That’s a really interesting question!

It’s important to note that hurricanes aren’t spiral-esque because they are heat engines. Hurricanes are heat moving engines in the sense that they are formed in part by thermal energy at equatorial latitudes and expend that previously thermal energy as wind and waves at higher-than-equatorial latitudes. But that is not why they are whirlpool shaped! Hurricanes are shaped like they are because they spin; they spin largely because of the Coriolis Effect, which is a force that arises from the Earth itself spinning.

Galaxies are fundamentally different creatures. Galaxies actually can’t really be compared to any other system we know of except for in some cases plasma. That’s because galaxies are not collisional systems. Basically the particles in a fluid, or the particles in the air, bounce off each other – they are “collisional.” That gives us some equations we can use to solve and describe what’s happening. While galaxies are full of stars, and sometimes the stars run into each other, the stars merge because they are born close to each other, and not because they’re acting like a gas. Collisions are how heat exchange happens between particles, so because galaxies aren’t collision, heat transfer doesn’t happen in the same way. Because the only relevant force is gravity, and galaxies are hundreds of billions of stars, we can’t describe what’s happening in neat equations and we have to use simulations, which are incredibly computationally expensive. TLDR; All that to say, galaxies are super weird, and it’s really hard to study why they look like they do, but they can’t really be compared to hurricanes because the underlying physics is so different.

We don’t have great theories for why spiral arms exist – or really, why they persist – they should go away pretty quickly! But generally speaking, hurricanes and galaxies look similar because they’re both spinning disks. But neither hurricanes nor galaxies look the way they do because of heat transfer!