What purpose have those grooves inside the dripper? I'm using the V60 dripper from Hario and was curious about the grooves inside the dripper. I think that they are present to slow down the water running through the filter and let the water pass as much as coffee powder as possible, but I'm not really sure. Is this really the intention of this grooves?
These grooves are for improving the flow of coffee through the filter. The grooves create space between the filter and the cone to permit little channels for the coffee to flow into the vessel after passing through the filter paper. I think the ridges also help "wick" the coffee away from the filter paper, helping the filter paper drain better.  

If the ridges are absent (as in Chemex cones, for example) the brewed coffee sometimes wells up between the filter paper and the cone. See also this question and my answer that compares the two styles of cones. 

As for the shape and location of the grooves, some are spiral-shaped, others are straight, staggered, etc. I don't notice any advantage of any style as long as they're present, and I suspect the shape and location is purely aesthetic or marketing, not significantly different in any functional way.  

EDIT: this article from Serious Eats suggests that the grooves additionally help "keep water distributed evenly among the bed of coffee grounds." Presumably this is related to the drainage I mention above, but was a more-legitimate source than my theories above, so I wanted to include.