- #1

sadegh4137

- 72

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whats's the physical meaning of curl?

and why it is a vector?

it's definition is line integral per volume. i can't understand why this is a vector.

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- Thread starter sadegh4137
- Start date

- #1

sadegh4137

- 72

- 0

whats's the physical meaning of curl?

and why it is a vector?

it's definition is line integral per volume. i can't understand why this is a vector.

- #2

HallsofIvy

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In particular, we can apply the curl of a vector to fluid motion- if [itex]v(x, y, z)[/itex] is the velocity vector of water, say, so that v is depends on the position but not time, the [itex]curl v= \nabla\times v[/itex] describes the "rotation" of the fluid. It is a vector because its direction shows the axis about which the fluid rotates while its length is the speed of rotation.

- #3

arildno

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- #4

K41

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We refer to to twice the angular velocity as "vorticity" and a fluid element which has zero vorticity is said to be irrotational. This means, in very basic terms that if we have a body axis (on the plane of the page)

Note, we can still allow for some distortion in the shape but this is a little harder to explain without diagrams (but its essentially related to having components of vorticity whereby you they still have a finite derivative but the two derivatives cancel when finding the curl since they are the same - this means we have a regular change in shape but zero total angular velocity here).

Regarding curl itself applied to fluids, the components of curl are actually the direction of the axis about which the rotation component is occurring.

- #5

Edgardo

- 705

- 15

Here's an intuitive explanation of the curl: http://youtu.be/Mt4dpGFVsYc

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