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- Author or Editor: I. Tzur x
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Abstract
One-dimensional time-dependent models of warm and cold clouds were constructed to test the electrical and precipitation development in the presence of a variety of charge separation mechanisms. The, models simulate charging by ion diffusion, the Wilson effect (ion conduction), polarization induction, the Workman-Reynolds effect and the thermoelectric effect. It was found that charging by ion processes does not significantly contribute to the electrical development of either warm (shallow or deep) of cold clouds. In cold continental clouds, without ice multiplication processes, charging due to ice-ice collisions did not significantly contribute to the electrical buildup because of the low concentrations of ice particles and their low electrical conductivities at low temperatures.
The most significant charging resulted from collisions of ice particles and water droplets. These collisions produced strong charging by both the inductive and non-inductive processes. It also was found that when both polarization and the Workman-Reynolds effect operate together, strong Acids develop. The resulting locations of the main charge centers and the corresponding electric fields in the model are in agreement with many recent observations, pointing to the presence of a negative charge center around the −10°C level. The effect of corona discharge from the ground on the ion concentration and ion charging near and below cloud base, and on the electrical conductivities within the cloud, also were found to agree well with many recent observations.
Abstract
One-dimensional time-dependent models of warm and cold clouds were constructed to test the electrical and precipitation development in the presence of a variety of charge separation mechanisms. The, models simulate charging by ion diffusion, the Wilson effect (ion conduction), polarization induction, the Workman-Reynolds effect and the thermoelectric effect. It was found that charging by ion processes does not significantly contribute to the electrical development of either warm (shallow or deep) of cold clouds. In cold continental clouds, without ice multiplication processes, charging due to ice-ice collisions did not significantly contribute to the electrical buildup because of the low concentrations of ice particles and their low electrical conductivities at low temperatures.
The most significant charging resulted from collisions of ice particles and water droplets. These collisions produced strong charging by both the inductive and non-inductive processes. It also was found that when both polarization and the Workman-Reynolds effect operate together, strong Acids develop. The resulting locations of the main charge centers and the corresponding electric fields in the model are in agreement with many recent observations, pointing to the presence of a negative charge center around the −10°C level. The effect of corona discharge from the ground on the ion concentration and ion charging near and below cloud base, and on the electrical conductivities within the cloud, also were found to agree well with many recent observations.
Abstract
A time-dependent model that simulates the interaction of a thunderstorm with its electrical environment is introduced. The model solves the continuity equation of the Maxwell current density that includes conduction, displacement, and source currents. Lightning phenomena are neglected and the electric field is assumed to be curl free. Corona, convection, and precipitation currents are not considered in this initial study and their contribution to the source function is not specified explicitly. As a preliminary test of the model we assume that the storm is axially symmetric in spherical geometry, the conductivity depends only on the vertical coordinate, the ground is equipotential, and far from the thunderstorm region the horizontal electric field is zero. These assumptions are for computational efficiency only and can be relaxed in more realistic studies.
The mathematical energy method is applied to the continuity equation to determine boundary conditions that are sufficient to form a well-posed initial-boundary value problem. This ensures the existence of a physical solution that depends continuously on the initial and boundary data. Then analytic techniques are applied to study the dependence of the solution on the properties of the medium. There are two time scales of the problem that are analyzed and discussed: one determined by the background electrical conductivity and the other by the time dependence of the source function. The assumed source function, which represents a mechanism by which charge is separated inside the storm, contributes to a portion of the solution in which the ratio of the displacement current over the conduction current increases with decreasing altitude, i.e., in the lower atmospheric region the displacement current can have an important role in the electrical interaction between the storm and its environment. It is also demonstrated that the source function can induce temporal phase shifts in the solution, which are dependent on altitude.
To obtain details of the solution, which cannot be obtained by analytic techniques. a stable numerical approximation of the continuity equation is introduced and analyzed. The resulting numerical model is used to examine the evolution of the displacement and conduction currents during the charge buildup phase of a developing thunderstorm.
Abstract
A time-dependent model that simulates the interaction of a thunderstorm with its electrical environment is introduced. The model solves the continuity equation of the Maxwell current density that includes conduction, displacement, and source currents. Lightning phenomena are neglected and the electric field is assumed to be curl free. Corona, convection, and precipitation currents are not considered in this initial study and their contribution to the source function is not specified explicitly. As a preliminary test of the model we assume that the storm is axially symmetric in spherical geometry, the conductivity depends only on the vertical coordinate, the ground is equipotential, and far from the thunderstorm region the horizontal electric field is zero. These assumptions are for computational efficiency only and can be relaxed in more realistic studies.
The mathematical energy method is applied to the continuity equation to determine boundary conditions that are sufficient to form a well-posed initial-boundary value problem. This ensures the existence of a physical solution that depends continuously on the initial and boundary data. Then analytic techniques are applied to study the dependence of the solution on the properties of the medium. There are two time scales of the problem that are analyzed and discussed: one determined by the background electrical conductivity and the other by the time dependence of the source function. The assumed source function, which represents a mechanism by which charge is separated inside the storm, contributes to a portion of the solution in which the ratio of the displacement current over the conduction current increases with decreasing altitude, i.e., in the lower atmospheric region the displacement current can have an important role in the electrical interaction between the storm and its environment. It is also demonstrated that the source function can induce temporal phase shifts in the solution, which are dependent on altitude.
To obtain details of the solution, which cannot be obtained by analytic techniques. a stable numerical approximation of the continuity equation is introduced and analyzed. The resulting numerical model is used to examine the evolution of the displacement and conduction currents during the charge buildup phase of a developing thunderstorm.
