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Newton, Euler equation and Navier-Stokes equation of fluid mechanics (2)

Why does Newton emphasis that a force must be derived from the phenomena of motions?
Because this is the best and the most accurate method, with which we can directly find the true causes and reasons (in Newton’s word, causes and reasons are just forces) of the motions.
Euler, Navier and Stokes do not follow Newton’s rule, and want to use pressure forces to describe all kinds of phenomena of fluid motions, this is a big mistake, nobody can guaranty that pressure forces are true causes and reasons of all kinds of fluid motions, because pressure forces are not derived from phenomena of fluid motions.
According to Newton’s rule, the forces, which will be used to describe all kinds of fluid motions, must be derived from the phenomena of fluid motions.
So Euler equation and Navier-Stokes equation are useless.

Newton is a Giant, so we must strictly follow him.
In mechanics, we just care about forces and motions, motions and forces, different kinds of forces produce different kinds of motions and different kinds of motions need different kinds of forces.
In mechanics, we just care forces, we do not need differential equations; we just see a gravity force when we see the solar system, we just see a centripetal force when we see hurricanes, and we just see a centripetal force and electromagnetic forces when we see sunspots, or in Newton’s word, we can derive a centripetal force from the phenomena of the fluid motions of hurricanes, and then we can use this centripetal force, and magnetic forces, to demonstrate the plasmas motions of the sunspots.

Batchelor, G. K. 1994 An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge.
Newton, I. 1686 Principia, Daniel Adee, New York (republished in 1848).

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Newton, Euler equation and Navier-Stokes equation of fluid mechanics (1)

Newton said in preface of his Principia that rational mechanics will be the science of motions resulting from any forces whatsoever, and of the forces required to produce any motions, accurately proposed and demonstrated. He said that for all the difficulty of philosophy seems to consist in this–from the phenomena of motions to investigate the forces of the nature, and then from these forces to demonstrate the other phenomena; and to this end the general propositions in the first and second book are directed. In the third book we give an example of this in the explication of the system of the world; for by the propositions mathematically demonstrated in the former books, we in the third derive from celestial phenomena the forces of gravity with which bodies tend to the sun and several planets. Then from these forces, by other propositions which are also mathematical, we deduce the motions of the planets, the comets, the moon, and the sea. I wish we could derive the rest of the phenomena of nature by the same kind of reasoning from mechanical principles.

Newton said that for all the difficulty of philosophy seems to consist in this–from the phenomena of motions to investigate the forces of the nature, and then from these forces to demonstrate the other phenomena. In fact, Newton’s main idea, or his principle of philosophy consists in this–from the phenomena of motions to investigate the forces of the nature, and then from these forces to demonstrate the other phenomena. Newton needs mathematical tools, when he investigates forces from the phenomena of motions and deduces other phenomena from these forces; so Newton writes book Ⅰand book Ⅱ; these two books are just mathematical tools. Book Ⅲ demonstrates Newton’s main idea or principle of philosophy–from the phenomena of motions to investigate the forces of the nature, and then from these forces to demonstrate the other phenomena; Newton derives gravity from celestial phenomena of the solar system, and then deduces other phenomena of the solar system by the gravity. Certainly Newton thinks that he can solve other natural phenomena by his main idea or principle of philosophy.

In fluid mechanics, we use Euler equation and Navier-Stokes equation to describe the phenomena of the fluid motions; Euler equation and Navier-Stokes equation use pressure forces, friction forces, buoyant forces, and coriolis forces etc.
It is obvious that Euler, Navier and Stokes did not fully understand Newton’s Principia, and did not follow Newton’s main idea or the mechanical principle.
Newton wants to derive forces from phenomena of motions, but Euler, Navier and Stokes do not; Newton wants to deduce other phenomena by the forces, which are derived from the phenomena of motions, but Euler, Navier and Stokes deduce the phenomena of fluid motions by pressure forces, friction forces, coriolis forces, and buoyant forces etc. and none of these forces is derived from phenomena of fluid motions.
Euler, Navier and Stokes omit the first process of Newton’s main idea or the mechanical principle: from the phenomena of motions to investigate the forces of the nature.
Why does Newton emphasis that a force must be derived from the phenomena of motions?

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Vortex models and sunspots.
Vortex models of sunspots are very important in history of sunspots. In fact, the stable nuclear fusion reactor model of the sunspot is a vortex model too, this model go a step forward from old vortex models of sunspots, because Hale’s vortex of sunspots will evolve into stable nuclear fusion reactors.

Hale, who discovered that every sunspot has strong magnetic fields, thought that the sunspots are vortices of the sun; these vortices drive the electrons move in circular orbits and produce the magnetic fields of the sunspots.
In above posts, I have already pointed out that sunspots are stable nuclear fusion reactors, if we use circular electric currents to simulate the magnetic fields of the sunspots.

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[author=”jamesr” date=1254411336]

Just because there is a current doesn’t mean the pinch is strong enough to collapse the filaments enough to heat them significantly as done in Z-pinch machines. The large current is spread out over a huge volume, so the local current density at any one point is still small.

The ions & electrons accelerated into the magnetic loops above the area of the sunspot do indeed reach a high velocity/temperature and so the electrons emit bremsstrahlung radiation at x-ray wavelengths. And I suppose there could be a very small chance of fusion for the most energetic ions, but it’s hardly a significant phenomena.

Flares and CMEs are spectacular and involve the transfer of huge amounts of energy from the magnetic field to the plasma surface of the sun, but in no way are they related to fusion.

Certainly, sunspots are very large, but so do circular electric currents (1,000,000,000,000 Amperes for middle size circular sunspots). The density of circular electric currents is approximate 5,000,000 amperes/meter along axial direction of eyewalls of sunspots.
Sunspots differ from Z-pinch devices, Z-pinch devices use pulse kind electric currents and use just electromagnetic forces, but sunspots are stable, the circular electric currents in eyewalls of sunspots are stable, and plasmas in eyewalls of sunspots are compressed by a centripetal force and electromagnetic forces. Hollow cylindrical plasmas with large circular electric currents cannot become sunspots if they do not pinch.
Some hydrogen bombs with black mushroom clouds certainly have pinch processes too. J. L. Tuck of England has achieved pinch processes in his Perhapsatron devices in early 1950s; the discharge electric currents in his devices are very small.

Who accelerate and heat electrons and ions in the magnetic loops above the sunspots?

You think that the huge amounts of energy of solar flares and CMEs come from magnetic fields of the sun, but my question is: where do these huge amounts of energy of magnetic fields of the sun come from?

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[author=”jamesr” date=1252947902]
Fusion in stars is incredibly inefficient & slow, hence why they last so long. The temperature in the core of only 10million degrees is only just enough to get the hydrogen to fuse. Further out the temperature drops rapidly till at the surface it is only 5400C. Sunspots are dark because they are upto 1000 degrees cooler. There is no way any fusion can occur at these cold temperatures and low density.

The temperatures of umbrae of the sunspots are approximate 4,500k; they are almost 1,000k lower than that of their surrounding photosphere.

Some mushroom clouds of hydrogen bombs are black too, that is, their temperatures are lower than that of their surrounding atmosphere.

The lower temperature of sunspots and hydrogen bombs is a simple phenomenon of gas dynamics.

The lower temperature phenomenon of sunspots is a proof, which can prove that sunspots are stable nuclear fusion reactors. But some people use this proof to reject that sunspots are stable nuclear fusion reactors.

I have a question: how to explain why temperatures of umbrae of the sunspots are lower than that of their surrounding photosphere?

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jamesr wrote:

The temperatures of umbrae of the sunspots are approximate 4,500k, why do you think that the temperatures of plasmas in eyewalls of sunspots are 4,500k? The temperatures of plasmas in eyewalls of sunspots are certainly above ten million Kelvin.
The velocity of the Evershed flow of the sunspot is very large (1-9km/s).

Where do you get that temperature from??
The velocity from dopper shift of spectra lines is indeed of the order of a few km/s but this is the bulk flow of material, and nowhere near the speed te ions need to fuse.
The average energy corresponding to 10million K is 862eV ( conversion factor 1eV = 11604K). a KE of 862eV corresponds to a velocity of 200km/s. However even at that temperature only the protons at the top end of the thermal speed distribution have a chance of fusing. A proton with kinetic energy of 10keV has a velocity of 1500km/s

There no evidence I know of that the temperature at any point in or around sunspots gets this high. Indeed the spectral data gives it away a bit. At the temperatures required you cannot get spectra lines. The plasma would be fully ionised; the electrons & ions have way too much energy to recombine and give off a visible photon.

In any case the particle denisty is way too low in the photosphere to have any meaningful fusion anyway.

On a side note – do you realise how unlikely fusion with ordinary hydrogen is? the cross sections (reaction probabilities) are measured in barns (cm^-24)
at 10keV the cross sections are as follows:
for D-T = 2.7E-2 barns
for D-D= 2.8E-4 barns
p+B11 = 4.6E-17 barns
p+p = 3.6E-26 barns

at 100keV it gets a little better, esp for the pB11
for D-T = 3.43 barns
for D-D= 3.3E-2 barns
p+B11 = 3E-4 barns
p+p = 4.4E-25 barns

ie the probablility of a ordinary hydrogen (p+p) reaction is over 20 orders of magnitude lower than D-T

Pinch, pinch, pinch.
In above posts, I have already pointed out that the eyewalls of sunspots have huge amounts of the circular electric currents (1,000,000,000,000 Amperes for middle size circular sunspots), so plasmas in eyewalls of sunspots are in pinch state, that is, in high temperature high density state, so stable nuclear fusion reactions can happen in eyewalls of sunspots.
Z-pinch fusion experiments are done almost every day; do you not believe these experiments?
Some CMEs and solar flares of the sun are caused by these pinch processes in the eyewalls of the sunspots.
Sunspots are ion-pumps and electron-pumps too; the X-ray photos of the sun reveal that almost all high temperature (above one million Kelvin) high energy phenomena of the sun are related to the sunspots.

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jamesr wrote:

The eyewalls of sunspots have huge amounts of the circular electric currents (1,000,000,000,000 Amperes for middle size circular sunspots), so plasmas in eyewalls of sunspots are in pinch state, that is, in high temperature high density state, so stable nuclear fusion reactions can happen in eyewalls of sunspots.
Why do you think that sunspots cannot have stable nuclear fusion reactions?

The current is irrelavent. It is quite easy on the sun to get large nett flows of quasi-neutral material, and hence large currents. The sun is after all quite big. But unless the individual ions are moving fast enough (ie. are hot enough) to overcome the coulomb repulsion you will get no fusion.

Now up in the corona is does for some reason get up to a million or two Kelvin, compared to the 4500K or so for a sunspot. so you could potentially have some fusion there – but even this is too cold to have any appriciable chance of fusion, never mind that it is so rareified that the chance of a collision of two ions is incredibly low.

Going back to your hurricane metaphor – the wind at the eyewall is fairly slow, the damge is done further out on the leading edge. But nowhere in a hurricance is there enough energy in the air to make is spontaniously combust or even the water in it boil.

James

The temperatures of umbrae of the sunspots are approximate 4,500k, why do you think that the temperatures of plasmas in eyewalls of sunspots are 4,500k? The temperatures of plasmas in eyewalls of sunspots are certainly above ten million Kelvin.
The velocity of the Evershed flow of the sunspot is very large (1-9km/s).

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jamesr wrote:

Somebody got cosmology wrong again.
Here is a quote from the infamous internet information source:
“The core is the only location in the Sun that produces an appreciable amount of heat via fusion: the rest of the star is heated by energy that is transferred outward from the core”
http://en.wikipedia.org/wiki/Sun

I certainly know it very well.
Astronomers think that the sun can maintain stable nuclear fusion reactions in its inner core just by a centripetal force (gravity), it is a good idea, but it cannot be verified by experiments, because nobody can go in inside of the sun. I must emphasis that physics is an experimental science.
Fusion scientists think that they can achieve stable nuclear fusion reactions just by electromagnetic forces, but they have not succeeded.
We do not know that heats can produce forces directly.
Sunspots kind stable nuclear fusion reactors are governed by a centripetal force and electromagnetic forces.

Fusion in stars is incredibly inefficient & slow, hence why they last so long. The temperature in the core of only 10million degrees is only just enough to get the hydrogen to fuse. Further out the temperature drops rapidly till at the surface it is only 5400C. Sunspots are dark because they are upto 1000 degrees cooler. There is no way any fusion can occur at these cold temperatures and low density.

In larger stars where the temperature & pressure is higher you can get other reactions such as the CNO cycle which make large stars burn much faster, hotter & brighter. Although there are certainly still large gaps in the knowledge of the internal workings of stars. The observations of millions of stars and their spectra, backed up by fusion probability cross section measurements on earth give us pretty good confidence that the fusion process in the core is the right model.

To get fusion on earth at any appriciable rate you need to satisfy the Lawson criteria. That is you need the product of temperature, particle density and confinement time to be above a critical value. Magnetic fields are useful in obtaining the confinement but if you don’t have the temperature to go with it nothing will happen.

For D-T reactions, which are by far the easiest, you need around 100million degrees (10 times hotter than the core of the sun) and for pB11 we will need an order of magnitude higher again. There are no shortcuts, or cunning ways to make it easier. To obtain breakeven (ie Lawson criteria) if you reduce one factor like temperature you need to make up for it with the others, eg by increasing the density.

For those that want to get into the hard core physics, these are good introduction: Nuclear Fusion Reactions and Plasma Physics. They may look a little scary but just skip over the equations if you just want an overview.

The eyewalls of sunspots have huge amounts of the circular electric currents (1,000,000,000,000 Amperes for middle size circular sunspots), so plasmas in eyewalls of sunspots are in pinch state, that is, in high temperature high density state, so stable nuclear fusion reactions can happen in eyewalls of sunspots.
Why do you think that sunspots cannot have stable nuclear fusion reactions?

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Breakable wrote: Somebody got cosmology wrong again.
Here is a quote from the infamous internet information source:
“The core is the only location in the Sun that produces an appreciable amount of heat via fusion: the rest of the star is heated by energy that is transferred outward from the core”
http://en.wikipedia.org/wiki/Sun

I certainly know it very well.
Astronomers think that the sun can maintain stable nuclear fusion reactions in its inner core just by a centripetal force (gravity), it is a good idea, but it cannot be verified by experiments, because nobody can go in inside of the sun. I must emphasis that physics is an experimental science.
Fusion scientists think that they can achieve stable nuclear fusion reactions just by electromagnetic forces, but they have not succeeded.
We do not know that heats can produce forces directly.
Sunspots kind stable nuclear fusion reactors are governed by a centripetal force and electromagnetic forces.

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We cannot get an answer just by studying sunspots, we must study other phenomena.
Sunspots must be similar to atomic bombs, hydrogen bombs and hurricanes, if sunspots are stable nuclear fusion reactors, why? Because all of them release huge amount of heats continuously or in pulse manner, they are heats phenomena.
Then, what are similarity and differences among atomic bombs, hydrogen bombs, hurricanes and sunspots?
(1) Eyes
The umbrae of the sunspots are just the eyes of the sunspots, like the eyes of hurricanes.
(2) Eyewalls and magnetic fields
The magnetic fields of circular sunspots can be simulated by long solenoids with large circular electric currents. These long solenoids are just eyewalls of the sunspots, like eyewalls of the hurricanes. There are heavy rains in the eyewalls of the hurricanes; but there are large circular electric currents and nuclear fusion reactions in the eyewalls of the sunspots.
(3) Evershed flow
Atomic bombs, hydrogen bombs, hurricanes and sunspots all have Evershed kind of outflows. But velocity of the Evershed flow of the sunspot is very large (1-9km/s).
(4) Low temperature
The temperatures of the sunspots and some mushroom clouds of hydrogen bombs are lower than that of their surrounding atmosphere.
(5) Latitude distribution and periodical cycles.
Hurricanes are similar to sunspots in latitude distribution and periodical variations of numbers.
(6) Energy
Atomic bombs, hydrogen bombs, hurricanes and sunspots all are heat phenomena.

Conclusion:
Some astronomers such as John Herschel and Hale think that sunspots are cyclone vortices of the sun.
In fact, sunspots are just hurricanes of the sun, and these hurricanes have large circular electric currents and nuclear fusion reactions in their eyewalls.
So sunspots are one kind of standard stable nuclear fusion reactors.
The complex structures and motions of atomic bombs, hydrogen bombs, hurricanes and sunspots are caused by heats, so heats can produce some kinds of forces directly (Notice: Do not use Euler equation and Navier-Stokes equation of fluid mechanics). Certainly, electromagnetic forces play a role in eyewalls of the sunspots.
But there is a problem: how to describe atomic bombs, hydrogen bombs, hurricanes and sunspots mathematically?

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