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This is an area near the equator where winds can be very erratic with long periods of calm. This is where the northeast and southeast trade winds meet. These air masses rise as they are heated by the sun, so there is little wind moving along the planet surface. Ships that sailed by wind were usually stranded here, hence the connotation of the term used when people's lives are stagnant. Tropical storms often form in this region due to the low air pressure, and high dew point.

ASCII Art diagram:

          

              air mass           air mass      
SE trade wind           __-^-__              NE trade wind
  --------->     ____--'       `--____       <---------
             ---'       doldrums      `----  surface 
                           |
                           |
                           |
                           |
                           | <-- equator