Shock wave from a lightning discharge

Jones, Donald L.; Goyer, Guy G.; Plooster, Myron N.

doi:10.1029/jb073i010p03121

Cited by 75 publications

(51 citation statements)

References 19 publications

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“…The pressure model predicts a maximum pressure of ∼7 GPa, smaller than the pressure thought to be required to generate shocked quartz, ∼10 GPa. One possible reason for this discrepancy is that the energy density of the lightning channel is higher (>10 MJ/m) than the assumed value of 3.3 MJ/m suggested by Jones et al []. There exists a large variation in estimates of the energy density of lightning.…”

Section: Discussionmentioning

confidence: 99%

“…Numerical evaluations show that the shock radius is

R = {((), \frac{4 E}{B ρ_{0}})}^{1 / 4} t^{1 / 2}

where the constant B ≈3.94. The pressure behind the shock front is

p_{1} = \frac{2 E}{B R^{2} (γ + 1)} = 0.212 E R^{- 2} .

If we take the energy density E = 3.3 MJ/m [ Jones et al , ], and if R ∼ a = 1cm is the radius of the lightning channel, then the shock pressure is

p_{1} \approx \frac{2 E}{B a^{2} (γ + 1)} = 7.0 normalGPa

which is smaller than the pressure range (≥10 GPa) required to generate shock lamellae in quartz [ Grieve et al , ]. However, if the energy density E is higher, for example, 10 MJ/m, the lower bound suggested by Collins et al [], then p 1 =0.212 E R −2 is large enough to generate a shock pressure of 21 GPa at the boundary of the lightning channel, sufficient to generate shocked quartz, and similar to pressures induced by meteorite impacts.…”

Section: Modelmentioning

confidence: 99%

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Generation of shock lamellae and melting in rocks by lightning‐induced shock waves and electrical heating

Chen

Elmi

Goldsby

et al. 2017

Geophysical Research Letters

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The very rapid energy release from impact events, such as those resulting from lightning strikes or meteorites, can drive a variety of physical and chemical processes which alter rocks and result in the formation of natural glasses (i.e., fulgurites and tektites). Fulgurite is the vitrified soil, sand, or rock resulting from lightning strikes. A thunderbolt is associated with air temperatures of up to 105 K, which can heat rocks to >2000 K within tens of microseconds. The rapid fusing and subsequent quenching of the surface of the rock leaves a distinctive, thin, garbled coating composed of a glassy to fine‐grained porous material. Previous studies on rock fulgurites found planar deformation features in quartz crystals within the target rock substrate, evidence of strong shock waves during fulgurite formation. In this paper, we simulated the shock pressure and temperature caused by an idealized lightning impact on rocks and compared the model results with observations on rock fulgurites from the literature. Our model results indicate that a lightning strike can cause >7 GPa pressure on the rock surface, generate a layer of fulgurite (of radius ∼9 cm), and leave a burned region (of radius ∼11 cm). The fulgurites found on rock surfaces share many features with sand fulgurites, but their spatial distribution is completely different, as sand fulgurites are hollow tube structures. Our study on rock fulgurites provides an indirect constraint on the energy of a lightning event and also demonstrates that the presence of shock features in rocks cannot be taken as unequivocal evidence for impact events.

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Section: Discussionmentioning

confidence: 99%

“…Numerical evaluations show that the shock radius is

R = {((), \frac{4 E}{B ρ_{0}})}^{1 / 4} t^{1 / 2}

where the constant B ≈3.94. The pressure behind the shock front is

p_{1} = \frac{2 E}{B R^{2} (γ + 1)} = 0.212 E R^{- 2} .

If we take the energy density E = 3.3 MJ/m [ Jones et al , ], and if R ∼ a = 1cm is the radius of the lightning channel, then the shock pressure is

p_{1} \approx \frac{2 E}{B a^{2} (γ + 1)} = 7.0 normalGPa

Section: Modelmentioning

confidence: 99%

Generation of shock lamellae and melting in rocks by lightning‐induced shock waves and electrical heating

Chen

Elmi

Goldsby

et al. 2017

Geophysical Research Letters

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“…After the shock front has expanded to R c , the cylindrical wave development can be replaced by spherical spreading [ Few , ]. The N wave amplitude is obtained by extrapolating the shock pressure to the characteristic radius R c by fitting the overpressure with the empirical equation [ Jones et al , ]

\frac{normalΔp}{p_{0}} = \frac{γ_{0}}{2 (γ_{0} + 1)} \frac{1}{A ([], {(1 + B η^{2})}^{3 / 8} - 1)}

where η = r / R c , A = (3/8) 3/5 C 8/5 and B = (8/3) 8/5 C −8/5 , with C ≈0.7[ Plooster , ].…”

Section: Generation Of the Initial Strong Shockmentioning

confidence: 99%

“…The strong shocks are obtained by solving equation numerically with boundary conditions given by . The shock‐to‐acoustic transition is calculated approximately by fitting the shock evolution with Jones' empirical equation [ Jones et al , ]. The N wave amplitude is approximated by extrapolating Jones' curve to r = R c .…”

Section: Generation Of the Initial Strong Shockmentioning

confidence: 99%

Predicting the characteristics of thunder on Titan: A framework to assess the detectability of lightning by acoustic sensing

Petculescu

Kruse

2014

J. Geophys. Res. Planets

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The search for lightning is an important item on the agenda for the future exploration of Titan.Thunder, as a direct lightning signature, can be used, together with electromagnetic signals, to corroborate and quantify lightning. Using Cassini-Huygens data and model predictions, the main characteristics of thunder produced by a potential 20 km cloud-to-ground tortuous discharge are obtained and discussed. The acoustic power released right after the discharge decreases with increasing altitude, owing to the ambient pressure and temperature gradients. Ray tracing is used to propagate sound waves to the far field. Simulated thunder waveforms are characterized by fairly long codas-on the order of tens of seconds-arising from the small acoustic absorption (∼10 −4 dB/km). In the low-loss environment, the principal thunder arrival will likely have a large signal-to-noise ratio ensuring a high detection selectivity. The spectral content depends on the amount of energy released during the discharge. For an energy density of 5 kJ/m, the dominant contribution lies between 50 and 80 Hz; for 500 kJ/m, it shifts to lower frequencies between 10 and 30 Hz.

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“…The theory of cylindrical shock waves is usually applied to the study of lightning discharges, 18 resulting in the simplest model of the phenomenon. Theoretical development on this subject started with the similarity solution of spherical shock waves introduced by Sedov 19,20 and Taylor, 21 in relation to the study of atomic explosions.…”

Section: Appendix A: Cylindrical Shock Wavesmentioning

confidence: 99%

Bead lightning formation

Ludwig

Saba

2005

Physics of Plasmas

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Formation of beaded structures in triggered lightning discharges is considered in the framework of both magnetohydrodynamic ͑MHD͒ and hydrodynamic instabilities. It is shown that the space periodicity of the structures can be explained in terms of the kink and sausage type instabilities in a cylindrical discharge with anomalous viscosity. In particular, the fast growth rate of the hydrodynamic Rayleigh-Taylor instability, which is driven by the backflow of air into the channel of the decaying return stroke, dominates the initial evolution of perturbations during the decay of the return current. This instability is responsible for a significant enhancement of the anomalous viscosity above the classical level. Eventually, the damping introduced at the current channel edge by the high level of anomalous viscous stresses defines the final length scale of bead lightning. Later, during the continuing current stage of the lightning flash, the MHD pinch instability persists, although with a much smaller growth rate that can be enhanced in a M-component event. The combined effect of these instabilities may explain various aspects of bead lightning.

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Shock wave from a lightning discharge

Cited by 75 publications

References 19 publications

Generation of shock lamellae and melting in rocks by lightning‐induced shock waves and electrical heating

Generation of shock lamellae and melting in rocks by lightning‐induced shock waves and electrical heating

Predicting the characteristics of thunder on Titan: A framework to assess the detectability of lightning by acoustic sensing

Bead lightning formation

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