Doldrums are caused by solar radiation from the sun. Because of this the sunlight beams warms the air and causes it to rise straight up instead of side to side (horizontally).
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The convection currents are formed due to heating of molecules.
When the liquid molecules are heated, the liquid becomes larger in size and lighter in weight. The heated molecules take up more space and rise to the top, while the cooler molecules comes to the bottom and takes the place. This cycle is known as the convection current.
Convection currents are the result of differential heating. Lighter which is less dense and warm material goes upward while on the other hand, heavier which is more dense and cool material sinks. This movement creates circulation patterns known as convection currents in the atmosphere.
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The iron in the earth's core is solid due to high pressure.
At the center of the earth is solid inner core, whose size is two-thirds of moon's size mad made up primarily of iron. The temperature in this core is equal to that of the sun's surface at 5,700 degrees Celsius. But the tremendous pressure caused by gravity prevents the iron from becoming liquid.
Surrounding this is the outer core made of nickel and small quantities of other metals and these remain liquid because the pressure here is a bit lower.