Vector form of the equations fluid mechanics.
WJPII
vectors as individual objects as in the traditional 4 equation representation
of Maxwell's equations? I ask this because I am used to working with
electrodynamics and would like to learn fluid mechanics without having to
change my intuitive process to handle tensor indices notation.
Also, can the equations of fluid mechanics be expressed in terms of quaternion
inner and outer products, like Maxwell's equations can? If they can, this would
be another way for me to get a grasp on fluid mechanics.
If no one knows of a way to do either of these, then maybe someon could point
me to a book that gives a thourough, slow paced introduction of indices
notation and tensors. Preferably such a book would focus on this topic and not
have a specific application (like fluid mechanics) as a major goal of the book.
Gerard Westendorp
>
> What is the vector form of the basic equations of fluid mechanics, treating the
> vectors as individual objects as in the traditional 4 equation representation
> of Maxwell's equations? I ask this because I am used to working with
> electrodynamics and would like to learn fluid mechanics without having to
> change my intuitive process to handle tensor indices notation.
>
Fluid dynamics is often written down for *incompressible* fluids.
However, these are not deterministic equations, because you have
to solve (div v)=0. Nature solves this by compressibility. This
means you get sound waves.
Another difference with Maxwell is the non-linear term
(v.grad)(rho v).
This is the one that causes all the chaos and turbulence.
The adiabatic frictionless equations are:
d(rho v)/dt = -grad p - (v.grad)(rho v)
d rho/dt = -div(rho v)
p = rho ^ kappa
> If no one knows of a way to do either of these, then maybe someon could point
> me to a book that gives a thourough, slow paced introduction of indices
> notation and tensors. Preferably such a book would focus on this topic and not
> have a specific application (like fluid mechanics) as a major goal of the book.
There are a few sites of people proposing ether theories ie. analogies between
fluid dynamics and Maxwell theory, or even theories of everything
based on
fluid dynamics. The elementary
particles are usually something like vortices. Kelvin had also tried some
of this.
I can recommend the Feynman Lecture on Physics which have a few good chapters
on fluid dynamics.
--
\______/_______Gerard________
http://www.xs4all.nl/~westy31/
Matthew Lybanon
R. Apel, _Principles of Ocean Physics_, Academic Press, 1987
(ISBN 0-12-058865-X). Chapters 3, 5, and 6 in particular should be what
you are looking for.
--
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| Matthew Lybanon | lyb...@nrlssc.navy.mil |
| Mapping, Charting, & Geodesy Branch | |
| Naval Research Laboratory | (228) 688-5576 |
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=================================================================
Paul Arendt
>What is the vector form of the basic equations of fluid mechanics...
>
>...maybe someon could
>point me to a book that gives a thourough, slow paced introduction of indices
>notation and tensors. Preferably such a book would focus on this topic and
>not have a specific application (like fluid mechanics) as a major goal of
>the book.
For index notation and tensors, the Shaum's Outline on Tensor Calculus
by David C. Kay is very thorough and chock full of worked examples.
But you can have your cake and eat it too: there is a Dover (cheap!)
book called "Vectors, Tensors, and the Basic Equations of Fluid
Mechanics" (or something very close to that). I don't recall the
author's name.
Christopher Tong
> But you can have your cake and eat it too: there is a Dover (cheap!)
> book called "Vectors, Tensors, and the Basic Equations of Fluid
> Mechanics" (or something very close to that). I don't recall the
> author's name.
The author is Rutherford Aris. Good book.
Robert Martinez
Paul Arendt wrote in message <8jgdr0$a37$1...@newshost.nmt.edu>...
>WJPII <wj...@aol.com> wrote:
>>What is the vector form of the basic equations of fluid mechanics...
>>
>>...maybe someon could
>>point me to a book that gives a thourough, slow paced introduction of
indices
>>notation and tensors. Preferably such a book would focus on this topic and
>>not have a specific application (like fluid mechanics) as a major goal of
>>the book.
>
>For index notation and tensors, the Shaum's Outline on Tensor Calculus
>by David C. Kay is very thorough and chock full of worked examples.
>book called "Vectors, Tensors, and the Basic Equations of Fluid
>Mechanics" (or something very close to that). I don't recall the
>author's name.
>
The author's name is Rutherford Aris and you can get it at your local Barnes
& Noble for $10. It's very well written.