I quite like this;
Prop walk or transverse propeller thrust is caused by the helical discharge from the propeller and its interaction with the rudder and hull. With an ahead movement of a right handed propeller:
The helical discharge from the propeller creates a larger pressure on the port side of the rudder.
A slight upward flow from the hull into the propeller area puts slightly more pressure onto the down sweeping propeller blades.
The net result is a tendency for a right handed propeller to give a small swing to port when running ahead.
Transverse thrust is of much greater significance when using an astern movement. The helical discharge from a right handed propeller working astern splits and passes forward towards either side of the hull. In doing so it behaves quite differently. On the port quarter it is inclined down and away from the hull whilst on the starboard quarter it is directed up and on to the hull. This flow of water striking the starboard quarter can be a substantial force capable of swinging the stern to port, giving the classic kick of the bow to starboard. (With acknowledgements to The Shiphandler's Guide, by Captain RW Rowe, FNI, published by The Nautical Institute)
There is even a small chance if I read it enough times, I'll understand it.