Given a pair of particles released at time t = 0 from a localized source. I would like to study the evolution of the mean-squared-angular velocity with respect to time for a given separation (for example r = 100 spatial units). Data obtained from fully resolved numerical simulations give at every time step the particle pair position and the three velocity components. My question is to know whether the following formula could be applied (please see below) in order to compute the angular velocity vector of the “rod” formed by these two particles. I don’t know if the dilatation / strain effects are included or not since the distance between the two particles is allowed to change with time. Any help would be highly appreciated! Thank you!
Dear Mohamed.
Thank you for your answer. However, the variables are all defined in the frame of reference and I would like to find out the rotation of the frame of our system relative to the frame of reference. Do you have any technical suggestion for the expression of omega including the strain?
Thank you Aria for the links. Mohamed has right when he told me that the strain effect has not been included in the formulation. I think now that Jeffery equation could solve the problem. I can extract the rotation component knowing the two velocity and positions. Please see the attached file herewith. I tried to use this formulation for simple analytical motions and I can nicely extract the rotation of the pair!
Thank you for your help!
best!!
a
Dear Bernd,
The particle pairs are released from sources and the initial separation in of the order of the Kolmogorov dissipative scale. These are just numerical experiments based on the resolution of the dynamics equations (DNS). They already gave a nice evolution of the mean-squared-separation.
Yes, exactly. In order to study the particle dispersion in 3D incompressible homogeneous isotropic turbulence. I used the formula indicated in the 4th answer, to compute just the rotation term and I get powerful results!
Hi Abdallah, I assume you mean rms values so that a statistical theory could do the job. I attach a paper which may give you some basic ingredients. At least I know what I would have to do to answer your question and I would be happy to do it en detail but I have too many other obligations for the next two months. If you have specific questions about my text then send a direct mail to [email protected]
Cheers, Helmut
Thank you Helmut for the answer as well as for the paper.
best
a
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