Viscous Heating

"N:dlzc D:aol T:com \(dlzc\)" wrote in news:UWx_h.297882
:

Dear John Schutkeker:

"John Schutkeker" wrote in
message
. 33.102...
"N:dlzc D:aol T:com \(dlzc\)" wrote in
news:Vea_h.233935
:

"John Schutkeker" wrote in
message
. 33.102...

But thanks for the red spot insight. These planets
aren't gas giants, but I don't know if that makes the
issue go away. I wonder if the presence of a surface
crust would be enough to suppress that.

If you are requiring an entirely fluid surface (???), then
you must have some vortex... if not two. One would
expect them at / near the poles. Unlike Jupiter.

The boundary condition between the mantle and crust
makes the vortex problem go away,

Actually, I think it does not. It would tend to "rotate" the
vortex "neutral axis" to be parallel to any differential rotation
between the core (if any) and the crust.

I'll bet you $500 that you can't prove it mathematically for either
Earth or Enceladus, your choice. If you can do it reliably, you can get
your name in the papers, for making the next insanely great discovery.

but if you'd still be willing to point my way to a page
that works the math for a free fluid surface, I'd be very
grateful. A man can never read too much math. ?

I have the text that brings this up at work ("5 Golden Rules").
I'll try and remember to post the necessary keywords to see if
you agree with my take on it.

I have the sequel, although not the original, but since it's only $30,
maybe it's time to whip out the ol' debit card. If you'd e-mail me
scans, I'd kiss your hand, because my artihitis has kept me away from
the library for over a year now.

John Schutkeker wrote:

Andy Resnick wrote in
:


John Schutkeker wrote:


AFAIK, Navier-Stokes (NS) is just a momentum balance equation, making
me ask, since when don't liquids obey the same force balances on a
differential fluid element as gasses? If that's true, what momentum
equation replaces NS, in the incompressible liquid case you
mentioned? There should be only one equation, and it's NS, although
the viscosity may be a complicted function, rather than a constant.
But it should still be NS, shouldn't it?

The NS equation*s* are for the *conservation* of momentum, and are a
simplification of Cauchy's first law of motion. To solve the general
flows you describe, one also needs the conservation of mass equations
and the conservation of energy equations.


I'm not familiar with Cauchy's first law of motion. Is it east enough
to wrote down here, or can you give me a link to a page that explains
it?

It's quite simple to write: D(pv)/Dt = div(T) + F, where p is the
density, v the velocity, D/Dt the material derivative, T the stress
tensor, and F the body force.



Whichever it is, I'm betting that it's a highly viscous liquid, more
like a paste or a putty, than what we're used to. Since nobody knows
anything about it, I'll have to just say that it seems obvious enough
that quantum effects will dominate the viscosity, and not hard-body
collisions, like a compressible gas.

Pastes are not viscous fluids. Is there a yield stress? And forget
quantum effects- for planetary-scale motions, quantum effects are
useless unless the temperature is near 0 K.


I believe Scott was saying that viscosity os due to intermolecular
interactions, whose physics is very complex. That complex physics
exists at all temperatures, not just near absolute zero.

Yes, and the beauty of continuum mechanics is that all of that
complexity can be subsumed into a constitutive equation, meaning the
microscopic details can be ignored.


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

Dear John Schutkeker:

On May 4, 5:27 am, John Schutkeker
wrote:
"N:dlzcD:aol T:com \(dlzc\)" wrote in news:UWx_h.297882
:

Dear John Schutkeker:

"John Schutkeker" wrote in
message
.33.102...
"N:dlzcD:aol T:com \(dlzc\)" wrote in
news:Vea_h.233935
:

"John Schutkeker" wrote in
message
15.33.102...

But thanks for the red spot insight. These planets
aren't gas giants, but I don't know if that makes the
issue go away. I wonder if the presence of a surface
crust would be enough to suppress that.

If you are requiring an entirely fluid surface (???), then
you must have some vortex... if not two. One would
expect them at / near the poles. Unlike Jupiter.

The boundary condition between the mantle and crust
makes the vortex problem go away,

Actually, I think it does not. It would tend to "rotate"
the vortex "neutral axis" to be parallel to any differential
rotation between the core (if any) and the crust.

I'll bet you $500 that you can't prove it mathematically
for either Earth or Enceladus, your choice.

I don't bet. As George Dishman could attest, I also don't do math
(well).

If you can do it reliably, you can get your name in the
papers, for making the next insanely great discovery.

but if you'd still be willing to point my way to a page
that works the math for a free fluid surface, I'd be very
grateful. A man can never read too much math. ?

I have the text that brings this up at work ("5 Golden
Rules"). I'll try and remember to post the necessary
keywords to see if you agree with my take on it.

I have the sequel, although not the original, but since
it's only $30, maybe it's time to whip out the ol' debit
card. If you'd e-mail me scans, I'd kiss your hand,
because my artihitis has kept me away from
the library for over a year now.

That sucks. I will not violate copyright.

However the appropriate section talks about Morse's Theorem; talks
about fluid flow around / between two cylinders (non-concentric...
parallel rollers); glances briefly across Thom Classification Theorem;
then talks about bifurcations, catastrophes, and equilibria. I am
pretty sure I read this section as *requiring* a rotating fluid over a
closed 2D surface, to have at least one "knot"... a vortex or other
anomaly.

As to whether it would apply to a fluid trapped between two
differentially rotating surfaces closed 2D surfaces, I don't see how
it could not also apply. It might limit the size, or constrain the
location, but ...

David A. Smith

Andy Resnick wrote in news:f1fa8d$4so$1
@eeyore.INS.cwru.edu:

The NS equation*s* are for the *conservation* of momentum, and are a
simplification of Cauchy's first law of motion. To solve the general
flows you describe, one also needs the conservation of mass equations
and the conservation of energy equations.

I'm not familiar with Cauchy's first law of motion. Is it east enough
to wrote down here, or can you give me a link to a page that explains
it?

It's quite simple to write: D(pv)/Dt = div(T) + F, where p is the
density, v the velocity, D/Dt the material derivative, T the stress
tensor, and F the body force.

This works for fluids, and not just elastic solids?

dlzc wrote in news:1178288470.465507.163000
@n59g2000hsh.googlegroups.com:

Dear John Schutkeker:

On May 4, 5:27 am, John Schutkeker
wrote:
"N:dlzcD:aol T:com \(dlzc\)" wrote in
news:UWx_h.297882
:

Dear John Schutkeker:

"John Schutkeker" wrote in
message
.33.102...
"N:dlzcD:aol T:com \(dlzc\)" wrote in
news:Vea_h.233935
:

"John Schutkeker" wrote in
message
15.33.102...

But thanks for the red spot insight. These planets
aren't gas giants, but I don't know if that makes the
issue go away. I wonder if the presence of a surface
crust would be enough to suppress that.

If you are requiring an entirely fluid surface (???), then
you must have some vortex... if not two. One would
expect them at / near the poles. Unlike Jupiter.

The boundary condition between the mantle and crust
makes the vortex problem go away,

Actually, I think it does not. It would tend to "rotate"
the vortex "neutral axis" to be parallel to any differential
rotation between the core (if any) and the crust.

I'll bet you $500 that you can't prove it mathematically
for either Earth or Enceladus, your choice.

I don't bet. As George Dishman could attest, I also don't do math
(well).

If you can do it reliably, you can get your name in the
papers, for making the next insanely great discovery.

but if you'd still be willing to point my way to a page
that works the math for a free fluid surface, I'd be very
grateful. A man can never read too much math. ?

I have the text that brings this up at work ("5 Golden
Rules"). I'll try and remember to post the necessary
keywords to see if you agree with my take on it.

I have the sequel, although not the original, but since
it's only $30, maybe it's time to whip out the ol' debit
card. If you'd e-mail me scans, I'd kiss your hand,
because my artihitis has kept me away fromthe library
for over a year now.

That sucks.

Yeah, it slows me down badly. I haven't been to the library for
eighteen months, but fortunately I've had other important things to do.
I'm just finishing a good project now, so I have no choice, because I
can't very well send it to a jourbal without having all my references in
proper order.

I think I've figured out a way to get over the hump, but I won't know
until I test it. Maybe I'll have to get used to the idea of being
incapacitated for a few days after every library trip. Time will
tell...

I will not violate copyright.

It's "personal use," and neither one of us is asking for money. But I
just ordered it on Amazon for $8, shipping included, so there's no
reason to quarrel. I'll pony up $8 without batting an eye, but it's the
$65 (used) textbooks that I think long and hard about.

Textbooks are a friggin' racket, and if their prices were lower, science
would advance a *lot* faster.

However the appropriate section talks about Morse's Theorem; talks
about fluid flow around / between two cylinders (non-concentric...
parallel rollers); glances briefly across Thom Classification Theorem;
then talks about bifurcations, catastrophes, and equilibria. I am
pretty sure I read this section as *requiring* a rotating fluid over a
closed 2D surface, to have at least one "knot"... a vortex or other
anomaly.

As to whether it would apply to a fluid trapped between two
differentially rotating surfaces closed 2D surfaces, I don't see how
it could not also apply. It might limit the size, or constrain the
location, but ...

I don't think that the surfaces rotate differentially. The mantle just
carries the crust.

Dear John Schutkeker:

"John Schutkeker" wrote in
message
. 33.102...
dlzc wrote in news:1178288470.465507.163000
@n59g2000hsh.googlegroups.com:
....
That sucks.

Yeah, it slows me down badly. I haven't been to the library
for
eighteen months, but fortunately I've had other important
things to do.
I'm just finishing a good project now, so I have no choice,
because I
can't very well send it to a jourbal without having all my
references in
proper order.

I think I've figured out a way to get over the hump, but I
won't know
until I test it. Maybe I'll have to get used to the idea of
being
incapacitated for a few days after every library trip. Time
will
tell...

I will not violate copyright.

It's "personal use," and neither one of us is asking for money.
But I
just ordered it on Amazon for $8, shipping included, so there's
no
reason to quarrel. I'll pony up $8 without batting an eye, but
it's the
$65 (used) textbooks that I think long and hard about.

Textbooks are a friggin' racket, and if their prices were
lower, science
would advance a *lot* faster.

Thought I'd zoom by my local college's bookstores. Thought I'd
pick up some used stuff for fairly cheap... like I used to "20
years ago". That is the price of limited readership, but *damn*.

However the appropriate section talks about Morse's Theorem;
talks
about fluid flow around / between two cylinders
(non-concentric...
parallel rollers); glances briefly across Thom Classification
Theorem;
then talks about bifurcations, catastrophes, and equilibria.
I am
pretty sure I read this section as *requiring* a rotating
fluid over a
closed 2D surface, to have at least one "knot"... a vortex or
other
anomaly.

As to whether it would apply to a fluid trapped between two
differentially rotating surfaces closed 2D surfaces, I don't
see how
it could not also apply. It might limit the size, or
constrain the
location, but ...

I don't think that the surfaces rotate differentially. The
mantle just
carries the crust.

If you have temperature variation, you will have differential
flow. But you tell "me".

David A. Smith

"N:dlzc D:aol T:com \(dlzc\)" wrote in news:9Cu%h.295208
:

Dear John Schutkeker:

"John Schutkeker" wrote in
message
. 33.102...
dlzc wrote in news:1178288470.465507.163000
@n59g2000hsh.googlegroups.com:
...
That sucks.

Yeah, it slows me down badly. I haven't been to the library
for
eighteen months, but fortunately I've had other important
things to do.
I'm just finishing a good project now, so I have no choice,
because I
can't very well send it to a jourbal without having all my
references in
proper order.

I think I've figured out a way to get over the hump, but I
won't know
until I test it. Maybe I'll have to get used to the idea of
being
incapacitated for a few days after every library trip. Time
will
tell...

I will not violate copyright.

It's "personal use," and neither one of us is asking for money.
But I
just ordered it on Amazon for $8, shipping included, so there's
no
reason to quarrel. I'll pony up $8 without batting an eye, but
it's the
$65 (used) textbooks that I think long and hard about.

Textbooks are a friggin' racket, and if their prices were
lower, science
would advance a *lot* faster.

Thought I'd zoom by my local college's bookstores. Thought I'd
pick up some used stuff for fairly cheap... like I used to "20
years ago". That is the price of limited readership, but *damn*.

I think that there's racketeering going on, because if prices were
lower, demand would rise.

However the appropriate section talks about Morse's Theorem;
talks
about fluid flow around / between two cylinders
(non-concentric...
parallel rollers); glances briefly across Thom Classification
Theorem;
then talks about bifurcations, catastrophes, and equilibria.
I am
pretty sure I read this section as *requiring* a rotating
fluid over a
closed 2D surface, to have at least one "knot"... a vortex or
other
anomaly.

As to whether it would apply to a fluid trapped between two
differentially rotating surfaces closed 2D surfaces, I don't
see how
it could not also apply. It might limit the size, or
constrain the
location, but ...

I don't think that the surfaces rotate differentially. The
mantle just
carries the crust.

If you have temperature variation, you will have differential
flow. But you tell "me".

I think that the no-slip condition at the boundary will be enough to
suppress it. There may be a lingering, miniscule differential flow, but
not enough to drive something so extreme as a Great Vortex. If it
existed on Earth, seismic measurements would have revealed it by now,
and thermal conditions are much more extreme on earth than Enceladus.

If you're absolutely convinced that I'm wrong, I wholeheartedly
encourage you to start doing the work, because if it turns out you're
right, you can be on the cover of Scientific American. It will give you
a fair shot at a Nobel Prize, but it's not my project, it's yours. Mine
is tidal heating of an sphere that has no vortex.

Even if you're right, I have to solve the simple problem before I can
solve the hard one. Solving the simplified problem will be an important
accomplishment for me, and I'm not going to complicate it so badly that
my project dies.

John Schutkeker wrote:

Andy Resnick wrote in news:f1fa8d$4so$1
@eeyore.INS.cwru.edu:


The NS equation*s* are for the *conservation* of momentum, and are a
simplification of Cauchy's first law of motion. To solve the general
flows you describe, one also needs the conservation of mass equations
and the conservation of energy equations.

I'm not familiar with Cauchy's first law of motion. Is it east enough
to wrote down here, or can you give me a link to a page that explains
it?

It's quite simple to write: D(pv)/Dt = div(T) + F, where p is the
density, v the velocity, D/Dt the material derivative, T the stress
tensor, and F the body force.


This works for fluids, and not just elastic solids?

Yes. The key is what you write down for the stress tensor. For
Newtonian fluids, off the top of my head, T = pI + m(grad[V] +
grad[V]^trans), where p is the pressure, I the unit tensor, m the
viscosity, grad[V] the velocity gradient, and the final term is the
transpose of the tensor grad[V].

For other materials, simply write down the stress tensor, whatever you
choose it to be, and off you go.

--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

Andy Resnick wrote in
:

John Schutkeker wrote:

Andy Resnick wrote in news:f1fa8d$4so$1
@eeyore.INS.cwru.edu:


The NS equation*s* are for the *conservation* of momentum, and are
a simplification of Cauchy's first law of motion. To solve the
general flows you describe, one also needs the conservation of mass
equations and the conservation of energy equations.

I'm not familiar with Cauchy's first law of motion. Is it east
enough to wrote down here, or can you give me a link to a page that
explains it?

It's quite simple to write: D(pv)/Dt = div(T) + F, where p is the
density, v the velocity, D/Dt the material derivative, T the stress
tensor, and F the body force.


This works for fluids, and not just elastic solids?

Yes. The key is what you write down for the stress tensor. For
Newtonian fluids, off the top of my head, T = pI + m(grad[V] +
grad[V]^trans), where p is the pressure, I the unit tensor, m the
viscosity, grad[V] the velocity gradient, and the final term is the
transpose of the tensor grad[V].

For other materials, simply write down the stress tensor, whatever you
choose it to be, and off you go.

I found this paper (http://tinyurl.com/ywp8vr), which looks like it's
saying the same thing that you are. Do you have any dispute with the
basic equations for Cauchy's Law and the Newtonian stress tensor, and
would you be able to tell me which textbook you used to study this
material?

John Schutkeker wrote:

snip


I found this paper (http://tinyurl.com/ywp8vr), which looks like it's
saying the same thing that you are. Do you have any dispute with the
basic equations for Cauchy's Law and the Newtonian stress tensor, and
would you be able to tell me which textbook you used to study this
material?


Dispute? I'm not sure what you mean. In any case, section 3 of your
reference has the "standard" derivation. The rest of the paper looks
decent, although the notation is slightly antiquated. I'm not aware of
a single textbook that has a decent presentation of the material- some
of the sources I have learned from a

Slattery "interfacial transport phenomena"
Truesdell "Classical Field Theories" (Handbook of Physics)
Segel "mathematics applied to continuum mechanics"


--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University