Is there a reliable way to identify regions with negatively-correlated winds?
My suggestion would be to do a Principal Component Analysis (PCA) or Empirical Orthogonal Functions (EOF) analysis on the wind data. The result of the analysis would be a set of modes of variability. You would be looking for modes that show areas that are large in magnitude but out of phase. As for the time scale, you need to check the eigenvectors and eigenvalues of the analysis to determine the scale of temporal variability.

You can find appropriate code in many places, for instance here.