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 $ΔT_s$ 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 $L$ of Hadley cells via a relationship between $ΔT_s$ and surface pressure difference $Δp_s$: an upper limit exists when $Δp_s$ does not grow with increasing $ΔT_s$. 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 $L$ and reaches zero for the largest observed $L$ 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 $Δp_s$ and $ΔT_s$ to kinetic energy generation are evaluated: $ΔT_s$ dominates in the upper atmosphere, while $Δp_s$ 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.

26 pages, 9 figures, 2 tables; re-organized presentation, more discussion and a new figure (Fig. 4) added; in Fig. 3 the previously invisible dots (observations) can now be seen

References in corpus (1)

• Comment on "The Tropospheric Land-Sea Warming Contrast as the Driver of Tropical Sea Level Pressure Changes" by Bayr and Dommenget

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