© Charles Chandler

 

The defining characteristic of a tornadic vortex is that the tightest radius is on the ground. From there, the radius expands in the direction of the flow. The constriction of the radius at the ground is caused by an extreme low pressure that supplies the necessary centripetal force. Above the ground, the low pressure relaxes in the direction of the flow, eventually faring into the lesser pressure deficit within the parent thunderstorm, and the radius expands with the loss of centripetal force approaching the source of the low pressure.

 

 

 

 

The tight radius at the ground is not just how we distinguish tornadoes from other types of vortexes. The concentration of energy at the ground is what makes tornadoes so destructive. In spite of skin friction, air moving along the ground in response to the extreme low pressure achieves its greatest speeds entering the vortex, and the revolution rate as well as the angular velocity relax with altitude. If the tightest radius and fastest air speeds were at the source of the low pressure inside the cloud, damage on the ground would be far less. So understanding the destructive power of a tornado necessitates identifying the force that constricts the radius at the ground.

 

In rough terms, a tornado can be considered a vacuum vortex, with a flow field motivated by the low pressure in the cloud above. But the extreme low pressure at the ground, away from the source of the low pressure in the cloud, is unexpected in an open thermodynamic system. If energy can neither be created nor destroyed, and if entropy always increases with distance from the source of the energy, the lowest pressure in any open-air vacuum vortex must always be at the source of the low pressure, which would be inside the cloud. There shouldn't be a way of getting an extreme low pressure away from the source of the low pressure, nor should the fastest air speeds be where the friction is the greatest (i.e., on the ground). Hence fluid dynamic principles do not allow the inverted funnel shape in a open system. Therefore, a tornado is some sort of closed system, in which one or more non-fluid dynamic forces modulate the flow field.

 

The only "non-fluid dynamic forces" present in the atmosphere (and especially in thunderstorms) are electromagnetic. So while the vacuum vortex is caused by fluid dynamic factors (i.e., the low pressure inside the cloud), the constriction of the radius at the ground can only be due to EM factors, as they are the only other physical forces present.

 

For EM factors to influence the behavior of air in a fluid dynamic vortex, they (obviously) have to be capable of exerting forces on the air. Since air is only infinitesimally responsive to the magnetic force, it can be confidently ruled out. Hence the constriction of the radius at the bottom can only be due to the electric force. We can also say with absolute certainty that for the electric force to alter the behavior of the air, the air has to be charged.

 

Because the tornadic inflow is clear, we know that it is free of water aerosols and rain drops. Relative humidity readings in the air are typically ~20%, meaning that the water content is less than .2% by volume. Liquid and solid water particles are the primary negative charge carriers in the storm, while the gaseous nitrogen and oxygen molecules are not good at hosting net negative charges. Hence the absence of liquid or solid water particles in the tornadic inflow suggests that any substantial space charge would have to be positive, not negative. This will be confirmed by other means later, but it is more straightforward to identify the sign of the space charge when first acknowledging that the air is, in fact, charged.

 

All other factors being the same, there are many ways that a space charge could influence the behavior of a gas, but we can limit the solution domain to only one possibility if we stick closely to definitions. We know that we are attempting to explain the constriction of the radius of a vacuum vortex, away from the source of the low pressure, with the fastest air speeds where friction is the greatest (i.e., on the ground). While such is impossible in an open thermodynamic system, these are the defining characteristics of a bottleneck flow in a closed system. (See .)

 

 

 

 

The air flows the fastest through the bottleneck, as the same volume of air has to move at a greater speed to get through a smaller aperture. In an ideal gas, with no friction, there would be no pressure gradient. But skin friction at the bottleneck increases with the square of the velocity, and this impedes the flow of air. Once past the bottleneck, the air accelerates rapidly, leaving an extreme low pressure at the bottleneck. Then the low pressure relaxes as the air approaches the source of the low pressure. Demonstrations of such behaviors use an apparatus similar to that in .

 

 

 

 

shows the results at different "swirl ratios" (i.e., the angular velocity divided by the vertical velocity). In the 1^st panel, slight angular velocity enables a narrow vortex that stays organized. In the 2^nd panel, with a larger swirl ratio, we see a phenomenon known as "vortex breakdown." Rotating rapidly while surrounded by stationary air, the vortex is subjected to friction, which begets turbulence. This allows the surrounding air, which lacks centrifugal force (because it is not rotating), to flow into the vortex. Once inside, it seeks the extreme low pressure at the base. A "downdraft" inside the vortex relieves the low pressure, and thereby reduces the centripetal force. This results in the rapid widening of the vortex just prior to its breakdown. Note that even in tightly-controlled conditions, this configuration is extremely unstable. In the 3^rd panel, with an even higher swirl ratio, vortex breakdown occurs at soon as the air exits the hole. And in the 4^th panel, the turbulence is so robust that it shrouds the vortex.

 

 

 

 

All of these distinctive forms have been observed in tornadoes.

 

 

 

 

 

 

 

 

So the laboratory research demonstrated that vortex breakdown can only occur if the low pressure is relaxing in the direction of the flow, and that the fastest air speeds occur at the lower boundary, not in spite of skin friction, but because of it, as this is what creates the bottleneck. And the researchers successfully recreated all of the distinctive tornadic forms. But they failed to demonstrate how air flowing through a bottleneck was relevant to the study of tornadoes, which are assumed to be open systems, incapable of bottleneck flows. The reason is that in the 1970s, they did not have the EM data and the EHD principles necessary to understand how the electric force could introduce closed-system properties into an atmospheric vortex. This can now be accomplished.

 

We have already acknowledged that the tornadic inflow is charged, and that this somehow results in the constriction of the radius at the ground. We have seen that in a bottleneck flow, the constriction comes from skin friction at the bottleneck. So we know that for charged air to create a bottleneck flow, it has to accentuate skin friction. If the air is charged, it will induce an opposite charge in the ground, resulting in an attractive force. With the air pulled down to the ground, skin friction then impedes the flow, producing the bottleneck.

 

 

 

 

We only need one more piece to have a complete description of the phenomenon. In the laboratory apparatus, the air encountered skin friction as it moved toward and through the lower aperture. In a tornado, the air encounters skin friction as it moves along the ground. But we need an "aperture" in which the inflow is released from its attraction to the ground — otherwise, the air would simply cling to the ground, and the low pressure aloft would get its air from elsewhere.

 

The properties of this "aperture" can be deduced with confidence. There is no changing the conductivity of the Earth, which supports an induced charge if exposed to charged air. So the only way to release the air from its attraction to the ground is to neutralize its charge. To neutralize a space charge, we need an equal supply of the opposite charge. We previously identified the sign of the space charge as positive. So we need a supply of electrons to neutralize the positive charge in the tornadic inflow.

 

There are two possible sources of electrons, and there is evidence that both are active electron donors. The first is the Earth itself. But it is not a flow of free electrons out of the Earth. Very few of the molecules in the tornadic inflow actually come into contact with the ground. Those get neutralized, but the neutralizing electrons do not spread readily through the low conductivity of the air. The most effective charge neutralization comes from charged dust that is lofted by the electric force into the tornadic inflow. This produces a mixture of positive and negative ions, where the charges haven't actually recombined, but the electric force binding the air to the ground is effectively neutralized, because the mixture is net neutral. The other electron donor is the massive negative charge region inside the storm, and somewhat surprisingly, this appears to be the more reliable source of electrons. The reduced pressure inside the vortex lowers the electrical resistance, thereby enabling a faster Townsend avalanche. The electrons can also flow faster through condensed water in the vortex wall than they can through the clear air at the ground. The electron drift within tornadoes has been confirmed by the magnetic field that it generates, by radio frequency interference, and in extreme cases, by glow discharges within the vortex. All of the data indicate that the current density is in the range of 100~250 amps.^1,2,3,4

 

By atmospheric standards, 100 amps is actually a lot of current. The current in a lightning strike can exceed 10,000 amps, but only for a thousandth of a second. If there was 1 strike every second, that would be an average of 10 amps. At one strike every 30 seconds, we have only .3 amps, and 100 amps sounds like a big number. Yet supercell thunderstorms are highly electrified, and have been recorded issuing over 25 strikes per second. Furthermore, while the tornado is active, the lightning strike rate falls to near zero,^5,6,7,8 suggesting that the tornado is draining the charge that otherwise would have produced lightning. The area experiencing the lightning deficit due to the tornado is typically 10 km², which is the size of the supercell itself. If we consider 25 strikes per second to be extreme, but 10 strikes per second to be more typical, and if all of that current is in a Townsend avalanche or glow discharge within the tornado instead of arc discharges, sustained 100 amp currents become possible. To look at it another way, the total charge in a supercell has been estimated at 100,000 Coulombs.² 100 amps equals 100 Coulombs per second. At that rate, it would take 1,000 seconds to drain all of the charge out of the cloud. That's 17 minutes, which is the typical duration of a tornado.

 

When viewed from another angle, 100 amps seems like too weak of a current to do anything at all. An EF1 tornado expends approximately 5 MW of power on the ground. That current is not directly responsible for that power.

 

But the significance of the current is not that all of it is thermalized, thereby generating all of the power spent on the ground. In fact, only a vanishingly small amount of thermalization occurs near the ground at the point of charge recombination. Rather, the current releases the tornadic inflow from its attraction to the ground. In other words, it provides the hole that enables the continuous flow through the bottleneck. The bulk of the power expended on the ground is just an artifact of the buoyancy of the air inside the vortex. There, the 100 amps does have a thermal significance. If the tornado is 300 m tall, and if the electric field is 5 kV/m,^1,9,10 we can then estimate the resistive heating from the current flowing through the tornado.

 

volts = 300 m × 5,000 V/m = 1,500,000 V

 

watts = amps × volts = 100 × 1,500,000 = 150,000,000 W

 

150 MW of resistive heating inside the vortex is the primary source of buoyancy, and is roughly twice the power of latent heating from condensation inside the tornado. The 5 MW that is lost to skin friction at the ground is small by comparison.

 

 

 

 

Given the current density, and assuming that the current is neutralizing the space charge in the tornadic inflow, if we know the charge density of the air, we can calculate how much charged air would have to be flowing into the tornado to absorb all of that current. Previous research estimated the number of charged particles in the tornadic inflow to be one part per billion (2.14 × 10¹⁴ charged particles/m³), and the charge per particle to be 3.20 × 10⁻¹⁷ C.¹¹

 

space charge = 2.14 × 10¹⁴ × 3.20 × 10⁻¹⁷ = 0.01 C/m³

 

The result is realistic, but the researchers assumed that the charges would be borne by microscopic aerosols (Ø 0.02 µm), which as noted above does not agree with the typical relative humidity readings. If we assume that the charged particles are all molecular ions missing only one electron, a reasonable estimate would be one part per million.

 

molecules in a cubic meter of air = 10²³

 

one charged molecule per million = 10¹⁷ ions/m³

 

1 coulomb = 1.60 × 10¹⁹ electrons

 

space charge = (10¹⁷ ions/m³) / (1.60 × 10¹⁹ electrons/coulomb) = 0.01 C/m³

 

So this way, we get 0.01 C/m³, which agrees with the estimate of 0.01 C/m³ from previous research. So let's see how much air, at that charge density, it would take to absorb 100 amps of current.

 

at 0.01 C/m³, 1 coulomb = 1 / 0.01 m³ = 160 m³

 

1 amp = 1 coulomb / second

 

current = 100 amps = 100 C/s = 100 × 160 m³/s = 16,000 m³/s

 

With that as the volume, we can then determine the horizontal velocity of the inflow.

 

depth of inflow layer = 1 m

 

circumference of tornado 100 m wide = 314 m

 

cylindrical surface of vortex mouth = 314 m²

 

velocity of inflow = 16,000 m³/s / 314 m² = 50.96 m/s

 

50.96 m/s is just barely into the EF2 range, which would seem appropriate for an electric current at the low end of the 100~250 amp estimates.

 

The current could actually be a lot less, if the space charge was less. If the air is clinging to the ground because of an electrostatic attraction, but picking up 5 MW of thermalized skin friction, we know that the minimum amount of charge to maintain this configuration will be the charge that can keep the air clinging to the ground, despite the buoyancy that results from 5 MW of heat.

 

First we'll consider the force of the electric field that is pulling the air toward the ground.

 

electric field = 5 kV/m

 

newtons = coulombs × electric field = 0.01 × 5,000 = 31.25 N/m³

 

Next we'll assume an inflow rate of 1,000 m³/s for an EF1, and apply 5 MW of heat to it, and see what that does to the temperature. Raising the temperature of 1 m³ of air by 1 °C in 1 second requires approximately 1,340 watts.

 

watts per m³ of air = 5 MW / 1,000 m³/s = 5,000 W/m³/s

 

temperature difference = 5,000 W/m³/s / 1,340 W/°C/m³/s = 3.73 °C

 

From the temperature difference, we can calculate the buoyancy.

 

mass of air at STP = 1.2 kg/m³

 

newtons = kilograms / 0.101971621

 

gravitational force at STP = 1.2 / 0.101971621 = 11.77 N/m³

 

standard temperature = 15.6 °C = 288.75 K

 

after frictional heating = 288.75 K + 3.73 = 292.48 K

 

temperature ratio = 288.75 / 292.48 = 0.987246991

 

gravitational force after heating = 11.77 N/m³ × 0.987246991 = 11.62 N/m³

 

buoyancy = 11.77 N/m³ − 11.62 N/m³ = 0.15 N/m³

 

With a downward electric force of 31.25 N/m³, and an upward buoyancy of only 0.15 N/m³, that's 208 times more electric force than buoyancy. With 2 orders of magnitude less electric force, the air would still stay near the ground until the electric charges are neutralized. So we'll consider 6.25 × 10⁻⁵ C/m³ to be the minimum space charge necessary to hold the air down as it is heated by friction. That's only 1 part per 100 million, and which will only take 1 amp of current to neutralize.

 

In conclusion, a tornado is a bottleneck vortex. The bottleneck is created by charged air clinging to the ground due to an induced opposite charge in the ground, which invokes skin friction. The air is released from its attraction to the ground when it is neutralized by charged dust lofted into the flow field, and by electrons flowing down from the cloud through the reduced electrical resistance inside the vortex. The current inside the vortex also provides a substantial amount of resistive heating, accentuating the buoyancy of the air in the tornado. This model is fully mechanistic, and is consistent with the available field data.