Why do wood pigeons behave like this?

I just saw two wood pigeons do this -

For about 2 seconds, they appeared to be viscously attacking each other, as they seemed to be hitting each other with their wings.  It looked like quite a scrap.

Then, very soon afterwards, one of the pigeons was "bowing" to the other one.

Then, very soon afterwards, the pigeon that was not doing the bowing movement made the familiar call of "woo woo woo-woo-woo woo".

What's going on please?  Thanks a lot.