The organising axis

Every figure, by regime

A shape does not decide how a fluid behaves around it. One dimensionless number does, and the same cylinder creeps, sheds or goes turbulent as that number crosses its thresholds. This is every figure on the site sorted by the hypothesis it was drawn under.

Every figure here carries a strip along its foot naming two things: the model that produced it, and the regime it holds in. That is an invariant of this site rather than a courtesy — a result quoted without its Reynolds or Mach number is a result quoted without its hypothesis, and a figure that cannot state its regime throws and stops the build.

This page is built by rendering all 3946 figure placements and reading those strips back out of the finished SVG, rather than from the code that wrote them. The two can differ, and where they do it is the picture that is right. 164 of the 171 generators used in essays are called at more than one regime, which is the difference between a family of figures and one picture shown repeatedly.

The bands below are one page each. They were one page in total until the collection passed three hundred and seventy essays, at which point the combined listing went past the raw-byte budget this site holds every page to — so the index carries the counts and each hypothesis carries its own rows.

The generators, by how far they are stretched

How many distinct regimes each generator has been asked to draw. One is a picture; several is a family.

ideal-limit 64 regimes
regime-collapse 61 regimes
nonlinear-wave 58 regimes
turbulent-limit 57 regimes
circulation-ledger 53 regimes
oscillating-wall 41 regimes
turbulent-exact 39 regimes
structure-and-mixture 36 regimes
constraint-and-freedom 34 regimes
applied-total 33 regimes
wrong-picture 31 regimes
what-a-wake-hands-back 29 regimes
how-long-viscosity-remembers 28 regimes
mean-field 27 regimes
ideal-exact 26 regimes
normal-shock 26 regimes
what-a-gas-carries-forward 26 regimes
what-a-parcel-remembers 26 regimes
extra-condition 25 regimes
viscous-exact 25 regimes
what-an-ideal-flow-keeps 25 regimes
what-turbulence-forgets 25 regimes
which-memory-a-number-decides 25 regimes
field-statistics 24 regimes
reactive-shock 24 regimes
hot-gas 23 regimes
profile-and-total 23 regimes
the-history-a-picture-leaves-out 23 regimes
how-long-a-machine-remembers 22 regimes
ideal-cylinder 22 regimes
regime-exact 22 regimes
siphon-profile 22 regimes
carried-region 21 regimes
ground-effect 21 regimes
surge 21 regimes
absolute-pressure 20 regimes
lift-exact 20 regimes
field-anatomy 19 regimes
compressible-exact 18 regimes
observer-and-strain 18 regimes
optical-response 17 regimes
pulsatile 17 regimes
thermal-layer 17 regimes
ejector-map 16 regimes
kinematic-exact 16 regimes
newtonian-lift 16 regimes
velocity-field 16 regimes
critical-points 14 regimes
lorenz-truncation 14 regimes
noise-scaling 14 regimes
bed-flow 13 regimes
coating-film 13 regimes
energy-budget 13 regimes
nozzle-duct 13 regimes
viscous-limit 13 regimes
kinematic-limit 12 regimes
convection-onset 11 regimes
sound-signal 11 regimes
wall-jet 11 regimes
bl-profile 10 regimes
overlap-layer 10 regimes
rotating-frame 10 regimes
bearing-film 9 regimes
flow-net 9 regimes
particle-paths 9 regimes
span-load 9 regimes
venturi-claim 9 regimes
vortex-decay 9 regimes
vortex-ring 9 regimes
cavitation-map 8 regimes
flight-envelope 8 regimes
hydraulic-jump 8 regimes
laminar-jet 8 regimes
moc-nozzle 8 regimes
moving-surface 8 regimes
regime-crossover 8 regimes
rotational-flow 8 regimes
transonic 8 regimes
added-mass 7 regimes
aerofoil 7 regimes
conformal-map 7 regimes
drop-profile 7 regimes
lifting-line 7 regimes
material-loop 7 regimes
plate-friction 7 regimes
stratified 7 regimes
two-element 7 regimes
unsteady-response 7 regimes
velocity-triangle 7 regimes
cavity-flow 6 regimes
closed-wake 6 regimes
control-volume 6 regimes
drag-split 6 regimes
edge-suction 6 regimes
expansion-fan 6 regimes
free-jet 6 regimes
least-energy 6 regimes
point-vortices 6 regimes
rarefied-channel 6 regimes
regime-axis 6 regimes
sailing-polar 6 regimes
shape-from-pressure 6 regimes
shock-tube 6 regimes
sphere-flow 6 regimes
supersonic-section 6 regimes
swept-wing 6 regimes
thin-aerofoil 6 regimes
wagner-lift 6 regimes
what-viscosity-is 6 regimes
bernoulli-limits 5 regimes
cascade-spectrum 5 regimes
corner-eddy 5 regimes
creeping-flow 5 regimes
delta-wing 5 regimes
flapping-wing 5 regimes
flutter-locus 5 regimes
gust-average 5 regimes
inverse-cascade 5 regimes
jet-breakup 5 regimes
machine-map 5 regimes
outer-boundary 5 regimes
panel-solve 5 regimes
pipe-transition 5 regimes
ram-cycle 5 regimes
reciprocity 5 regimes
specific-energy 5 regimes
stirring 5 regimes
suction-layer 5 regimes
taylor-dispersion 5 regimes
tunnel-blockage 5 regimes
viscous-cylinder 5 regimes
wander 5 regimes
bubble-collapse 4 regimes
corner-flow 4 regimes
flap 4 regimes
jet-force 4 regimes
layer-that-stops 4 regimes
meter 4 regimes
moody-chart 4 regimes
pi-groups 4 regimes
pitot-error 4 regimes
pressure-poisson 4 regimes
separation-onset 4 regimes
shear-heat 4 regimes
sphere-drag 4 regimes
tail-balance 4 regimes
transient-growth 4 regimes
two-wings 4 regimes
vortex-stretch 4 regimes
wake-plane 4 regimes
wake-rollup 4 regimes
wave-system 4 regimes
wheel 4 regimes
actuator-disc 3 regimes
fanno-rayleigh 3 regimes
isentropic-curves 3 regimes
parcel-split 3 regimes
stokes-loop 3 regimes
ball-side-force 2 regimes
rayleigh-onset 2 regimes
resolution-cost 2 regimes
shear-instability 2 regimes
thermal-entry 2 regimes
vortex-pair 2 regimes
branch-cost 1 regime
closure-count 1 regime
equal-transit 1 regime
expansion-loss 1 regime
karman-model 1 regime
moment-about 1 regime
wall-law 1 regime

The figure library · What is refuted here · All essays

Kinematics only — an identity about the field, whatever moves it

Any Reynolds number — viscosity is absent

An exact Beltrami solution of Euler — steady, inviscid, three-dimensional

Re → 0 — creeping flow, inertia absent

Set by the reduced Reynolds number Re·(h/L) — not by Re

Set by the film's aspect ratio — one length small enough to delete inertia

Re below 1 — creeping, no wake at all

Re 1 to 47 — attached, or a steady standing pair

Re 47 to 10³ — the wake sheds

Re 10³ to 2·10⁵ — laminar separation, wide wake

Re above 2·10⁵ — turbulent boundary layer

Swept in Reynolds number — the figure is about the variation, not one value

Swept in pipe Reynolds number — the figure is about the variation

Re below 2300 in a pipe — the exact solution, and the flow takes it

Set by the channel Reynolds number — internal flow between walls

Set by the pipe Reynolds number — internal flow, not a wake

Set by the wedge angle and the flux — a purely radial similarity flow

Set by the suction coefficient — a layer held at a fixed thickness

Set by the vortex Reynolds number Γ/ν — circulation against viscosity

Swept in pore Reynolds number — the figure is about where the linear law stops

Set by the jet's own Reynolds number — its width and its centreline speed

Re_p below 10 in a bed — Darcy's law, and the linear term carries it

Re_p 10 to 86 in a bed — both of Ergun's terms matter

Set by the pore Reynolds number — a bed, not a body in a stream

Set by the Womersley number — the radius against a cycle's diffusion depth

Set by the position along a duct — x⁺ = x/(D·Re·Pr), axial conduction dropped

An averaged wall condition — one length standing in for a structure

Set by the Péclet number — advection against molecular diffusion

Set by the tip-speed and advance ratios — a rotor with blades rather than a disc

Boundary-layer theory — Re large enough that the layer is thin, and the number cancels

Set by the reduced frequency — linear unsteady aerofoil theory, planar wake

Set by the reduced frequency — how much of its own wake the section is still in

Trimmed level flight — the hypothesis is a force and a moment balance

Set by the Keulegan–Carpenter number — whether the flow has time to make a wake

Set by a stated gust distribution — the average of a curve, not of a flow

A self-excited oscillator — a caricature of a wake, with no fluid in it

The limit of vanishing viscosity — where the answer does not follow the parameter

Second order in the amplitude — a mean flow driven by an oscillation with none

Set by being local — an exponent the geometry fixes, at any scale

A truncation — a model system standing in for a flow, and named as one

Stated in the wall's own variables — a friction velocity, a roughness, a kappa

Set by a stated closure — a model rather than the equations

Set by the class of fields compared — same boundary values, same flux

Set by the Rayleigh number — buoyancy against diffusion

Set by the Brinkman number — the heat a shear makes against the heat conducted away

Vorticity as an object — a sheet, a patch or a filament, inviscid throughout

The narrow-gap limit — a Taylor number that is also a Rayleigh number

A topological count — linking and writhe, of curves rather than of a field

Set by the domain's symmetry — images where they exist, a map where they do not

Linear free-surface theory — an inviscid flow that radiates, and therefore drags

An ensemble statistic — a distribution over material elements, not a field

Set by the cavitation number — the pressure margin above vapour

Set by the fluid's transport coefficients — a stated gas at a stated state

Stated by the turbulence's own statistics — a dissipation, a scale, a spectrum

Set by the Ekman number — viscosity against the planet's rotation

A closure evaluated in a strain — a model's own algebra, with no flow round it

A reduced set of equations — Prandtl's, Stokes' or the triple deck's, with what was dropped named

Set by the Rossby number — inertia against the planet's rotation

A comparison class at fixed boundary data — admissible fields, with no equation being solved

A translating body's dipole — added mass from the disturbance's own energy, inviscid

Set by the pressure's own Poisson equation — its source is Q, and the sign of Q decides

A resultant on a closed contour — the shape entering only through the circulation

A loading in harmonics — where the induced drag is a sum of squares of the departure

An aeroelastic boundary — a root of the characteristic quartic, quasi-steady

A yield stress — a fluid with a threshold below which it does not shear at all

A converging film — Reynolds' equation, whose load separates into a bracket in the taper alone

A free jet's similarity solution — momentum conserved, the scale fitted

A field built from a stated spectrum — a statistic, not a solution

Linear stability of a parallel flow — an eigenvalue problem with no Reynolds number in it

A constructed solenoidal field — exact derivatives, and not a solution of anything

A chaotic advection map — deterministic, area-preserving, and exponentially unpredictable

A shock read by its strength — the expansion of the Hugoniot about a sound wave

Set by the intermittency factor — turbulent some of the time

The method of characteristics — one-dimensional unsteady flow, with two invariants

A wave's second-order transport — a constraint on an integral, and not on a profile

A logarithmic correction — exact in a limit, and approached at a constant rate per decade

A shell model — a nonlinear cascade with no space in it

A number's provenance — how it was located, rather than what flow it belongs to

Fully developed duct flow — the Reynolds number scaled out, leaving only the cross-section

Set by the boundary data and the mesh — an elliptic solve, not a flow model