Fractal Modeling of Lightning, Blue Jets, and Gigantic Jets

Open Access
- Author:
- Riousset, Jérémy André
- Graduate Program:
- Electrical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 29, 2010
- Committee Members:
- Victor P Pasko, Dissertation Advisor/Co-Advisor
Victor P Pasko, Committee Chair/Co-Chair
John David Mathews, Committee Member
Hampton Nelson Shirer, Committee Member
Douglas Henry Werner, Committee Member - Keywords:
- transient luminous event
gigantic jet
blue jet
streamer-to-spark transition
streamer-to-leader transition
spark
arc
leader
streamer
plasma
lightning
storm
thundercloud - Abstract:
- Blue jets and gigantic jets are transient luminous events in the middle atmosphere that form when conventional lightning leaders escape upward from thundercloud tops and propagate toward the lower ionosphere. These events are believed to be initiated by ‘classic’ parent lightning discharges, when they escape upward from cloud tops. The present study builds upon a previously introduced lightning model that combines the hypotheses of equipotentiality and overall charge neutrality of the lightning channel with the fractal approach allowing to describe the stochasticity and branching of the discharge [<i>Riousset</i>, 2006]. The lightning model has been validated by comparison of the simulated lightning discharge with lightning mapping observations made by the New Mexico Tech Lightning Mapping Array (LMA) during a thunderstorm on July 31, 1999. This validation allows us to confidently apply the model to investigation of the conditions for the initiation of jet discharges, which represents one of the key goals of the research of this dissertation.</br> </br> Although the various types of intracloud and cloud-to-ground lightning are reasonably well understood, the cause and nature of upward discharges remains a subject of active research. Based on the idea first expressed by <i>Petrov and Petrova</i> [1999] that jets could be the extension of classic lightning discharges initiated within the cloud boundaries, this dissertation demonstrates the fundamental physical similarities between the various kinds of electrical discharges known to occur in the thundercloud. In collaboration with colleagues at New Mexico Tech, a combination of observational and modeling results is reported and indicates two principal ways in which upward discharges can be produced. The modeling indicates that blue jets occur as a result of electrical breakdown between the upper storm charge and screening charge attracted to the cloud top; they are predicted to occur 5–10 s or less after a cloud-to-ground or intracloud discharge produces a sudden charge imbalance in the storm. A new observation is also presented of an upward discharge that supports this basic mechanism. Gigantic jets are indicated to begin as a normal intracloud discharge between dominant midlevel charge and a screening-depleted upper level charge that continues to propagate out the top of the storm. Observational support for this mechanism comes from similarity with ‘bolt-from-the-blue’ discharges and from data on the polarity of gigantic jets. Upward discharges are analogous to cloud-to-ground lightning and their explanation provides a unifying view of how lightning escapes from a thundercloud.</br> </br> How charge imbalances form in the thundercloud has been first suggested by <i>Wilson</i> [1921], but their impact on the initiation and early stages of development of blue and gigantic jets has not been addressed in the refereed literature. To address this question, a two-dimensional axisymmetric model of charge relaxation in the conducting atmosphere is developed. It is used in conjunction with the lightning model to demonstrate how realistic cloud electrodynamics leads to the development of blue and gigantic jets. This model accounts for the time-dependent conduction currents and screening charges formed under the influence of the thundercloud charge sources. Particular attention is given to numerical modeling of the screening charges near the cloud boundaries. The results demonstrate the important role of the screening charges in local enhancement of the electric field and/or reduction of net charge in the upper levels of the thundercloud. This model shows that the accumulation of screening charges near the thundercloud top produces a charge configuration leading to the initiation of blue jets, and the effective mixing of these charges with the upper thundercloud charge may lead to the formation of gigantic jets. </br> </br> The visual appearance of the observed jet discharges indicates that these events may be associated with significant heating of the air in the regions of atmosphere near cloud tops through which they propagate. Many of the small-scale features observed in jets can be interpreted in terms of streamers, which are needle-shaped filaments of ionization embedded in originally cold (~300 K) air. After appropriate scaling with air density, these features are fully analogous to those that initiate spark discharges in relatively short (several cm) gaps at near-ground pressure. Thus, we develop a model of the streamer-to-spark transition to study this transition from cold, weakly ionized plasma to thermalized spark at various altitudes (or equivalently, ambient air densities) in the Earth atmosphere. The model is a fully one-dimensional (1-D) axisymmetric, axially invariant thermodynamics model coupled to a zero-dimensional (0-D) chemical kinetics scheme. In this dissertation, the model is applied to study the scaling properties of air heating in streamer channels under conditions of constant electric field. The model results on characteristic heating times τ<sub>br</sub> appear to be in excellent agreement with the available laboratory measurements conducted in short discharge gaps at ground and near-ground pressures. The results demonstrate a significant acceleration of the heating at lower air densities, with effective heating times appearing to scale closer to 1/<i>N</i> than to 1/<i>N</i><sup>2</sup> predicted on the basis of simple similarity laws for Joule heating, where <i>N</i> is the ambient air density. This acceleration is attributed to strong reduction in electron losses owing to three-body attachment and electron–ion recombination with reduction of air pressure. The results also indicate that at low ambient air densities, the channel conductivity and the air temperature increase very rapidly in comparison with the gas dynamic expansion time (i.e., τ<sub>br</sub>≤<i>r</i><sub>s</sub>/<i>c</i><sub>s</sub>, where <i>r</i><sub>s</sub> is the streamer channel radius and <i>c</i><sub>s</sub> is speed of sound). Thus both constant-density and constant-pressure approximations to channel dynamics commonly used in previous studies at ground pressure lead to nearly identical streamer-to-spark transition times.