Two-point correlation to identify vortex cores

Hello everyone,

I am trying to imitate the follwing:

Source: Wang, J. S., Feng, L. H., Wang, J. J., & Li, T. (2018). Görtler vortices in low-Reynolds-number flow over multi-element airfoil. Journal of Fluid Mechanics, 835, 898-935.

Which is to findthe two-point correlation functions between swirling strength and velocity for estimation of the conditionally averaged velocity field given a vortex core.

I have multiple files that contains velocity and location at different time steps, I can also use image processing as well if nessecary.

Any idea if there is a matlab package out there that could help do such thing?

Appreciate your help and thank you!

Answer 1

[Ayush]

Hi Hussein,

I understand that you need some direction as to which MATLAB packages to utilise to find two-point correlation for identifying vortex cores.

The following MATLAB functions and their corresponding toolboxes can be utilised for your use case:

1. The “imread” and “imgradient” functions from the Image Processing Toolbox can be used to process the images and extract relevant information that could be helpful for vortex detection. Please refer to the below documentations to know more about the “imread” and “imgradient” functions respectively:

- https://www.mathworks.com/help/matlab/ref/imread.html

- https://www.mathworks.com/help/images/ref/imgradient.html?s_tid=doc_ta

2. The “xcorr2” or "xcorr” functions from the Signal Processing Toolbox can be used to determine the correlation between swirling strength and velocity for estimation of a given vortex. Please refer to the below documentations to know more about the “xcorr2” and “xcorr” functions respectively:

- https://www.mathworks.com/help/signal/ref/xcorr2.html?s_tid=doc_ta

- https://www.mathworks.com/help/matlab/ref/xcorr.html?s_tid=doc_ta

3. The “corr” and “corrcoef” functions from the Statistics and Machine Learning Toolbox can be used to define a coefficient matrix for the correlations between swirling strength and velocity which would be useful to indicate vortex cores. Please refer to the below documentations to know more about the “corr” and “corrcoef” functions respectively:

- https://www.mathworks.com/help/stats/corr.html?s_tid=doc_ta

- https://www.mathworks.com/help/matlab/ref/corrcoef.html

I hope it helps,

Regards,

Ayush Misra