound and ballistic-conductance.

This is the original 1970 paper describing UHMWPE as novel fiber-

https://www.tandfonline.com/doi/abs/10.1080/00222347008229373

Oddly enough, Nylon remains a mainstay polymer in state-of-the-art rigging, complimenting the low-stretch property of UHMWPE. In applications with shock and surge loads, Nylon can absorb the excess energy and return it after the load peak, where UHMWPE might violently shatter or vaporize, or shock-damage other components.

A final introductory aspect of AWE is Kite Network Metamaterial Topology, a fast emerging AWE engineering paradigm in acoustic and mechanical metamaterials. Networked Kitematter fulfills all criteria cited that identify a MetaMaterial as such. A future kite network with km scale cells would easily comprise both the largest and least dense engineered material (neglecting density of entrained air).

Mechanical Metamaterials take many novel forms but share fundamental properties, like negative-index phonon refraction, topological-insulator/edge-modes, and auxetic response. Puzzle challenge: Identify specific kite-based metamaterial mechanisms (answers soon).

https://bertoldi.seas.harvard.edu/pages/harnessing-instability-design-mechanical-metamaterials

Recopying this paper link Paul provided, that I missed earlier. Another representative paper in a proliferating literature. Will post some missing domain survey links when I relocate them.

https://arxiv.org/pdf/2002.10607.pdf

`Moving on to the Materials Science of "polymerizing the sky" with kite networks, to sustainably harvest abundant kinetic energy of upper wind. A barrel of oil made into power kites can offset hundreds of barrels that might otherwise be burned for energy. The key power soft-kite utility parameter is strength or power-to-mass. One material stands out, Ultra High Molecular Weight Polyethylene (UHMWPE), about 10x stronger than steel by mass. Ethylene is the non-toxic waxy coating many plants use to conserve moisture. Under heat and high pressure, the ethylene hydrocarbon monomer is extended into parallel crystals >100k units long, the carbon atoms double-bonded, and crosslinked by hydrogen bonds. Short of graphene tubes, with triple bonded carbon, UHMWPE is the best engineering fiber since Nylon. UHMWPE is a liquid-crystal (it will creep), but its Debye temperature is comparable to diamond, so its physics are native QM, not just analogous, over a large scale-invariant spectrum. The speed-of-sound in tensioned UHMWPE can reach 50km/sec, similar to diamond. Elsewhere I have cited an example of a ship hawser towing a ship by a ship with a power of work of 10MW, yet remains cool to the touch. This sort of wonderful phonon physics frozen-wave power super-conductance has hardly been seriously studied, "hidden in plain sight". A few related physics concepts exist, like second-sound and ballistic-conductance. This is the original 1970 paper describing UHMWPE as novel fiber- https://www.tandfonline.com/doi/abs/10.1080/00222347008229373 Oddly enough, Nylon remains a mainstay polymer in state-of-the-art rigging, complimenting the low-stretch property of UHMWPE. In applications with shock and surge loads, Nylon can absorb the excess energy and return it after the load peak, where UHMWPE might violently shatter or vaporize, or shock-damage other components. A final introductory aspect of AWE is Kite Network Metamaterial Topology, a fast emerging AWE engineering paradigm in acoustic and mechanical metamaterials. Networked Kitematter fulfills all criteria cited that identify a MetaMaterial as such. A future kite network with km scale cells would easily comprise both the largest and least dense engineered material (neglecting density of entrained air). Mechanical Metamaterials take many novel forms but share fundamental properties, like negative-index phonon refraction, topological-insulator/edge-modes, and auxetic response. Puzzle challenge: Identify specific kite-based metamaterial mechanisms (answers soon). https://bertoldi.seas.harvard.edu/pages/harnessing-instability-design-mechanical-metamaterials Recopying this paper link Paul provided, that I missed earlier. Another representative paper in a proliferating literature. Will post some missing domain survey links when I relocate them. https://arxiv.org/pdf/2002.10607.pdf`

An insight into Topological Edge Modes cited in recent posts:

Edge Modes in MetaMaterial Science are commonly described as waves moving around the edge of a topologically insulated bulk.

https://www.pnas.org/content/112/47/14495

However, under Galilean Invariance, its just as valid to see the bulk as the flowing part, and Edge Modes as stationary boundary-layer dynamics.

Therefore, we can indentify atmospheric Jet Streams as Topological Insulator and Edge Mode cases. Bulk Jet Flow comprises a Topological Insulator lubricated by Edge Mode vortices. We can also see Edge Modes in Boundaries between bulk volumes and areas in relative motion. This extends Topological identifications in Atmospheric Science.

We can see that for Airborne Wind Energy as kinetic energy harvesting between bulk opposed geo flow, polymer AWES tethers span a Boundary Edge Mode layer (aka Surface Boundary Layer). This amounts to a Phonon Tunneling Mode, as described in this reference copied from a related topic.

On virtual phonons, photons, and electrons; Gunter Nimtz 2018; Physikalisches Institut, Universtat zu Koln https://arxiv.org/pdf/0907.1611.pdf

`An insight into Topological Edge Modes cited in recent posts: Edge Modes in MetaMaterial Science are commonly described as waves moving around the edge of a topologically insulated bulk. https://www.pnas.org/content/112/47/14495 However, under Galilean Invariance, its just as valid to see the bulk as the flowing part, and Edge Modes as stationary boundary-layer dynamics. Therefore, we can indentify atmospheric Jet Streams as Topological Insulator and Edge Mode cases. Bulk Jet Flow comprises a Topological Insulator lubricated by Edge Mode vortices. We can also see Edge Modes in Boundaries between bulk volumes and areas in relative motion. This extends Topological identifications in Atmospheric Science. We can see that for Airborne Wind Energy as kinetic energy harvesting between bulk opposed geo flow, polymer AWES tethers span a Boundary Edge Mode layer (aka Surface Boundary Layer). This amounts to a Phonon Tunneling Mode, as described in this reference copied from a related topic. On virtual phonons, photons, and electrons; Gunter Nimtz 2018; Physikalisches Institut, Universtat zu Koln https://arxiv.org/pdf/0907.1611.pdf`

Engineering requirements vary greatly for harvesting consistent coherent wind, which is fairly rare, and chaotic wind, which is quite common. In analogy with Networked Computing, its the difference between a highly parallel synchronous process and a highly distributed asynchronous one.

Rheological Chaos is a novel subject in a geophysical context with, as [Asokan 2005] asserts, "implications for certain areas of chaos theory, such as a new intermittency route to chaos and the possibility of non-trivial collective behavior in spatially extended systems".

Two References-

Review of chaos in the dynamics and rheology of suspensions of orientable particles in simple shear flow subject to an external periodic force; 2005; K. Asokan, C.V. Anil Kumar, J.Dasan, K. Radhakrishnan, K. Satheesh Kumare, T.R. Ramamohan

https://doi.org/10.1016/j.jnnfm.2005.06.003

An oobleck dynamics paper-

https://www.pnas.org/content/116/42/20828

Edge Waves and Internal Waves are a rich source of interesting dynamics "in spatially extended systems" under periodic forcing, like our geophysical cases.

Let us conjecture that vortical excitations in air, as quasi-particles, correspond to the "orientable particles" in the general rheological literature.

We can begin to appreciate the geoengineering potential of Topological Surgery of the Atmosphere, not just Energy Harvesting, crudely considered.

`Engineering requirements vary greatly for harvesting consistent coherent wind, which is fairly rare, and chaotic wind, which is quite common. In analogy with Networked Computing, its the difference between a highly parallel synchronous process and a highly distributed asynchronous one. Rheological Chaos is a novel subject in a geophysical context with, as [Asokan 2005] asserts, "implications for certain areas of chaos theory, such as a new intermittency route to chaos and the possibility of non-trivial collective behavior in spatially extended systems". Two References- Review of chaos in the dynamics and rheology of suspensions of orientable particles in simple shear flow subject to an external periodic force; 2005; K. Asokan, C.V. Anil Kumar, J.Dasan, K. Radhakrishnan, K. Satheesh Kumare, T.R. Ramamohan https://doi.org/10.1016/j.jnnfm.2005.06.003 An oobleck dynamics paper- https://www.pnas.org/content/116/42/20828 Edge Waves and Internal Waves are a rich source of interesting dynamics "in spatially extended systems" under periodic forcing, like our geophysical cases. Let us conjecture that vortical excitations in air, as quasi-particles, correspond to the "orientable particles" in the general rheological literature. We can begin to appreciate the geoengineering potential of Topological Surgery of the Atmosphere, not just Energy Harvesting, crudely considered.`

A few notes regarding the nano-to-cm-to-km-to-planetary-scale of "polymerizing the sky" for upper wind energy.

UHMPE molecules are ultra long liquid-crystal chains (~500k monomer units). This gives high Q properties that collectively extend to multi-km scale. Polymer fibers are twisted into threads, giving them a chiral spin property. Threads are further twisted into strands that are braided into lines and ropes that are often knotted in use.

These Topological Properties, of twisting, braiding, and knotting, are simultaneously mathematically abstract and tangibly embodied. Its modern topology right before our eyes. The mundane tangibility of "rag and string" somehow blinded topologists, until material scientists eagerly started adopting their concepts.

Network Theory and Engineered Fractals began even in the Paleolithic Age, as everyday embodiments. Fish nets are networks; the knots are nodes connected to each other by antinodes. Woven and knitted fabrics are networks. Biological networks go back billions of years; leaves are networks, brains are networks, and so on. Often units are called “cells”. A lot of mathematics is topologically ordered; network-based. Fractals are networks, as are graphs. Everything from quantum-computing to kite-networks is being governed by these principles.

Airborne Wind Energy Systems (AWES) are thus topological polymer load-path networks of tethers and bridle lines, fabric and seams. We no longer have to look at these as mathematically intractable objects. We now have formalizations spanning the nano to planetary scale spectrum (and beyond). We can rigorously prove, in principle, that there is ample upper-wind energy to sustain civilization, and subscale-validated technological means (Power Kite Networks) to harvest that energy.

https://en.wikipedia.org/wiki/Knot_theory

https://en.wikipedia.org/wiki/List_of_knot_theory_topics

`A few notes regarding the nano-to-cm-to-km-to-planetary-scale of "polymerizing the sky" for upper wind energy. UHMPE molecules are ultra long liquid-crystal chains (~500k monomer units). This gives high Q properties that collectively extend to multi-km scale. Polymer fibers are twisted into threads, giving them a chiral spin property. Threads are further twisted into strands that are braided into lines and ropes that are often knotted in use. These Topological Properties, of twisting, braiding, and knotting, are simultaneously mathematically abstract and tangibly embodied. Its modern topology right before our eyes. The mundane tangibility of "rag and string" somehow blinded topologists, until material scientists eagerly started adopting their concepts. Network Theory and Engineered Fractals began even in the Paleolithic Age, as everyday embodiments. Fish nets are networks; the knots are nodes connected to each other by antinodes. Woven and knitted fabrics are networks. Biological networks go back billions of years; leaves are networks, brains are networks, and so on. Often units are called “cells”. A lot of mathematics is topologically ordered; network-based. Fractals are networks, as are graphs. Everything from quantum-computing to kite-networks is being governed by these principles. Airborne Wind Energy Systems (AWES) are thus topological polymer load-path networks of tethers and bridle lines, fabric and seams. We no longer have to look at these as mathematically intractable objects. We now have formalizations spanning the nano to planetary scale spectrum (and beyond). We can rigorously prove, in principle, that there is ample upper-wind energy to sustain civilization, and subscale-validated technological means (Power Kite Networks) to harvest that energy. https://en.wikipedia.org/wiki/Knot_theory https://en.wikipedia.org/wiki/List_of_knot_theory_topics`