La corrélation d’espace du géopotentiel du niveau moyen

The statistical structure of the fluctuations of local changes in geopotential is studied using the equation gz = RT valid at the level of the so-called mean energy level of the atmosphere, which is also the level of geostrophic advection. It is shown that the two-dimensional random scalar field H(x, y) is anisotropic horizontally, that is to say, the correlation moment BHH of two points depends not only upon the distance r between them, but also upon the orientation of the straight line joining the two points in the horizontal plane. The explicit form of this dependence is given.

In order to evaluate the contribution of the non-linear term, one must introduce the advection equation and the assumption of quasi-normality, generally accepted in turbulence theory.

Finally, the particular case of a gaussian correlation function for the geopotential BHH(r) is envisaged.