The “hidden torque”: the art, for a torque, to dominate everywhere and appear in no equation

Abstract

The effect of the superficial fluid layers (atmosphere and ocean) on the Earth rotation occurs by means of three torques: the pressure torque (or mountain torque) arising from a difference of pressure on the two sides of a mountain, the gravitational torque, due to the interaction between the Earth masses and the fluid masses, and the friction torque. For the equatorial component, the Earth bulge plays a very important role: there is a pressure torque acting on the equatorial bulge and a gravitational torque associated with the attraction of the Earth dynamical flattening (degree 2 order 0 form factor) by the fluid mass. Due to the large scale and the size of the bulge, this effect is dominant for the equatorial components of the torque. In all the atmospheric and oceanic Global Circulation Models (GCMs), the ellipticity of the Earth (and of its gravitational potential) does not appear explicitly in the equation/boundary conditions. It was already known from previous studies that the part of this torque due to the interaction of the fluid with the solid Earth is, nevertheless, to be accounted for in the angular momentum budget. In this paper, we extend this study to the additional atmospheric pressure torque due to the fact that the ocean surface is ellipsoidal, and show that this part is fully compensated by the Earth reaction to the associated ocean forcing. In the case of the ocean, we also discuss the source of this ellipsoidal torque geographically, using the output of the CLIO model.