[MUSIC] All right... We have seen that there are two fundamental concepts that we can not stop talking about them. They are related to marine circulation in a very important way, we spoke in the previous session of the force of the pressure gradient. The force of the pressure gradient remembers that it is a horizontal force that is generated because there are different pressures on the same horizontal surface. An isogeopotential call, iso that means the same thing, geopotential is the height within a field of gravity. And on the other hand we have the Coriolis force. Why is the sea inclined? We have the idea that the sea is always flat. Or it seems that we take it as a reference of the flat sea. Why? Because from a distance if we look at it and take the waves for the horizon, by definition, is what gives us the horizontal part. And yet, when we see the sea from the satellite or from another place, or do our calculations, we realize that the sea is not horizontal. That is, averaging, taking out the waves, taking out the tides, as it turns out that there are places where the sea is higher, others below. And therefore from what we have seen previously, there must be horizontal forces that would tend to make the sea outside the slope, or down the slope. And yet it stays this way, why is it always bombed? So here is a key concept that is Coriolis force, what is this force? This is a force that appears when there is movement by the fact that we see the circulation. From the sea or the atmosphere or the circulation of any object above the earth's surface. From our point of view we are with our feet on the ground. The head upwards which means just in the opposite direction to the direction of gravity. Well if we are standing gravity it would be like an arrow that would cross us from head to toe. This is the vertical axis defined by gravity and then there are horizontal axes that are simply horizontal but referring to our current position. But the earth rotates, the earth has rotation. Of course, the moving masses are just the same as they are in rotation, they tend to go in the direction they have to go. And yet, the axes of reference, with which we are seeing in motion, turn. If we turn, and the water is there, we see that the water moves. This is more or less where the subject of what is the force of Coriolis. We will also see that the Coriolis force is a force that is not the same everywhere in the world. At the equator is zero, at the pole will be maximum, but it depends on the speed. That is, when we are still there there is no force acting, and when we put a movement on us acts the Coriolis force. We do not notice it, logically, because we will see that it is of a very small magnitude. The Earth, therefore, tour and when we are somewhere on the planet. Let's put this gentleman on the pole or on the equator. And if we see what happens by turning the earth. Well, after eight-eighths of a lap, that is, a whole lap, this person will have made a turn on itself. But this not, this will have turned well with the planet, but on its vertical axis has not rotated. That is, he has not turned around. This has not turned, this has gone around. And if we were in an intermediate latitude, it turns out that for example at 30 degrees latitude this person would rotate once every two days. In fact, this is because the vertical, which is what marks the vertical axis in the reference axes above the earth. This we call the vector which gives the magnitude of the spin and the direction of this spin. Because it only acts in part and, in Ecuador does not act. That is, we have an important difference between what is this force in the Pole and in Ecuador. Let us now imagine that we are in middle latitude. We are like superman. We watch the sun rise and we catch a ball and we throw it with all our force towards the sun. We are above the Earth, in middle latitudes, in the northern hemisphere, this is very clear. How can we represent this? For we can represent it, first of all, with fixed axes in the sun. We are raised above the surface of the planet, we're like Superman and we throw the ball. What happen? That the ball evidently goes towards the sun, and that little house that was on the horizon moves, but we see that the ball goes in a straight direction towards the sun. This is when we see the movement from a distance from the planet, with some reference axes that are not rotating with the planet. What happens, however, when we do we take fixed axes of reference on the planet? What we see is that the one who moves is the sun. This is what we see. This is the way we want to understand and explain the world. So if now we throw the ball in this situation towards the sun, what will happen? For the ball turns to the sun, the house will always be in the same place and the ball will deviate. Of course, seen this way we would say: this ball deviates because there is a force that pushes it, that wall of force. We have to write this force, because we see it. But in reality we are moving. But if we want to represent well and do correct calculations, we have to put it in our representations with reference to our axes. And this force is important, not important, how it acts? In fact this force, we will see, that in this scheme, the deviation that occurs with a certain time T, This would be a hypothetical calculated distance, by the speed of the ball and the time that has elapsed, that is to say, the distance elapsed is u by T. The angle, this we can measure it this way because we know which is the deviation part of the angle that has traveled. Because we are at a certain latitude, and we have moved with a time T, we have traveled a certain angle, we have turned something. Therefore this twist we can calculate and this distance, this deviation can be calculated by simple multiplication of the radius by angle. This deviation, as we have accelerated, we moved the ball, we could assimilate it as the distance of a uniformly accelerated movement, with an acceleration 'a'. What acceleration is it worth? Because by replacing we realize that this acceleration is the speed of the ball twice Omega Phi sinus. That is, this part we will call you coriolis parameter and this is the speed of the ball. This acceleration is perpendicular to U. That is, it does not make the ball go faster or slower. All it does is push it aside. He pushes it sideways, so the ball we pull straight, but from our point of view, the ball is pushed with an acceleration that is exactly this. It depends, therefore, on the acceleration of the speed of the ball. The faster it goes, the greater the velocity of the deviation and according to this parameter of Coriolis. This parameter of Coriolis has some units that are the same as those of rotation, that is, the inverse of time. When we multiply by the speed will give us therefore an acceleration. It is null in Ecuador as you have seen, because here the vertical axis say, is following the line of the base of the turn. And it is worth average values in middle latitudes. We put numbers at a latitude of 45 degrees. Or a coriolis parameter of ten raised to minus four seconds, minus one. A sea current of 1 meter per second, would give us an acceleration of coriolis of the same. That is, average latitudes, a current of one meter per second is a strong current, it is a really important current. Like the one that might be from Gulf Stream for example. It would have a Coriolis acceleration that is of this magnitude. Of a magnitude that really corresponds to an almost imperceptible inclination. Imagine that we have the sea inclined, let's see what this component is worth which is the horizontal component that is the one that would move the water to the side, that is, to make it go down the slope, a very gentle slope. If we have a 'u' velocity stream, multiplied by the Coriolis parameter. It could be that this equals what the component would be, this component of gravity multiplied by the sine of this angle. Notice that this angle is not latitude or anything, but simply the angle of inclination. This would mean that there is a situation, where the current makes that the force of the pressure gradient is compensated for by Coriolis force. This is what is called a Geostrophic equilibrium, that is, is an equilibrium situation where a tilt of the sea could be maintained by the existence of a current that compensates with Coriolis this inclination. And if we put numbers here, we realize that a difference of ten centimeters in 100 kilometers, for example, gives a required current value of ten centimeters per second. Ten centimeters per is a typical current, that is, the water can be stopped, zero. And the water may move very fast, very strong currents, one meter per second. Most commonly it is between 10, 20 or 30. That is, between these two values is the majority of marine currents. And the inclinations that would correspond to a geostrophic balance with these velocities, are inclinations of this order of magnitude. What are 10 centimeters in 100 kilometers ?, very little. Indeed, in the Mediterranean for example, in this area, Barcelona is here, these are the Balearic Islands, if we make a section in this area. And we see the distribution of temperatures and salinities. We see that the Mallorca part of the water is less salty, in the part of the coast it is less salty. That is, we have modified Atlantic water in the south of Mallorca, we have water near the coast less salty, due to the rivers and the continental contributions. And the distribution of densities we have less dense water, and less dense in this part, denser waters here the surface of the water is, exaggerating much, greater here than here. That is, this is expanding, floating. And that means there is a pressure gradient force toward here and a pressure gradient force toward here. That they are compensated can be compensated by Coriolis forces, if the stream comes parallel to the coast to the south. And without advancing things, the current goes towards the northeast by the part of Mallorca. Now yes, we are actually talking about these slope currents, here would be the zone of modified water of the Atlantic, water of the coast, dense water in the center. And this is a typical residual current that occurs in these situations. That is, we have currents associated with a density difference. The water is more swollen here and here, than here in the center. This is something you've known about for a long time. This is a drawing corresponding to a publication of Chinikov of the year 1966, is of the first calculations that made, of distances between isobars. Made from data from boats, from campaigns where profiles were taken, of temperature and of salinity and were constructed, the density distribution was calculated. And the distance was calculated, summing the specific volumes, to see the distance that was between the isobara of 1000 meters, for example, and the isobara of 500, which is this case. And seeing these distances, one realizes that in this zone, the water is sunken and it is higher at the edges. Therefore, these arrows indicate which has to be the direction and the magnitude can be calculated from the current would compensate, that the current may not be exactly the same because there are more factors, more forces that act. But in principle, between 1000 meters deep or 1000 decibels and 500 decibels of pressure, this distance, the distribution of this distance gives us a topography, and this topography is related to circulation. And look, we talk about the circulation, of the water that enters here, the intermediate levantina. This cyclonic type circulation with a dense part in the center and a circulation approaching Gibraltar. This map is one of the first to be obtained, but of course, currently possible from satellite, or through tracks that go on their own, submarines, etc. One can have a lot more data and can have many more details of the circulation. But what is the overall global scheme, this is what was also done initially for the oceans. Therefore we have with this example the sample that the Mediterranean, it really is, it has all the ingredients of what a small ocean is. An ocean accessible to humans and actually across the history has taught us many things.