Heat engines and heat pumps in a hydrostatic atmosphere: How surface pressure and temperature constrain wind power output and circulation cell size
Abstract
The kinetic energy budget of the atmosphere's meridional circulation cells is analytically assessed. In the upper atmosphere kinetic energy generation grows with increasing surface temperature difference \ Ts\ between the cold and warm ends of a circulation cell; in the lower atmosphere it declines. A requirement that kinetic energy generation is positive in the lower atmosphere limits the poleward cell extension \ of Hadley cells via a relationship between \ Ts\ and surface pressure difference \ ps\: an upper limit exists when \ ps\ does not grow with increasing \ Ts\. This pattern is demonstrated here using monthly data from MERRA re-analysis. Kinetic energy generation along air streamlines in the boundary layer does not exceed \40\~J~mol\-1\; it declines with growing \ and reaches zero for the largest observed \ at 2~km height. The limited meridional cell size necessitates the appearance of heat pumps -- circulation cells with negative work output where the low-level air moves towards colder areas. These cells consume the positive work output of the heat engines -- cells where the low-level air moves towards the warmer areas -- and can in theory drive the global efficiency of atmospheric circulation down to zero. Relative contributions of \ ps\ and \ Ts\ to kinetic energy generation are evaluated: \ Ts\ dominates in the upper atmosphere, while \ ps\ dominates in the lower. Analysis and empirical evidence indicate that the net kinetic power output on Earth is dominated by surface pressure gradients, with minor net kinetic energy generation in the upper atmosphere. The role of condensation in generating surface pressure gradients is discussed.
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