I'll try complement the current answers with a bit of fluid mechanics intuition. (You can replace "particle" with "boat" in what follows.)
You are using a simple transformation but not the simplest vector field (the identity), so maybe this makes it a little harder to visualize.
If you applied no transformations to this vector field, it would look like rays coming out of the origin. A plot like the one you are using can be thought of as the motion of a particle driven by the ocean's current with velocity equal to the value of the vector field in that point. A particle feeling this velocity-field would be driven outwards with a speed proportional to the distance from its position to the origin (that is, with increasing speed).
More specifically, let $O$ be the origin. This velocity field at a point $P$ can be visualized as an arrow starting from $P$ and extending in the direction $OP$ up to the point $2P$, so that the distance from the origin to the tip of the arrow is twice the distance form $O$ to $P$.
In the first case (90 degrees), the perpendicular transformation is strong enough to make it tangential to the circle with radius $OP$ centered at the origin. This makes the particle in the velocity field move along the circle, which is what your plot shows.
In contrast, the second transformation (30 degrees) is not as strong: it only deviates the arrow a bit in a counterclockwise manner (still starting from $P$). A particle feeling this rotated vector field will be carried away in a $30$-degree angle from the line connecting its position to the origin, and with a velocity equal to the distance from the origin. This can be seen in the plot: the distance traveled by the particle stays for a longer way in a simliar direction, so the curvature of its trajectory decreases while its speed increases.
If you want a clearer visualization of the transformation you could start applying it to a constant vector field and see what happens, or maybe one that varies only with $x$.