Circulation Definition: Understanding Positive, Null, and Negative Circulation

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In summary, positive circulation means the circulation is in the counterclockwise direction, negative circulation means the circulation is in the clockwise direction, and null circulation means there is no net rotational motion.
  • #1
Jhenrique
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1st which is the math definition for circulation (##\Gamma = \int_s \vec{f}\cdot d\vec{s}##)? And 2nd, what means positive, null and negative circulation?
 
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  • #2
The "math definition" for circulation is exactly what you give: [itex]\int \vec{f}\cdot d\vec{s}[/itex].

I think you mean a geometric or physical "interpretation" of the circulation. In that case, "circulation" of a vector function is the total of the components of [itex]\vec{f}[/itex] that are tangent to the circle over which you are integrating. Physically, it is the total motion around the axis (the line through the center of the circle and perpendicular to it).

"positive circulation" means the circulation is in the counterclockwise direction, "negative circulation" is in the clockwise direction, and "null circulation" means there no net rotational motion.
 
  • #3
Well, I can to compute the flux through of a closed or open surface, so, can I compute the circulation through of a closed or open curve too?
 
  • #4
You can certainly compute the line integral of a vector field over a closed or open curve...but in the case of an open curve, I don't think you'd call it "circulation" anymore.
 
  • #5
HallsofIvy said:
Physically, it is the total motion around the axis (the line through the center of the circle and perpendicular to it).

What circle?

Doesn't the expression make sense for arbitrary paths? Or, for that matter, arbitrary dimensions, so that the concept of "axis" won't necessarily make sense?
 
  • #6
chogg said:
What circle?

Doesn't the expression make sense for arbitrary paths? Or, for that matter, arbitrary dimensions, so that the concept of "axis" won't necessarily make sense?

I believe they are talking about the circulation of a fluid field, defined as the line integral of the velocity vector field around an (arbitrary) closed circle.

See: http://en.wikipedia.org/wiki/Circulation_(fluid_dynamics)
 
  • #7
Maybe I'm being too pedantic. By "circle", you just mean an arbitrary closed path, right?

If so, I do not see what value is added by introducing the concept of an "axis" in this situation.

Also in the "chogg being too pedantic" category:

HallsofIvy said:
"positive circulation" means the circulation is in the counterclockwise direction, "negative circulation" is in the clockwise direction, and "null circulation" means there no net rotational motion.

Wouldn't this be exactly backwards if the path is clockwise? Doesn't "positive" simply mean the net rotation is along the path, whichever direction the path takes?

Seems to me like it's more natural to express it relative to the path, instead of having to define what one means by (counter-)clockwise.
 

1. What is circulation and why is it important?

Circulation is the movement of something, such as air or water, in a circular pattern. In terms of weather, it refers to the movement of air in the atmosphere. Understanding circulation is important because it helps us predict weather patterns and understand how different factors, such as temperature and pressure, can impact the movement of air.

2. What is positive circulation?

Positive circulation, also known as cyclonic circulation, occurs when air moves in a counterclockwise direction in the Northern Hemisphere and clockwise in the Southern Hemisphere. This type of circulation is associated with low-pressure systems and often brings stormy weather.

3. What is null circulation?

Null circulation, also known as anticyclonic circulation, occurs when air moves in a clockwise direction in the Northern Hemisphere and counterclockwise in the Southern Hemisphere. This type of circulation is associated with high-pressure systems and often brings clear and calm weather.

4. What is negative circulation?

Negative circulation, also referred to as meridional circulation, occurs when air moves in a north to south or south to north direction. This type of circulation is often associated with extreme weather events, such as heat waves or cold snaps.

5. How do positive, null, and negative circulation impact the weather?

The type of circulation present in a given region can greatly impact the weather patterns in that area. For example, positive circulation can bring storms and precipitation, while null circulation can bring clear and calm weather. Negative circulation is often associated with extreme weather events, but can also bring a mix of different weather conditions depending on the specific factors at play.

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