# What is Vorticity: Definition and 32 Discussions

In continuum mechanics, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along with the flow. It is an important quantity in the dynamical theory of fluids and provides a convenient framework for understanding a variety of complex flow phenomena, such as the formation and motion of vortex rings.Mathematically, the vorticity

ω

{\displaystyle {\vec {\omega }}}
is the curl of the flow velocity

u

{\displaystyle {\vec {u}}}
:

ω

×

u

,

{\displaystyle {\vec {\omega }}\equiv \nabla \times {\vec {u}}\,,}
where

{\displaystyle \nabla }
is the del operator. Conceptually,

ω

{\displaystyle {\vec {\omega }}}
could be determined by marking parts of a continuum in a small neighborhood of the point in question, and watching their relative displacements as they move along the flow. The vorticity

ω

{\displaystyle {\vec {\omega }}}
would be twice the mean angular velocity vector of those particles relative to their center of mass, oriented according to the right-hand rule.
In a two-dimensional flow,

ω

{\displaystyle {\vec {\omega }}}
is always perpendicular to the plane of the flow, and can therefore be considered a scalar field.

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1. ### How did they get that the vorticity = 2##\omega##?

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3. ### Vorticity and Curl of Velocity

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4. ### Proving Vorticity of Flow in Rotating Cylinder

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5. ### Compressible inviscid vorticity convection w Rankine Vortex

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6. ### Invariance of direction of vorticity

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7. ### Why Prandlt Mixing Length Theory works at all?

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8. ### I Degredation of a Circular Flow

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9. ### Discover the Lagrangian for 2D Vortices | Essential Homework Equations

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10. ### Unsteady vorticity transport equation: codes available?

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11. ### Divergence of vorticity vector is zero--intuition behind it

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12. ### Interpretation of vorticity with non-vanishing strain tensor

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13. ### Fortran How to calculate vorticity using fortran

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14. ### Vorticity and Flux of Vector Field ##\vec{f}## Explained

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15. ### Fuids - vorticity from viscocity

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16. ### Does this vorticity plot make sense?

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17. ### Velocity and Vorticity of a Tornado Calculation

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18. ### Fluid Dynamics - Spanwise Vorticity of Turbulent Boundary Layer

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19. ### Calculating Potential Vorticity of a Parcel of Air

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20. ### Solving the Vorticity Equation for Flow: Why Use This Method?

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21. ### Calculating Vorticity of 2-D Flow Motion

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22. ### Differing definitions of expansion, shear, and vorticity

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23. ### Vorticity of Aircraft Trailing Vortices

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24. ### Vorticity and Stokes theorem

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25. ### Evaluating Vorticity in a Parallelepiped Domain

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26. ### Stokes' theorem Vorticity problem

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27. ### Vorticity boundary condition

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28. ### Proving Fluid Flow Velocity & Vorticity Equation

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29. ### Vorticity Diffusioin Homework: Steady State Solution

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30. ### Aircraft wings - Kelvins Circulation Theorem and the conservation of vorticity

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31. ### Vorticity is equivalent to angular momentum?

Hi all. In Fluid dynamics, is vorticity equiavlent to angular momentum? It seems that vorticity is twice of the rate of rotation of a fluid element at a point, and angular momentum is the density times the rate of rotation of a fluid element, so they just differ by some constant? But it is...
32. ### Vorticity where angular velocity is function of r

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