Buoyancy-driven air flows within the mound

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The Macrotermes nest concentrates a high rate of metabolism (roughly 50-200 watts) within a fairly compact volume (a spheroidal nest roughly a meter in diameter). This high metabolic power density is sufficient to warm the nest a few degrees Celsius above the surrounding soil. The high metabolic rate also produces metabolic water at a fairly good clip, which can raise nest humidity. Both reduce air density, and can impart a slight buoyancy to the nest air.

Since the 1960's, with the publication of Martin Lüscher's famous thermosiphon model, metabolism-induced buoyancy has been thought to be a principal driver of air flows within the mound. (See here for a short description).

Our work indicates that the thermosiphon model is probably incorrect. This is not to say that metabolism-induced buoyancy is not important. Rather, it is important in some far more interesting ways than Martin Lüscher imagined it to be. Scroll down on this page read more about this:

Can metabolism-induced buoyancy drive a circulation of air?
Air flow in the chimney is tidal, not unidirectional

Go back one page to read about the mound's interaction with wind. The next page considers how wind and metabolism-induced buoyancy interact:

How likely is it that metabolism-induced buoyancy could drive an upward flow of air in the mound? 

For thermosiphon ventilation to work, there must be sufficient buoyancy to actually drive a flow. We assessed the likelihood of this from measurements of temperature and humidity in the nest and chimney (right). These measurements can then be used to calculate a density of the air at these locations. If density of nest air, for example, is less than the density of air in the chimney, there will exist a net buoyant force that could move air upward from the nest into the chimney. If air in the nest is denser than in the chimney, on the other hand, the air will be stably stratified and will not move.

Generally, temperatures within the nest are warmer than those in the chimney, and nest humidity is generally higher than humidity in the chimney. Both conditions impart a net buoyancy of the nest air with respect to the chimney. It is therefore possible for metabolism-induced buoyancy to move air upwards. But is it likely? Complicating the likelihood are two considerations:

Using the means and variances of the measurements of temperature and humidity (which were taken at various times of day and year), we calculated the probability that air in the nest would be lighter than air in the chimney. We also assessed the likelihood that density of the nest air would differ from the density of the chimney air by various factors (10, 20, and 30 grams per cubic meter). The magnitude of the buoyancy difference is expressed as the Grashof number (Gr), a dimensionless number which accounts for the ratio of the buoyant forces to the viscous and inertial forces: the larger the Grashof number, the greater will be the likelihood of a buoyancy-induced flow.

In a nutshell, it is unlikely that density gradients of any magnitude exist that could favor buoyant flow. There is, at most, a roughly 20% chance that nest air will be lighter than chimney air, (blue trace, right). Most of this comes from very small density differences, insufficiently powerful to drive a flow.

Larger density differences that could drive buoyant flows are even less likely. There is, for example, only a 6% chance that density of the nest air will be 10 grams per cubic meter lighter than the chimney air (green trace, right).

To drive a buoyant flow, Grashof numbers in the high thousands are generally considered sufficient. To get to Grashof numbers near 10,000, for example, a density difference of 20 grams per cubic meter is required. The likelihood these would occur is less than 1% (orange trace, right). The likelihood of larger gradients verges on the infinitesimal (red trace, right).

While density gradients do occur that could favor thermosiphon flow, these will rarely be sufficient to drive much of a flow, and certainly not the kinds of streaming flows envisioned by Martin Lüscher's model.


Air flow in the chimney is tidal, not unidirectional

The thermosiphon model proposes that metabolism-induced buoyancy lofts air up into the chimney with sufficient force to drive a circulation of air within the mound. If this is so, then air should always flow upward in the chimney. This can be tested using tracer gas pulse-chase experiments (right). Inject a bolus of tracer gas into the chimney or nest, and detect it at a sensor located above the injection point (below left). If the flow is as the thermosiphon model suggests it is, tracer will appear at the upper sensor a short time after the injection, and should show only a single peak.

The actual flow in the chimney is more complex. A typical trace is shown in the graph above. Tracer injected into the top of the nest eventially shows up in the chimney, but in multiples peaks, not a single one. This indicates that air flow in the chimney is tidal, as it is in our own lungs, not unidirectional as the thermosiphon model predicts. Peaks arise when tracer-laden nest air is lofted into the chimney. Lows arise when fresher air from the top of the mound, unburdened with tracer, is forced down the chimney.

Air in the chimney appears to be delicately balanced between buoyant forces pushing it up, and strongly-filtered wind driven forces that can either drive air downwards or upwards (right). A parcel of air in the chimney will move according to the resultant of several forces. Metabolism-induced bouyancy will always push chimney air up (red arrow). Wind-induced pressure may force air downwards, or draw it upwards, depending upon the direction and magnitude of wind (blue arrow). The resultant (green arrow) may be directed upward, or downward, depending upon the relative magnitudes of the multiple forces operating on it. In an environment where winds are turbulent, always changing direction and speed, movements of air within the chimney will be tidal, not unidirectional.

Thus, ventilation in the Macrotermes nest is similar to a type of ventilation in bee nests that I called pushmi-pullyu ventilation when I wrote about it in The Extended Organism. A bee nest also has a focus of high metabolic power density in the hive, which is usually situated in the upper parts of cavities in trees (below). Buoyant forces impart a net upward vector to air movements in the nest, just as they do in the Macrotermes nest. If the hive needs to be ventilated, bees are stationed at the hive entrance to fan in place. When they fan, this imparts a forceful vector to the nest air that opposes the upward vector of metabolism-induced buoyancy. Air is therefore pushed through the hive entrance according to the resultant of these two forces (pushmi). When the bees stop fanning, the metabolism-induced buoyancy vector now dominates: as the nest air "springs back", fresh air is drawn into the hive (pullyu). Because the bees alternately fan together and rest together, the hive is tidally-ventilated.