Fair weather electric charge transfer by convection in an unstable planetary boundary layer

Abstract

A second-order-closure model for the upward turbulent transport of electric charge in an unstable, atmospheric, boundary layer is developed. The model identifies the surface fluxes of heat and momentum and the thickness of the "mixed layer" as the primary meteorological parameters determining the strength of this convection current. The planetary boundary layer is shown to function as a local generator, mechanically producing an electromotive force (EMF) which opposes the normal downward charge in fair weather. Numerical solutions of the model show that this EMF can apparently become as large as 130 kilovolts in cases of extreme instability, reducing the net downward current density locally by about 44%.Two charge sources near the surface are considered for this model. The Blanchard bubbling effect applies only over the oceans, where it is shown to be less important than the electrode effect as a source for convection currents. The largest convection currents are predicted over land, where very unstable mixed layers can form due to strong solar heating during the daytime. The intense convection in these layers generates substantial EMF's with the charge provided by the electrode-effect source.A simplified version of the turbulent electrode effect is developed for use as a charge source in the convection-current model. Asymptotic analysis is applied to the conservation equations for small ions to show that the conductivity profile in the electrode layer becomes independent of the conduction process in the limit of strong turbulent mixing. In this limit, which is found to be applicable to the atmospheric boundary layer under most circumstances, the electrode effect can be described simply by a charge-conservation equation with an externally determined, mean conductivity profile decreasing to zero at the surface.The convection currents predicted by the second-order-closure model, together with information about the columnar resistance, should explain the hitherto poorly understood diurnal variations of electric field and current density observed at land stations.

The influence of convective current generator on the global current

“…where z 0 is roughness scale of the Earth's surface (z 0 ≈ 2.5×10 −3 m) (Monin and Yaglom, 1965;Willet, 1979), in this case is E (z)=Ē…”

“…This system of equations may be supplemented with the equation determining the density of turbulent electrical current ρ v z . For its estimation one may use either diffuse approximation: ρ v z =−D T (z) ∂ρ ∂z or develop the method of its estimation based on the closure of correlation moments of the third order, as it was done for convective-unstable boundary layer (Willet, 1979). The results of computer simulations considered in this paper have show that for convective-unstable boundary layer with inversion: K=4×10 −4 m −1 for H =10 3 m. All other stratifications of boundary layer give the values of K much higher than the value of K for convective-unstable boundary layer.…”

“…(3) has been obtained by the presentation of quantities f =f +f and averaging the initial equations in horizontal plane:f = 1 S f dS (Monin and Yaglom, 1965;Willet, 1979).…”

Studies of an artificially generated electrode effect at ground level

“…This problem has to be considered in at least a two-dimensional approximation, taking into account the limited volume and the wind passing through. One-dimensional theories of the electrode effect have been developed by many investigators (see Hoppel, 1967;Willett, 1978Willett, , 1979Tuomi, 1982). We will assume that in the absence of an electric field supplied between the grid and the ground, the space charge under the grid is distributed uniformly.…”

“…Israel, 1971): the imbalance between positive and negative atmospheric ions, related to the atmospheric electric field in the surface layer. The mathematical description of the electrode effect under convection and turbulent mixing is given by a number of authors (Chalmers, 1967;Hoppel, 1967;Willett, 1978Willett, , 1979Willett, , 1983Tuomi, 1982). However, the results of numerous experiments are confusing.…”