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True Gravity in Atmospheric Ekman Layer Dynamics
  • Peter C Chu
Peter C Chu
Naval Postgraduate School

Corresponding Author:pcchu@nps.edu

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True gravity is a three-dimensional vector, g = igλ+jgφ+kgz, with (λ, φ, z) the (longitude, latitude, height) and (i, j, k) the corresponding unit vectors. The vertical direction is along g, not along k, which is normal to the Earth spherical (or ellipsoidal) surface (called deflected-vertical). Correspondingly, the spherical (or ellipsoidal) surfaces are not horizontal surfaces (called deflected-horizontal surfaces). In the (λ, φ, z) coordinates, the true gravity g has longitudinal-latitudinal component, gh = igλ+jgφ, but it is neglected completely in meteorology through using the standard gravity (-g0k, g0 = 9.81 m/s2) instead. Such simplification on the true gravity g has never been challenged. This study uses the atmospheric Ekman layer as an example to illustrate the importance of gh. The standard gravity (-g0k) is replaced by the true gravity g in the classical atmospheric Ekman layer equation with a constant eddy viscosity (K) and a height-dependent-only density ρ(z) represented by an e-folding stratification. New formulas for the Ekman spiral and Ekman pumping are obtained. The second derivative of the gravity disturbance (T) versus z, also causes the Ekman pumping, , in addition to the geostrophic vorticity with DE the Ekman layer thickness and f the Coriolis parameter. With data from the EIGEN-6C4 static gravity model, the global mean strength of the Ekman pumping due to the true gravity is found to be 4.0 cm s-1. Such evidently large value implies the urgency to include the true gravity g into the atmospheric dynamics.
27 Oct 2021Published in Journal of Geophysical Research: Atmospheres volume 126 issue 20. 10.1029/2021JD035293