Frequently asked questions
How can speed diverge while energy stays finite?
Energy depends on speed squared integrated over volume. In the paper, the region of intense motion shrinks quickly enough for its energy to decrease even as its speed grows. Near the center, fluid spirals inward and exits along the axis; the core becomes progressively thinner relative to its height.
The hard part is keeping the applied force smooth all the way through the singular time. The paper uses oscillatory pulses and successive corrections to cancel otherwise singular terms in the momentum balance. Our finite pulse families and numerical forcing do not reproduce or certify that entire construction. Tracking the target is a solver check; proving those cancellations is a separate mathematical task.
Paper: Theorem 1.1 & §2 ↗ Lean formalization ↗ What reproduction would require ↗
Do we save the full refined field?
Yes. The accepted Oliver parent and Mali continuation saved all three velocity and all three force components in double precision at every cell of all five levels, for all 320 output times. The hierarchy stores 12,055,040 cells; 10,810,304 are active after coarse cells covered by finer levels are excluded. The complete fields remain in the retained native archives.
The movies sample 256² pixels per fixed plane using the finest containing native cell, without spatial interpolation. Fine structure can still be absent from these display pixels. The isometric panel reconstructs magnitude surfaces from the native fields; its interpolation is for visualization only. The grid row shows actual active cell edges, including the irregular outer refinement bands. This site publishes the verified movies and mesh views from the joined archive lineage.
How much storage does that take?
Each full native snapshot contains 12,055,040 × 6 × 8 bytes of field data: 551.84 MiB. All 320 snapshots represent 172.45 GiB before headers, checkpoints and derived render files. These figures include covered coarse cells because they are stored even though they are excluded from composite norms.
How does movie time relate to simulation time?
All 320 saved states appear in order, with no interpolation or dropped frames. Ordinary states hold for 0.2 seconds, the initial rest state for one second, and the final state for half a second. GIFs and videos use the same holds. The output schedule becomes denser toward the endpoint, so five saved frames per second is not a uniform simulation-time clock. The displayed timestamp identifies the actual state. Frame times and playback record
Which planes do the movies show?
Both movies show a vertical x–z slice at y = 0 and a horizontal x–y slice at z = 0. These planes remain fixed throughout the run. The velocity and forcing movies use the same planes.
How much computation does the run require?
The from-rest parent took about 131.20 hours of integration on Oliver, followed by its archive audit. The accepted continuation was then computed separately on Mali from the verified checkpoint. We have not measured a combined FLOP count for this AMReX calculation.
How is peak speed measured?
The homepage number is the native solver's full-field peak-speed diagnostic at the accepted endpoint, t = 0.9975, reported in model units. It is not the maximum of the reduced display pixels and does not change as the movie plays.