what the circle is showing
Time: the sun is a photoperiod (peak at noon, dark at night) carrying a fixed
daily-mean flux; the floor has real thermal mass (air + lake water), so its temperature is a
damped, lagged diurnal wave (it stores heat by day, releases it by night — the energy closes
over the day, not each instant). Convection follows the sun; the night-mode jets ventilate the
stagnant dark hours. The line graph is the active field vs radius along the two draggable
angle cuts (A/B) — temperature and pressure are axisymmetric so they coincide, while humidity
and wind vary with the lakes/jets beneath each cut; the dashed line marks the half-scale
figure-of-merit. Energy: the daily-mean light over the floor circumference leaves as
εσT⁴ over the (larger) skin circumference — that balance fixes the mean radiator
temperature, and the reservoir/floor sit above it by the heat-pipe and contact ΔTs (heat flows
outward, so the floor is always the warm end). Temperature hangs a dry centrifugal
adiabat (cp·T+Φ=const, Φ=−½ω²r²) off the floor; the inversion is
solved, not set — the axial sun absorbed by the greenhouse gases (chiefly the solved water
vapour, τ=κW+τ₀) is radiated from the warm axis to the cold floor,
σ(T_axis⁴−T_floor⁴)=(1−e^−τ)F, which is what makes "up" hot. Pressure is
centrifugal hydrostatic balance dP/dr=ρω²r with the local temperature. Humidity
is solved, not set: the lakes ARE the cold reservoir water, so they both source the vapour
and cap it (saturation over cold water) — the floor humidity follows the lake coverage;
the vapour scale height is solved too, as a buoyancy length H_q≈MIX·w/N set
by the mixing against the inversion's stability. The jets ventilate — lofting floor
moisture upward, conserving the water. Fog here is mist over the cold lakes (the
warm-floored bore is sub-saturated, so it's dew, not rain). Wind is a
convective scale (B·z_i)^⅓ choked by the inversion's stability, plus the fountain's
induced breeze, in a frame where Coriolis (f=2ω) dominates (Rossby ≪ 1). The inner rim carries the
ratchet topography — asymmetric teeth that let lakes (constant-radius arcs) sit at all.