Time 0 kyrRiver base level 0 mUpper –Middle –Lower –Dripstone growth 0 mm/yrloadingFPS 0

Drag to orbit, wheel or pinch to zoom. Rock plugs shrink as each level dissolves open; turquoise water follows the water table; cream stalactites and stalagmites grow once a level is drained. Bottom-right: river base level against time with the three cave levels.

Karst Cave Levels: Water-Table Drop, Conduit Dissolution and Dripstone Growth

A limestone hillside is cut open. As the river valley deepens, the base level falls past three horizons: each fracture dissolves into a cave while the river stands at its level, then drains and grows stalactites drop by drop.

Time

Rock and water (sets when each level opens)

Dripstone

Live readouts

How far each level has dissolved open

Longest stalactite in each level

Missions

Pick a mission; status is evaluated on the full timeline.

Independent numerical checks

Controls

Drag / one finger: orbit; wheel / pinch: zoom. The Camera button cycles hero, upper cave and lower levels.
The Time slider scrubs the whole 50 000-year story; Play runs it at the chosen speed (kyr per second).
Incision rate is how fast the river lowers the base level. A slow fall keeps the river at each level longer, so the cave has more time to dissolve open.
Fracture aperture, hydraulic gradient and dissolution rate decide how long a fracture needs to break through. Drip interval and supersaturation set the dripstone growth rate.

The science

Fracture flow. Laminar flow between two smooth walls follows the cubic law: flow per unit width q = ρ g i a³ / (12 μ) for aperture a and hydraulic gradient i. For fractures in series the harmonic sum of a⁻³ over the path (200 m, 40 cells) is used, so the narrowest part controls the flow.

Dissolution kinetics. The wall retreats at v = v₀ (1 − c/c_eq) below 90 % saturation and v = 1000 v₀ (1 − c/c_eq)⁴ above (continuous at 90 %), the calcite behaviour described by Dreybrodt and others; v₀ = 0.5 mm/yr and c_eq = 0.2 kg/m³ are model values of the right order [перевірити за джерелом]. Along the path q c_eq du/dx = 2 ρ_s v(u), solved exactly cell by cell. Water is almost saturated after a few metres, so a long fracture needs many kiloyears before it breaks through (aperture ≥ 1 cm); afterwards water stays aggressive and the wall retreats at the kinetic rate.

Levels. A level grows while the river base level lies within its outlet window (3 m). A slow fall gives a longer window; a fast fall can leave a level closed. This is the standard idea that horizontal cave levels record stillstands of the base level; real systems also have flow from several recharge points.

Dripstone. Axial growth G = Δc V_d η / (ρ_s π r²) · (1 yr / T_d) with drop volume V_d = 0.1 mL, tip radius r = 5 mm and deposition efficiency η = 0.02 (model values). Growth begins only after the level has drained and is open (at least half its design height).

Simplifications. Chamber shapes are fixed templates opened by the computed fraction; a single dissolving fracture per level; no sediment, collapse, mixing corrosion, CO₂ changes or climate variation; stalactite and stalagmite do not merge into columns in the numbers. Educational virtual model, not a prediction for any real cave. Models built with Blender, scene by Three.js.