[MUSIC] So how does the Coriolis acceleration affect flows? It's a really interesting phenomenon known as geostrophic motion. So imagine that you have some sort of a push force. So this could be high pressure on one side of a column of gas and low pressure on the other. Or it could be wind blowing over the surface of the water intending to push the water in some direction. So what the water does initially, if you push it in some direction, is it goes in that direction, in the same direction as you push it. And when it starts going in that direction, you arise a Coriolis acceleration which is always going at 90 degrees to the direction that it's moving. So what this is acting to do is pull the direction of the flow around, to rotate it, the same way as the direction of the ball in the merry-go-round was deflected by the Coriolis acceleration. So after a little while, the flow is not going the same direction as you're pushing it anymore. It's sort of rotated off to the side and the Coriolis is always following the flow here, and eventually you end up with the equilibrium state which is what it sort of relaxes to and then stops changing. So it can stay in this equilibrium state forever, where the flow is actually astonishingly going at 90 degrees to the side of the way you are actually pushing it. And in this way, the Coriolis, which is 90 degrees then to the flow, is now pushing back, exactly counteracting the push force. And so that's why this is equilibrium, because those forces can cancel each other out. You can't even look at a weather map without seeing the effect of geostrophic motion. So a hurricane is basically a hole in the atmosphere where the pressure is lower, the atmospheric pressure, than it is in the surrounding air. So you remember that the pressure is just the result of the weight of the air on top of your head in the atmosphere, and so this low pressure at the ground, in the center of a hurricane just means that there's less air piled up there. And the difference in the air pressure is leading to a push force going from high pressure to low pressure. So, you would think in a non-rotating frame, if you had higher pressure of gas here and lower pressure there, it would just go from the high pressure to the low pressure and fill in the whole. But due to the geostrophic motion, you have the flow in the atmosphere is going at 90 degrees to the way you're pushing it. It's going around like this. And then where the flow is going in this direction, the Coriolis is pointing at 90 degrees to that. And so the Coriolis is reaching this state of equilibrium, where it's pushing back against the push force in the geostrophic equilibrium. So it is as if you made sort of a hill side or a dip in a membrane or something like that and you set a marble on it. And in a non-rotating frame it would just roll to the bottom of the hill. But in a rotating frame, it doesn't go the way you're pushing it. It goes sideways to it, and so it goes around and around and around. Only very slowly does it go down. And this is why hurricanes last as long as they do. There's also a feature on Jupiter called the Great Red Spot, which as far as we know has been there for centuries. And it's just one of these sorts of systems where the pressure imbalance and the flow going around and around and around in geostrophic motion, and that's why it can last for so long. You also see the effect of geostrophic motion in ocean flow. So the Gulf Stream is a giant river of water in the North Atlantic. And actually the sea level is about one meter higher on one side of the Gulf Stream than it is on the other, which, it's a very wide feature so you never see a wall of water a meter high, it's too spread out to be that obvious. But you can measure it, and if you measure also the pressure at some level underneath the ocean level, you have higher pressure here where the sea level is higher because you have more stuff over your head than you do here where the sea level is lower. So you have a pushing force going in this direction, and then in geostrophic motion you have the Gulf Stream, which is an arrow going into the board here, at 90 degrees to the direction that you're pushing it. So in order to simulate the way that the atmosphere and the ocean carry heat from the low latitudes to the high latitudes, we have to understand about how flow occurs on a rotating sphere. [MUSIC]
