Does the Sun orbit the Milky way in a (kind of) flat or inclined orbit or more of a sine wave? I know it can't be a perfect ellipse or smooth orbit due to all the matter in every direction, and our Sun could be affected by a gravity assist of sorts if it passes close enough to another massive star. I also know that galaxy orbits are different than Solar System orbits because most of the mass is in the dark matter halo and as a result, the outer stars orbit faster than in a standard orbit, so there's a number of variables.

But, if we ignore gravity assists, is the sun mostly in a standard, or lightly inclined orbit around the center of the Milky way or more sinusoidal?

Reason I'm asking - see (attached and in my opinion, bad) article, and picture included.



I've seen pictures like this before that suggests that the Solar System moves in a kind of sine wave motion. I've seen estimates between 26 and 32 million years with the solar-system, rising above then below the plane of the Milky way with consistency (and perhaps, mass extinctions tied to this movement).   

I can kind of see that happening, as the sun rises above it might have more gravitational pull below it drawing it back down and you kind of have a horizontal velocity to displacement cycle creating a sine wave in the orbit. That makes logical sense, but I'm wondering if that 26-32 million year sine wave type of movement is generally accepted or more somebody's imagination. Is anything definitive known about stars' orbits within galaxies?
It is correct that the sun bobs "up and down" (relative to the plane of the galaxy as it orbits the galaxy, and it takes about 64 million years  to complete a full cycle, so it does pass through the plane of the galaxy every 32 million years or so (there are quite large error bars on those numbers.) 

This idea is uncontroversial, but it gets caught up in other theories that are less well established (for example the idea that there are dense clumps of dark matter in the galactic plane, that can have disrupt the Oort cloud, or otherwise cause mass extinction) or are simply nonsense (the idea that the solar system is a "vortex").

Phil Plait rubbishes this second idea on his blog, and includes some further discussion of the "bobbing" path of the sun. He notes that the disk is about 1000 ly thick, and we bob up and down by about 200 light years every 64 million years.

Lisa Randall's is a serious scientist, who would have no truck with "solar system vortices", and the ideas in her book are reasonable, but not uncontroversial. We have no evidence of dense clumps of dark matter, nor do we know exactly where the Earth was 65 million years ago. We last passed through the galactic plane about 3 million years ago, without serious consequences.