RE: [asa] Freeman Dyson on Climate Change

Thanks George from points some of the exact solutions of the
Navier-Stokes equation.

Moorad

-----Original Message-----
From: George Murphy [mailto:gmurphy@raex.com]
Sent: Tuesday, April 17, 2007 3:09 PM
To: Alexanian, Moorad; PvM
Cc: wdwllace@sympatico.ca; asa@calvin.edu; Glenn Morton
Subject: Re: [asa] Freeman Dyson on Climate Change

----- Original Message -----
From: "Alexanian, Moorad" <alexanian@uncw.edu>
To: "PvM" <pvm.pandas@gmail.com>
Cc: <wdwllace@sympatico.ca>; <asa@calvin.edu>; "Glenn Morton"
<glennmorton@entouch.net>
Sent: Tuesday, April 17, 2007 12:14 PM
Subject: RE: [asa] Freeman Dyson on Climate Change

The Navier-Stokes equations are nonlinear, which have no known analytic
solutions. Therefore, one uses approximations to solve them, which
effects are no always clear to understand. Of course, I am not sure if
one knows all the physics that may be contained in the Navier-Stokes
equations. For instance, can it explain turbulence?

There are exact solutions of the N-S equation: The steady flow of an
incompressible fluid between parallel plates or through a pipe with
cylindrical cross section are examples in which the nonlinear terms are
zero. There are also a few problems that can be solved exactly when the

nonlinear terms don't vanish: Section 23 of Landau & Lifshitz' _Fluid
Mechanics_ gives a few. They are highly idealized, & the flow will be
unstable for sufficiently large Reynolds' number, which gets into the
problem of turbulence. L & L address that in Chapter III.

Shalom
George
http://web.raex.com/~gmurphy/

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Received on Tue Apr 17 18:30:31 2007