Fig 1.
a) An idealised cross-section through a karst massif presenting the main hydrological zones, recharge modes and conduit/fracture system in the vadose zone. b) A single channel extending between two entrances E1 and E2 at elevations z1 and z2. Tin and Tout are the temperature of the massif and the outside temperature. The sum of the pressure changes along the blue line gives the driving pressure for the ventilation (see Eqs 3 to 6).
Fig 2.
Variation of air density with temperature for different values of CO2 and relative humidity (RH).
Insert shows the concept of the virtual temperature: air with T = 21.5°C, RH = 0 and atm has a virtual temperature Tv = 20.2°C.
Fig 3.
(a) and simplified profiles of Pisani Passage (b) and Brezimeni Passage (c). Arrows in profiles indicate the direction of airflow in winter (blue arrows) and summer (red arrows) d) Geographic position of Postojna. e) Relation between airflow velocity in Pisani Passage and outside temperature. f) Relation between airflow velocity in Brezimeni Passage and outside temperature. Grey dots present a point cloud of two years of measurements and the black line is the square root fit. Figures a, b, c and d adopted from [14].
Fig 4.
Anticipated airflow direction and magnitude in warm (top) and cold (bottom) periods for different settings. a) Uniform slope and cross-section, b) L-shaped outline, c) Passage with a smaller diameter in the upper section.
Fig 5.
Left: Geometry and parameters of the system. The passage is shown by the blue line. Right: Excerpt with two pipe segments and the surrounding cylindrical rock mass.
Table 1.
Model parameters.
Fig 6.
Airflow velocity, driving pressure, relaxation length and temperature at three different locations in the tube for the case with the constant outside temperature at Tout = −5°C.
Fig 7.
Air temperature along the tube (left section, arrow indicating airflow direction) and the rock temperature in near tube region at 20, 40 and 80 days.
Fig 8.
Outside temperature (blue/red), airflow velocity (black) and air temperatures (dashed) at L/4, L/2 and 3L/2 for the standard case with periodic outside temperature.
Fig 9.
a) Absolute airflow velocity as a function of ΔT for the standard case with an annual temperature period. The upper axis shows the outside temperature. The arrows and curve colours indicate the progress in time. b) Temperature profile along the tube at four time steps for the basic case with an annual temperature cycle. Values denote the number of days from the start.
Fig 10.
a) Airflow velocities, external temperature and temperature at L/2 during the annual cycle for the two nonuniform outlines sketched in the insert in Figure b. b) Airflow pattern ∣v(ΔT)∣ for the two different outlines. Arrows indicate the progress of time. The total simulation time is 750 days.
Fig 11.
Airflow velocities, external temperature and temperature at L/2 during annual cycle for the two cases with change in pipe diameter (see insert in Fig 12).
Fig 12.
Airflow pattern |v(ΔT)| for scenarios with change in cross-sections as shown in the insert.
Colours indicate the progress in time as given in the bar codes.
Fig 13.
a) Initial evolution of the airflow velocity and relaxation length for a V-shape case with constant external temperature (Tout = −5°C). The insert shows a geometry of the system, L = 1 km, D = 2 m, δz = 0.03 m. b) Long-term evolution of airflow velocity, relaxation length and temperature at the knickpoint, T(L/2).
Fig 14.
a) Airflow velocity and external temperature in a V-profile for 750 days of the standard periodic cycle. b) Airflow pattern, ∣v(ΔT)∣, follows a hysteresis loop encircling the grey zone.
Fig 15.
Left: A simplified profile of part of the Kačna Cave (Slovenia). Arrows show winter airflow direction and air temperature on a red (warm) to blue (cold) colour scheme. Dashed lines indicate unexplored airflow pathways. Right: photograph of ice formation on the stalagmites taken during cold period in February 2012. The approximate position of stalagmites is indicated by a black star in the profile.
Fig 16.
Airflow velocity and outside temperature for a V-shape system, where wall temperature along the section marked blue is set to 0°C.