Hello there,
In your case, a particle system would be helpful, but you might not have access to that.
The way I would approach this would be by slowly building up layers of arrows via pre-comping. I’ve made an example AE project below for you:
To create the spirals of arrows, I would just take the same approach again, but this time, instead of beginning from a straight line, I would start from a slightly curved line and then begin building up the layers.
Using the turbulent displace effect in moderation can be powerful, too.
Good luck!