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Bubble-induced cave collapse.

Girihagama L, Nof D, Hancock C - PLoS ONE (2015)

Bottom Line: Using familiar theories for the strength of flat and arched (un-cracked) beams, we first show that the flat ceiling of a submerged limestone cave can have a horizontal expanse of 63 meters.Using familiar bubble dynamics, fluid dynamics of bubble-induced flows, and accustomed diving practices, we show that a group of 1-3 divers submerged below a loosely connected ceiling rock will quickly trigger it to fall causing a "collapse".In these experiments, a metal ball represented the rock (attached to the cave ceiling with a magnet), and the bubbles were produced using a syringe located at the cave floor.

View Article: PubMed Central - PubMed

Affiliation: Geophysical Fluid Dynamics Institute, The Florida State University, Tallahassee, Florida, United States of America.

ABSTRACT
Conventional wisdom among cave divers is that submerged caves in aquifers, such as in Florida or the Yucatan, are unstable due to their ever-growing size from limestone dissolution in water. Cave divers occasionally noted partial cave collapses occurring while they were in the cave, attributing this to their unintentional (and frowned upon) physical contact with the cave walls or the aforementioned "natural" instability of the cave. Here, we suggest that these cave collapses do not necessarily result from cave instability or contacts with walls, but rather from divers bubbles rising to the ceiling and reducing the buoyancy acting on isolated ceiling rocks. Using familiar theories for the strength of flat and arched (un-cracked) beams, we first show that the flat ceiling of a submerged limestone cave can have a horizontal expanse of 63 meters. This is much broader than that of most submerged Florida caves (~ 10 m). Similarly, we show that an arched cave roof can have a still larger expanse of 240 meters, again implying that Florida caves are structurally stable. Using familiar bubble dynamics, fluid dynamics of bubble-induced flows, and accustomed diving practices, we show that a group of 1-3 divers submerged below a loosely connected ceiling rock will quickly trigger it to fall causing a "collapse". We then present a set of qualitative laboratory experiments illustrating such a collapse in a circular laboratory cave (i.e., a cave with a circular cross section), with concave and convex ceilings. In these experiments, a metal ball represented the rock (attached to the cave ceiling with a magnet), and the bubbles were produced using a syringe located at the cave floor.

No MeSH data available.


Related in: MedlinePlus

The drag / buoyancy loss ratio (k) as functions of bubble volume (α) and the vertical bubble velocity (WB).The ratio decreases as α increases and WB decreases. However, the ratio is always small (compared to unity) for any α and WB, hence the drag force is negligible compared to the buoyancy loss.
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pone.0122349.g009: The drag / buoyancy loss ratio (k) as functions of bubble volume (α) and the vertical bubble velocity (WB).The ratio decreases as α increases and WB decreases. However, the ratio is always small (compared to unity) for any α and WB, hence the drag force is negligible compared to the buoyancy loss.

Mentions: It is important to realize that there are actually two opposing bubble-induced forces acting on the rock. The first is the reduced buoyancy discussed above and the second is an opposing force directed towards the ceiling by the excess pressure, resulting from the arrest of the vertical fluid speed at point A (Fig 8). This force has not been discussed yet and will now be addressed. We refer to it as a drag-force (not lift) even though it is pointed vertically, because, by definition in fluid dynamics, drag is a force parallel to the flow whereas lift is perpendicular to the flow. To estimate this drag-force we apply Bernoulli’s principle between points A and B noting that, in the absence of vorticity, one can apply Bernoulli’s principle between any two points in the field, not only between points on the same stream line,WB2/2+PB/ρW=PA/ρW(11)Here, PB the pressure at point B (Fig 8), is equal to PA 0, where PA 0 is the pressure at A without the rock present in the field. PA is the pressure at point B. WB is the weight of the ceiling rock in water. The excess force on the rock, due to the stagnation point at A, is at the most, where, R is the radius of the ceiling rock. Using Archimedes Law, the bubble induced buoyancy loss is α times weight of displaced fluid = 2 πR3αρWg /3. This is much greater than the aforementioned excess force on the rock, as Fig 9 clearly demonstrates. The non-dimensional number (k) is the ratio of the excess force on the rock at point A (drag) to the bubbles induced buoyancy loss.


Bubble-induced cave collapse.

Girihagama L, Nof D, Hancock C - PLoS ONE (2015)

The drag / buoyancy loss ratio (k) as functions of bubble volume (α) and the vertical bubble velocity (WB).The ratio decreases as α increases and WB decreases. However, the ratio is always small (compared to unity) for any α and WB, hence the drag force is negligible compared to the buoyancy loss.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4388830&req=5

pone.0122349.g009: The drag / buoyancy loss ratio (k) as functions of bubble volume (α) and the vertical bubble velocity (WB).The ratio decreases as α increases and WB decreases. However, the ratio is always small (compared to unity) for any α and WB, hence the drag force is negligible compared to the buoyancy loss.
Mentions: It is important to realize that there are actually two opposing bubble-induced forces acting on the rock. The first is the reduced buoyancy discussed above and the second is an opposing force directed towards the ceiling by the excess pressure, resulting from the arrest of the vertical fluid speed at point A (Fig 8). This force has not been discussed yet and will now be addressed. We refer to it as a drag-force (not lift) even though it is pointed vertically, because, by definition in fluid dynamics, drag is a force parallel to the flow whereas lift is perpendicular to the flow. To estimate this drag-force we apply Bernoulli’s principle between points A and B noting that, in the absence of vorticity, one can apply Bernoulli’s principle between any two points in the field, not only between points on the same stream line,WB2/2+PB/ρW=PA/ρW(11)Here, PB the pressure at point B (Fig 8), is equal to PA 0, where PA 0 is the pressure at A without the rock present in the field. PA is the pressure at point B. WB is the weight of the ceiling rock in water. The excess force on the rock, due to the stagnation point at A, is at the most, where, R is the radius of the ceiling rock. Using Archimedes Law, the bubble induced buoyancy loss is α times weight of displaced fluid = 2 πR3αρWg /3. This is much greater than the aforementioned excess force on the rock, as Fig 9 clearly demonstrates. The non-dimensional number (k) is the ratio of the excess force on the rock at point A (drag) to the bubbles induced buoyancy loss.

Bottom Line: Using familiar theories for the strength of flat and arched (un-cracked) beams, we first show that the flat ceiling of a submerged limestone cave can have a horizontal expanse of 63 meters.Using familiar bubble dynamics, fluid dynamics of bubble-induced flows, and accustomed diving practices, we show that a group of 1-3 divers submerged below a loosely connected ceiling rock will quickly trigger it to fall causing a "collapse".In these experiments, a metal ball represented the rock (attached to the cave ceiling with a magnet), and the bubbles were produced using a syringe located at the cave floor.

View Article: PubMed Central - PubMed

Affiliation: Geophysical Fluid Dynamics Institute, The Florida State University, Tallahassee, Florida, United States of America.

ABSTRACT
Conventional wisdom among cave divers is that submerged caves in aquifers, such as in Florida or the Yucatan, are unstable due to their ever-growing size from limestone dissolution in water. Cave divers occasionally noted partial cave collapses occurring while they were in the cave, attributing this to their unintentional (and frowned upon) physical contact with the cave walls or the aforementioned "natural" instability of the cave. Here, we suggest that these cave collapses do not necessarily result from cave instability or contacts with walls, but rather from divers bubbles rising to the ceiling and reducing the buoyancy acting on isolated ceiling rocks. Using familiar theories for the strength of flat and arched (un-cracked) beams, we first show that the flat ceiling of a submerged limestone cave can have a horizontal expanse of 63 meters. This is much broader than that of most submerged Florida caves (~ 10 m). Similarly, we show that an arched cave roof can have a still larger expanse of 240 meters, again implying that Florida caves are structurally stable. Using familiar bubble dynamics, fluid dynamics of bubble-induced flows, and accustomed diving practices, we show that a group of 1-3 divers submerged below a loosely connected ceiling rock will quickly trigger it to fall causing a "collapse". We then present a set of qualitative laboratory experiments illustrating such a collapse in a circular laboratory cave (i.e., a cave with a circular cross section), with concave and convex ceilings. In these experiments, a metal ball represented the rock (attached to the cave ceiling with a magnet), and the bubbles were produced using a syringe located at the cave floor.

No MeSH data available.


Related in: MedlinePlus