Cyclopian Cyclones

For the past 2 weeks, I've been struggling with a question from Papou, as well as struggling with a stomach bug which probably didn't help, but I finally have an answer! Papou wondered, How does the Coriolis affect hurricanes in the northern hemisphere and what is the percentage centrifugal velocity increase/decrease at the eight points on the compass assuming the hurricane is moving directly East to West?

Coriolis force is one of the fictitious forces that appear in a rotating reference frame, along with the centrifugal and Euler forces. If you look at articles on why hurricanes spin the way they do, they'll give explanations about how the speed of the Earth's rotation varies depending on how close to the pole you are, which causes the Northern edge of the hurricane to be pushed one direction, and the Southern edge pushed the other way. This explanation makes sense, but it didn't fit with my algebraic understanding of the Coriolis force.

If you look up the equation for the Coriolis force, you'll see it stated as

where Ω is the angular velocity of the rotating frame (for Earth, 2π/day), and v is the velocity of an object in the rotating frame. You may notice, there's no mention of radius here, which is why I was confused by the articles I was reading.

I decided to follow the default route for Physics: Simplify until things make sense! Let's imagine a hurricane directly over the North Pole. A key feature of hurricanes is the eye, which is a region of low pressure at the center. Low pressure in the middle means air will tend to flow from the outside in. As that air accelerates though, it will have a velocity perpendicular to the angular velocity, which is pointing straight up in this case. That will cause the Coriolis force above to push the air in a counter-clockwise direction, exactly what we're expecting.

I tried to put together a full simulation of the pressure difference driving the air inward, but then being balanced by the Coriolis force spinning it in a circle. Unfortunately, I couldn't come up with a model of the pressure that didn't vastly overpower the Coriolis force, so I ended up simplifying things a bit more: We assume the pressure difference causes a constant force inward, and then see how that changes under the effect of the Earth's rotation vector, projected into the local plane of Florida (27.7° N latitude):

For this simulation, I used a diameter of 300 miles and a Category 3 windspeed of 120 mph, but again, I had to fudge a bit to get things to work.

As for the second part of the question, centrifugal force doesn't really come into things here. For most places on the Earth, centrifugal force points upward, so its only effect on the hurricane would be a vertical circulation of the air. That may have an effect in reality, but I'm only considering a 2D model here, so it doesn't really apply.

I always have a hard time picturing these 3D systems, with interacting vectors and different reference frames, but I hope I've given a reasonable explanation for how these types of weather events form. I'm betting there's a way to connect my understanding of Coriolis forces to the one commonly given, but I can't puzzle it out. Thanks for another great question, Papou!