Limits...
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

Streamline of bubbles around a semi-hemispherical ceiling rock.The radius of the ceiling rock is R. The ceiling rock is completely immersed in water. Bubbles released by the divers create a flow around the rock. Point “A” represent the stagnation point on the ceiling rock whereas “B” represents a point at the same depth where there is no ceiling rock. The bubble terminal velocity is WB. Because of the bubble flow, there is an excess pressure exerted on the ceiling causing a drag on the rock.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4388830&req=5

pone.0122349.g008: Streamline of bubbles around a semi-hemispherical ceiling rock.The radius of the ceiling rock is R. The ceiling rock is completely immersed in water. Bubbles released by the divers create a flow around the rock. Point “A” represent the stagnation point on the ceiling rock whereas “B” represents a point at the same depth where there is no ceiling rock. The bubble terminal velocity is WB. Because of the bubble flow, there is an excess pressure exerted on the ceiling causing a drag on the rock.

Mentions: As a simple example, consider a semi-spherical rock (Fig 8) with a radius of half-a-meter (0.5 m) attached to the ceiling of a cave. The ceiling is 5 meters below the water surface in the basin into which the spring debouches and its bottom is 2 meters below its ceiling. It is 2 meters broad and has minimal flow in it. The rock weighing 706 kg in air, weighs 445 kg in water without bubbles. A cave diver lingers near the bottom of the cave, under the rock, releasing gas at a typical breathing rate of 16 liters per minute (about 0.6 cubic feet per minute). Note that these 16 liters per minute are normally measured in reference to surface air consumption (i.e., volume of air per minute consumed at atmospheric pressure), not the consumption of pressurized gas at depth. However, since the diver’s absolute lungs volume times the breathing rate (not consumption of pressurized gas) does not change with depth, it is also 16 liters at depth (though this gas is normally under higher pressure than it is at the surface). These 16 liters turn into 18 liters upon rising from the bottom to the ceiling of the cave, because the surrounding pressure reduces from an absolute pressure of 1.7 atmospheres (i.e., ambient plus atmospheric) at the bottom to 1.5 atmospheres at the top of the cave.


Bubble-induced cave collapse.

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

Streamline of bubbles around a semi-hemispherical ceiling rock.The radius of the ceiling rock is R. The ceiling rock is completely immersed in water. Bubbles released by the divers create a flow around the rock. Point “A” represent the stagnation point on the ceiling rock whereas “B” represents a point at the same depth where there is no ceiling rock. The bubble terminal velocity is WB. Because of the bubble flow, there is an excess pressure exerted on the ceiling causing a drag on the rock.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0122349.g008: Streamline of bubbles around a semi-hemispherical ceiling rock.The radius of the ceiling rock is R. The ceiling rock is completely immersed in water. Bubbles released by the divers create a flow around the rock. Point “A” represent the stagnation point on the ceiling rock whereas “B” represents a point at the same depth where there is no ceiling rock. The bubble terminal velocity is WB. Because of the bubble flow, there is an excess pressure exerted on the ceiling causing a drag on the rock.
Mentions: As a simple example, consider a semi-spherical rock (Fig 8) with a radius of half-a-meter (0.5 m) attached to the ceiling of a cave. The ceiling is 5 meters below the water surface in the basin into which the spring debouches and its bottom is 2 meters below its ceiling. It is 2 meters broad and has minimal flow in it. The rock weighing 706 kg in air, weighs 445 kg in water without bubbles. A cave diver lingers near the bottom of the cave, under the rock, releasing gas at a typical breathing rate of 16 liters per minute (about 0.6 cubic feet per minute). Note that these 16 liters per minute are normally measured in reference to surface air consumption (i.e., volume of air per minute consumed at atmospheric pressure), not the consumption of pressurized gas at depth. However, since the diver’s absolute lungs volume times the breathing rate (not consumption of pressurized gas) does not change with depth, it is also 16 liters at depth (though this gas is normally under higher pressure than it is at the surface). These 16 liters turn into 18 liters upon rising from the bottom to the ceiling of the cave, because the surrounding pressure reduces from an absolute pressure of 1.7 atmospheres (i.e., ambient plus atmospheric) at the bottom to 1.5 atmospheres at the top of the cave.

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