NONLINNEAR ELECTRICAL PROCESSES IN FOGS AND CLOUDS
Department of Earth Science, Meteorology, Uppsala University, Uppsala, Sweden
In the present paper we treat electrical processes in radiation fog and clouds in weak convection. The cloud formation has in a long time been an important part in the meteorological research. The study of the properties and behaviour of fog is also important in consequence of the economic and hygienic results which follow the incidence of dense fogs. We often define fog as a surface cloud sufficient thick to cause hindrance to traffic. In fog the combination of point discharge and chemical processes can also play a role from environmental point of view, see Borra et. al., (1997).
Very few processes are linnear in atmospheric physics and especially when electrical processes are added. In many cases the turbulence is also included causing a more stochastical structure of the phenomena. In the atmosphere we have in the lowest layer (less than 1 mm) molecular diffusion and in the layer up to about 100 m logarithmic types of wind profiles determined by the turbulence caused by the friction. From 100 to about 1 km the Ekman wind spiral dominates the wind stucture. In the free atmosphere with negligible friction the geostrophic wind structure dominates the motion. Non of them are hence linnear.
Since the time of Benjamin Franklin the observational problem is now being remedied by modern instrumentation. But the charging mechanisms in clouds and fogs are numerous. Some are simple and whereas others are very complex. Several important mechanisms are poorly understood.The electrification of fog and weak clouds is, therefore, still less than perfectly understood. There is also still currently much debate about the physical process by which lightning initiates in thunderstoms. In the last 30 years projects have focused on the complex interaction between cloud dynamics, microphysics and charging processes that lead to strong electrification. The processes are strongly nonlinnear. Clouds involve rapid vertical rearrangement of deep air layers. Large processes promote and shape air motions. These processes control development of precipitation. About 85 % of the atmospheric mass is located in the layers below 13 km. The vertical circulation of air in clouds is a result of density differences.The imbalance due to the density differences is represented by a net upward force. These processes are also nonlinnear.
There are two major categories of charging mechanisms in clouds: the micro-scale separators and the cloud-scale separators. The first category includes creation of ion pairs and charge separation in the small turbulence scale. Electification on the cloud scale is connected to more large scale turbulence; thermic turbulence or convection.
When a charge is attached to water drops the relative motion between the charge and the atmosphere (mobility) becomes exceedingly small compared to the ionic mobility, and the transport of charge is determinde by the turbulence of the atmosphere itself. If we only take charge diffusion in consideration the ion-transport equation on the microscale near a cloud droplet gives the charge flux or the current density for a ion component Ji as:
Ji = ρiU + ρiBiE - Di ρi (1)
where ρi is the ion-charge density, U is the air velocity, Bi is the ion mobility for small ions and D molecular diffusivity. If we instead study large-scale transport of ions it is characterized by currents from bulk and eddy transport of ions along with the field- driven drift. In this charge-flux equation the term Di ρi vill now be repaced by K ρi, where K is the eddy diffusivity. The above charge process includes nonlinnear terms.
The distribution and motion of the electric charge in and around a cloud is complex and changes continously as the cloud evolves. But we have still a rudimentary picture of how charge is distributed.
On the other hand electrical forces can shape air motion. Previous studies (Jonsson and Vonnegut, 1993) have shown that even small whirlwinds can also be created under the influence of an electric field.
In the large scale the persistence of fog is always remarkable when one considers that the particles of fog clouds, however, small they will be, must be coninually sinking through the air which holds them. There is still controversy in the litterature concerning radiation fog formation. One set of observation suggests that fog forms during a lull in turbulence, while other observations suggest that increased turbulence leads to fog formation. But we now know that the radiation cooling and the turbulence is controlling the formation of radiation fog. About 1 hour before the sunset the negative radiation balance leads to a cooling and the weak turbulence is controlling the formation of the fog. The fog formation starting above the ground and an attachment of ions to the fog droplets occurs, which leads to negative space charge density in the fog, 30 – 100 pCm-3, and a sedimentation current on
average -1.4 pAm-2.
Before the formation of radiation fog the conditions are determined by a strong electrode effect, where the balance equation for the small ions is included. It can be given by:
dn/dt = q – αn2 –βnZ (2)
where n is the small ion number density, q is the ionization rate, α is the recombination coefficient for small ions, Z is the particle concentration, and β is the effective ion-aerosol attachment coefficient. This ion formation is also connected to nonlinnear processes.
Variations that depend on time or height are variations that are assocoated with a specific phenomenon . The most well known is the atmospheric electric fog effect in advection fog. The conductivity decreases markedly in fog and that the start of the decrease may precede the actual fog onset.
The formation of fog over land seems to be an even more complicated process than over sea due to the more complex surface conditions over land. Periods of significant radiation fog developments appear when the wind speed at 10 m level is about 0,5 to 1 m/s. In the fog the intensity of the the electric field pulsation increase by more than an order of magnitude and the spectral properties indicate an ordinary chaotic turbulent structure. There is also in radiation fog a distinct tendency of quasy-periodic oscillations of the electrical parameters on a time scale longer than 10 minutes.
The travel was supported by The Swedish Foundantion for International Cooperation in Research and Higher Education.
1. J-P. Borra, R.A. Ross, D. Renard, H.Lazar, A. Goldman and M. Goldman, J. Phys. D:
Appl. Phys. 30 (1997), 84-93.
2. H.H. Jonsson and B. Vonnegut, J. Geophysical Research, 1993, Vol. 98, 5245-5248