I have three velocity components u, v, and w in one vertical flow facing plane. I want to measure a vorticity component for the same. As per my knowledge we can calculate one component only but in old literature I read they found 2 components of vorticity. My query is how to calculate it?
1st of all what do you mean by "3 velocity components in one plane"? If there are all three components of velocity vector, they can't lie in one plane obviously (2 components can of course be in one plane and if velocity vector field isn't potential it can have 1 component of vorticity, --perpendicular to the plane). In general case if velocity field is 3D, vorticity vector may have all three components (from definition of vorticity as a vector product of Nabla and Velocity vector: vort=Nabla x V(x,y,z).)
Alex i am using seven hole probe for the measurement of total pressure,static pressure,velocity. You might be knowing with seven hole probe you can measure all the three velocity component. yes it is but obvious we can plot only one vorticity component from this results but there is a well reputed thesis by Farmer. He used some logic behind it for calculation of three vorticity component. You can read
http://archive.org/details/inletdistortionv00farm
You may want to look at this MS thesis where a 7- hole probe is used to analyze flow properties of a turbulent flow in the wake of a 3-D bump. I believe some vorticity measurements are extracted from the velocity field.
http://tinyurl.com/ln2l3se
IF you have a field of 3d velocity vector you will have a field of 3d vorticy vector. but in your case that you have 3 velocity components in a 2d plane although 3 component of vorticity may exsist but you may be able to compute only one component ,the same as plane, i.e. if you have x-plane (plane normal to x axis) you can only compute x component of vorticiy since Omega_x = dw/dy - dV/dz. where W and V are component of velocity vector in z and y directions respectively.
If you wish to compute other component of vorticity you should provide aditional data for derivative computing.
@Alex: actually no!!! consider you have data in y palne (xz), to compute Omega_x you need dW/dy but continuity equation (dU/dx+dV/dy+dW/dz=0) only provide dW/dz NOT dW/dy !!!
Other than vorticity which parameter will give idea of low momentum fluid?
@Mohsen: Indeed so. You probably need more assumptions about the fluid flow under investigation...
Three velocity at a point or in plane ???? Given you have many points on a plane where you have the set of three components of velocity, you can take the gradients in the velocity component for two axes (the dimension of plane). For the third axis you need to traverse the probe in the third dimension so the planar condition mentioned fails.
So as per your constraints mentioned in the question you can check the nearest points on the plane and get the change in velocity components with respect to the distance (for both the axis on the plane). later you can play with the gradients to get at max two vorticity components.
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