This is about the simplest example of a non-linear flow regulator. A right triangle opening. Since the angles are equal, the area of the opening equals 1/2 the base times the height, the height and base are equal so area equals 1/2h^2.
This is the main part of the design of a number of fluid flow automatic controls. By having a spring control the pressure required to change the value of "h", the controller can be calibrated for a range of flow control provide the pressure of the fluid is regulated. If you consider the widest point of the base as the equator and the point one of the poles, you have one of the may control features of Earth's climate. The blue line would be the thermal equator or the hemisphere mean. As the average temperature of the hemisphere increases, the mean would shift toward the point or pole.
What may be harder to visualize is that there would also be a simple regulator in the atmosphere. Because of gravity, the air density decreases with altitude, the resistance to flow decreases with altitude or h. The atmosphere doesn't have an easy to determine base though. It would have its narrowest base at the global thermal equator and its widest base at the closest pole. Since the fluids vary from water to photons, what the fluid in question "sees" may not be what we might "see". For the system to be stable, all the fluids would have to "see" the same average area. So if you know what any one fluid "sees" you can estimate what all the other energy "fluids" would have to see on average, for the Earth to exist. Since the Earth does exist, this simple regulator can be the main module of a climate model.
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