by Don Duerr
This weekend, I came across the thread "Thermal Trigger Nonsense" which was resurrected by a few posters over the past few days. It looks like the topic has already been run through the wringer, but after reading the thread and reviewing Peter Gray's original article, it appears some misconceptions about buoyancy still need to be hung out to dry. For instance, in his article Peter Gray states: "I am not suggesting that every time the ground absorbs 8.2 million calories of sunlight, a usable thermal will be formed. Instead, this energy (when conducted to air) creates ... buoyancy." Similar ideas were expressed in a number of other posts in the nonsense thread, such as the claims that air heated at the ground exhibits a lifting or Archimedes force. Since I've done a bit of study on this subject, I'll try to share some thoughts that help me understand buoyancy and how it may apply to thermal production. [NOTE ADDED: When I got on the computer this afternoon to make final edits to this post, I saw in the nonsense thread that Mike has posted a link to a reply article by Dennis Pagen; I had not seen that article before but, after a quickly review, it appears to make some similar points as well as a few other important points I've not addressed below]
To begin, it is essential to understand that a uniform layer of heated air directly overlying a flat uniform ground surface will not have a buoyancy force acting on it. Moreover, adding energy through heating does not create buoyancy or otherwise generate a lifting force on the air, apart from mere expansion.
A heated layer of air -- even though it happens to be less dense than overlying air -- is still acted upon by gravity (downward force) and by the weight of the overlying air column (also downward force). A uniform heated layer of air will not experience an upward buoyancy force or "Archimedes' force" unless a supply of cooler denser can make its way down underneath, between the surface and the heated layer, so as to apply an upward force from below.
PeterW, Tor-Erik and Craig have articulated this principle to varying degrees in their posts in the nonsense thread. In response, Peter G said "Try holding a hot air balloon down if you think the force isn't real." This argument is inapplicable because a hot air balloon is already surrounded on all sides by cooler denser air, even when tethered close to the ground. The same is not true of an extended horizontal layer of heated air that overlies a flat uniform surface. This is a critical distinction.
To see this more clearly, consider a small hot air balloon that is cylindrical in shape (like an upright beer can) and has a smooth flat bottom. Let's say the balloon, with its heated air contents, weighs 900 pounds (400 kg), and let us further assume its top and bottom surfaces each have areas of 10,000 square inches (6.5 m2). At sea level STP, the bottom surface of the balloon would have 147,000 pounds (66591 kg) of force pushing up on it from the underlying ambient air (10,000 sq. inches * 14.7 pounds/sq.in.). The top of the balloon, being above part of the air column, experiences a slightly lower pressure from the overlying air. Let's say the ambient pressure at the top surface is 14.6 psi, so the total downward force the top surface experiences is 146,000 pounds. The ambient air along the bottom surface pushes up on the balloon with 1000 pounds (453 kg) more force than the ambient air along the top pushes down. Since the balloon weighs only 900 pounds (400 kg), the balloon is buoyant and will rise, impelled by 100 pounds (45 kg) of lifting force from below.
Now consider what happens if the balloon is sitting in perfect air-tight contact with the ground so that the ambient air is not able to get underneath the bottom surface. In this case, there will be no force pushing up on the balloon from underneath, so the balloon will not experience buoyancy and will not rise. Break the contact so air can get under and the balloon will release and rise.
This is not so different from the behavior of a suction cup. When the cup is placed against a smooth surface and air is evacuated from the inside of the cup, the ambient outside air pushes on the outer surface of the cup at 14.7 psi at sea level STP. If the cup has a surface area of 10 square inches, the pressing force would be nearly 150 pounds; it would take considerable strength to pull the cup straight off the surface. If a pin hole is poked through the cup, or if the rim of the cup is lifted to create a gap, then air from outside will flow in and equalize the pressure on both sides of the cup. There will no longer be a net force pressing the cup to the surface; even a toddler could lift the cup now.
It isn't suction from the inside that holds a suction cup on, it is pressure from the outside. Likewise, buoyancy is not a consequence of something pulling up from above but of something pushing up from below.
With this understood, it is easy to see that a uniform layer of heated air covering flat ground is not subject to a buoyant force because there is no surrounding cooler air mass to push up from below. The heated layer at the surface is in a metastable stratified state - an unstable configuration the can persist so long as the system is not disrupted.
In the absence of buoyancy, before cool air makes its way underneath, warm air in the unstable surface layer can still be displaced upwards. This can happen when there is a perturbation or vertical variation in the stratification. In such situations, cooler air, being denser and experiencing greater gravitational pull than the warm air, can push its way down through a low spot in the heated layer and force some of the lighter warmer air out of the way. Technically speaking, this squeezing mechanism should not be called buoyancy; hydraulic forcing may be a more accurate term. If the layering remains horizontally uniform, however, cooler denser air cannot push down into the warmed air because, without an irregularity, the downward force is the same over the entire layer. (It's a bit like placing a plywood sheet on a waterbed - there's no place for the water to push up). It takes a perturbation or variation in the layering to destabilize the system and begin the lifting process.
There are real-world examples of similar unstable stratification in fluids. Consider a lake which freeze over during the winter. When the ice surface melts in the spring and wind and waves agitate the water, the lake water will "turnover"; the cool dense water near the surface moves down and the warmer underlying layers upwell. Even tropical lakes that do not freeze over can stratify in a metastable state. For instance, Lake Nyos in Cameroon, Africa, apparently experienced a rare catastrophic turnover event in 1986 that released vast amounts of CO2 which had accumulated in a stratified deep water layer of the lake; more than 1700 people died. See http://www.geology.sdsu.edu/how_volcanoes_work/Nyos.html.
On the question of thermal triggering, most people naturally focus their attention on how the heated air moves up (e.g., thermal "dripping up" off a hill like a drop of water dripping down from the roof of a cave, etc.). However, given the nature of buoyancy, it may be more instructive to ask how cooler overlying air makes its way down into the layer of warmed air at the surface.
In his article, Peter G explains his "Realistic Model" as follows: "Air above heated ground gradually warms, expands and begins to rise.... As the air slowly rises, it forms an indistinct dome. Near the ground, cooler ambient air moves in to replace the rising air...." This reasoning, while it sounds logical, is IMHO invalid, or at least incomplete, for two reasons. First, as discussed above, a uniformly heated layer of air overlying an extended uniform surface will not spontaneously begin to rise (expand yes, rise no). Nor will it have reason to spontaneously gather into a dome, indistinct or otherwise. Second, this model completely ignores the critical issue of how some of the cooler overlying air gets through and under the warmed layer in the first place; the underflow of cooler air is treated as an afterthought when, in fact, it may be a key ingredient and instigator of the release.
If one simply assumes cooler overlying air can sneak around any time without impetus, or that it can spontaneously appear underneath a wide layer of warmed surface air at any instant, then of course one will have no need for a trigger mechanism. But in reality, the overlying air does not have such magical properties. Before buoyancy can play a role, there has to be a mechanism that allows or compels the cooler overlying air to make its way underneath a stratified layer of heated surface air. If we understand how this happens, it will help us better understand how heated air is released, and perhaps this will improve our ability to find useful thermals.
Here are a few thermal release mechanisms that seem plausible to me.
1. Uniform sloping surface facing the sun, no wind. The heated leaning air column has lower density (and hence weight) than a similar column of unheated air. Also, heated air at the bottom of the slope will be subject to slightly greater pressure from the overlying ambient air compared to the heated air farther upslope. So the overlying cooler air pushes down at the bottom and squeezes the rarified warm air up the slope, anabatically, in the direction of least resistance (i.e., least gravitational opposition, lightest overlying air mass). Cooler air pushes in from below; it doesn't get sucked in to fill a void. During the first stage of this process, cooler ambient air has not actually gotten underneath the warmed layer when the upslope flow begins, so the initial mechanism of lifting is probably better described as hydraulic forcing, not buoyancy. Once the supply of heated air is squeezed out, cooler air will then cover the slope. This would shut off the upslope flow until the new layer of surface air is heated to sufficiently low density to be squeezed upward as before. Slightly heated air, being only a slightly less dense than the ambient air, would be squeezed upslope very slowly, allowing more heating and gradual acceleration. If the replacement air flowing in from above is sufficiently cool at first, it could cause a brief katabatic flow down the slope.
2. Conical hill with uniform heating, no wind. Similar to a uniform slope, but cooler ambient air now pushes down from around the base of the hill and squeezes the warm air upslope from all sides where a thermal ultimately releases at the crest. Once it is pushed above the summit, the thermal bubble (for lack of a better word, no surface tension implied) is continually surrounded by cooler denser air, which pushes up from the bottom. This causes the warm air mass to rise, at least so long as it doesn't cool faster than the surrounding air. At this stage buoyancy is playing a key role. If this reasoning is valid, it is probably not accurate to say thermals are "wicked up" hills or ridges; it is probably more accurate to say a thermal is "squeezed up" by the denser overlying air pushing down near the bottom of the slope. In column thermals that are continually connected to the ground for a sustained period, it may be the case that hydraulic forcing continues to act even after the top of the thermal is well above the crest of the ground. Buoyancy may play a supporting role but may only dominate once the thermal detaches or is undercut by cooler air.
3. Differential heating over flat smooth surface, no wind. If an area of the ground is dark, has lower albedo, or otherwise heats more than an adjacent area (e.g., shaded by a cloud or trees), the heated air layer overlying the ground will not be uniform but will be thicker above the area subject to the greatest heating. This is a scenario where the heated air layer could form a dome. Thus, somewhere near the boundary between the areas of differential heating, the heated air layer will slope upwards, and the thermal layer will not be uniformly horizontal. The configuration will be similar to that of a heated air layer overlying a sloped surface, and the ambient air near the bottom of the slope can squeeze down and force the heated air up in a similar way.
4. Wind flowing over a uniform surface. Wind can cause variations in the thickness of the heated air layer. These variations could destabilize the system and allow cooler denser overlying air to squeeze down and push heated air upwards, initiating rise and release of a thermal.
5. Wind flowing over a highly irregular surface subject to various degrees of differential heating. Multiple mechanisms exist to generate variations in the thickness of the thermal layer overlying the ground. Thermal events may seem random. Prediction may be difficult or impossible. Wind eddies over abrupt terrain features could provide a means for cooler denser air to get quickly underneath a pool of heated air and thus generate buoyancy. This might result in abrupt releases.
6. Mechanical disruption in stratification over flat uniform ground. Just as a hill creates a destabilizing variation in the thermal stratification, so too can a moving object. For instance, warmed surface air is pushed up and over a moving tractor. If this occurs in a flat field that is uniformly heated and fairly unstable, the induced rise in the heated layer could provide an avenue for the cooler denser overlying air to squeeze down around the sides and cause the release of a thermal, much like a thermal is squeezed up and released from a small hill. In this theory, a tractor can act as a trigger, not because it adds more heat to the air it moves through, but because it displaces an already warmed layer of air upwards and thereby destabilizes a metastable state. It is conceivable that a sailplane or hang glider swooping down into or near a uniformly heated layer overlying the ground could have a similar destabilizing effect. I doubt the motion of a rabbit or other small animal could create sufficient disruption in the thermal layering to trigger a release, though if a highly unstable situation could arise, small-critter triggering is at least conceivable.
7. Small-scale convection. As Craig noted in one of his posts in the nonsense thread, even over a uniform surface there will be small-scale convection in the air heated by a surface. If you look across the hood of a dark colored car on a hot day, small scale convection reveals itself as a wavering of light. (Air at different temperatures/densities has different indices of refraction so light passing through the heated convective air is refracted in different ways, making distant objects look distorted). It is possible that many small-scale convection cells could occasionally work together to create sufficient net upward motion to trigger the release of a sizeable thermal or, from the other perspective, create enough variation in the thermal layer to allow the cool air above to squeeze off a thermal. IMHO, however, small-scale convective cells should (at least, over a uniform surface) tend to average out, not add together. They also tend to mix with overlying air and cool fairly effectively, which tends to suppress their growth. Nevertheless, it is at least conceivable that small scale convection could provide sufficient destabilization to trigger the release of a sizeable thermal.
In summary, I think Peter Gray did a good job debunking some of the unfounded thermal myths such as surface tension and the bubble theory. He also presented some nice analysis on the properties of heated air masses. Unfortunately, though, I think he overlooked the subtle but important role cooler overlying air plays in thermal release. When this role is examined carefully, it appears there may exist mechanisms which could properly be called thermal triggers. Ironically, we also find that to understand how warm air rises, we may first need to understand how cool air descends.
DISCLAIMER: With higher education and an ability to manipulate numbers often come some undesired by-products, things like closed-mindedness, inflated ego, and a capacity to persuade others to believe something that may not be true. So please keep in mind that the ideas I've outlined here are just that - theories seeking to explain some complex phenomena. Although I believe the ideas may be essentially correct, I do not know them to be absolutely valid, particularly in the real world where such simplified and idealized models usually have limited application. These are just a few thoughts that came to me after reading Peter's article and the thread on thermal trigger nonsense. There could be other mechanisms which trigger thermals, and the mechanisms I've outlined above could be incorrect or incorrectly described. If you detect some questionable or flawed reasoning, or if you see other possible explanations for thermal release, please post them for consideration and discussion.
Don Duerr, Pinedale, Wyoming USA ©