How to find similar time series?
Since the time-series are annual, the data points you have for each time-series are limited and also quite distant (the values are 1 year apart). So I wouldn't use Dynamic Time Wrapping on your data. 

If you are interested in comparing the patterns, a very simple approach would be Pearson's correlation. Keep in mind that this will not compare the actual values but the patterns (i.e. if the values have similar fluctuations with the years, so for example time-series [1 2 3 4] would have higher correlation with [5 6 7 8] than with [1 1 2 2])

If you are interested in both values and pattern, I would use a distance-based metric: Euclidean Distance, Manhattan distance etc. I believe you will find this post interesting, where the mathematical background of similarity is explained. Also, python implementations of several distance metrics in python (including cosine-similarity) can be found in this blog-post.