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wrote:
hi
quickly, what's the difference between Lagrangian velocity and Eulerian
velocity?
I think I understand Lagrangian velocity, but what's Eulerian velocity?
(context: fluid kinematics)
The difference is the frame of reference. Eulerian coordinates are
fixed in space and the fluid moves. So the velocity has to take into
account that a volume element may undergo deformation in addition to
gross motion, and this is written as D/Dt, where D/Dt = @/@t + V*del,
where @ = partial and del = gradient. In english, D/Dt has two
components that can be explained easily like this-
D(the weather)/Dt = @(the weather)/@t + v*del(the weather), which means
the weather changes both by sitting still and letting the weather change
(@/@t), but the weather can also change by getting on a plane and going
somewhere else (v*del(the weather))
Sometimes D/Dt is called the "material derivative" or "total derivative".
Lagrangian coordinates move with the fluid element, and so one needs to
keep track of how the coordinates change in time with respect to an
initial set of coordinates, which is the Jacobean, Reynolds transport
theorem, stuff like that.
There is no real difference between the two- they can be transformed
into each other. Sometimes it's more convenient to work in Eulerian
coordinates, sometimes Lagrangian coordinates.
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
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