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Essays arrive in groups rather than one at a time. The most recent group is below in full, and every earlier one after it, newest first.

Essays arrive in groups rather than one at a time, and a group usually opens up a subject not covered before. Between one group and the next nothing changes, so a reader who has seen the most recent group has seen everything.

17 September 2026

17 essays on what is taught wrongly, flows and fields, fluids at work, regimes and numbers, compressible flow, circulation and lift, transition and turbulence and ideal flow

The throat holds the hammer back only while its cavity lasts. Left, pressure at the closing valve (red) and at the upstream face of the venturi (gold); right, the throat's cavity volume; after the valve shuts with a 5 mL cavity in the throat. The valve sees the full Joukowsky rise of 14.8 bar at once. The wave reaches the venturi 33.3 ms later, and for the next 7.9 ms the upstream pipe hears nothing: its pressure stays at 5 bar while the cavity is squeezed. When the cavity closes at 41.3 ms the surge passes into the upstream pipe at 13.8 bar above its steady pressure.

What is taught wrongly

A choked throat buys time, not silence

A venturi whose throat has reached vapour pressure passes a flow the downstream pressure cannot change, and it is tempting to read that as isolation: whatever happens downstream, the upstream pipe will not hear it. Slam a valve downstream and it hears it. The cavity at the throat holds the surge back only for as long as it takes to fill, and then lets 93 per cent of it through.

6 figures

Rolls turning side by side, with the fastest downwind water where they sink. The fastest-growing mode at a Langmuir number of 0.13, looking downwind, over two roll spacings of 2.89 decay depths and 4 decay depths down. The closed curves are streamlines of the overturning; the dashed curves are contours of the downwind velocity the rolls carry, positive under the lines where the water sinks. At the surface the cross-wind flow converges onto those lines, which is where floating foam and weed collect as windrows. The amplitude is arbitrary, as in any linear mode.

Flows and fields

The drift that turns a current into rolls

A current carrying a Stokes drift feels a force the drift makes out of the current's own vorticity, and under a wind that force is unstable. It turns the surface layer into rolls lined up downwind, with windrows where they sink. The rolls need both the current's shear and the drift's; their growth rate sees only the product; and the split between the two decides which motion gets the energy.

8 figures

Six nozzles, six pump curves, and where each one is best. The head ratio a water jet pump delivers against the flow ratio it entrains, for six area ratios from a narrow nozzle to one filling four-fifths of the throat. A wide nozzle makes a tall, steep curve that is finished at a small flow; a narrow one makes a low, long curve. The dots are each curve's best-efficiency point. Nozzle, suction, throat-friction and diffuser losses are included at borrowed representative values, and the mixing loss is computed.

Fluids at work

The nozzle that is best at one thing

Put the four losses back into a jet pump and three questions get three answers. The most head comes from a nozzle four-fifths of its throat, in closed form; the best efficiency from one a quarter of it; and the most flow from whichever nozzle is smallest, because flow has no optimum at all.

8 figures $A wave that travels and a wave that spreads. A harmonic pressure wave's amplitude and its instantaneous value along a tube, over two wavelengths of the inviscid wave, at four Womersley numbers. At α = 15 the wave marches on, a little weaker each wavelength. At α = 5 it is visibly damped. At α = 2 it is nearly gone within a wavelength. At α = 0.5 there is no wave to speak of: the disturbance falls away within a small fraction of the inviscid wavelength, as heat does into a wall.$ Regimes and numbers

The pulse that has to travel

In a rigid tube the Womersley number decides the shape of an oscillating flow. Make the wall elastic and the pressure pulse has to travel, a second number appears — the tube's length in wavelengths — and the first number turns out to decide something more basic than the profile: whether the tube carries a wave at all, or only a disturbance that spreads like heat.

6 figures

The kept transport spirals into nothing as the sea deepens. The net Lagrangian transport as a vector, scaled on the Stokes transport, traced as the water depth increases from a quarter of an Ekman depth to eight, for an 8-second swell with an eddy viscosity of 0.01 m²/s. Shallow water keeps the whole transport pointing with the waves, at the right-hand end. As the sea deepens the vector shortens and swings to the right, crosses the across-wave axis near two Ekman depths, and winds into the origin, which is the open ocean's exact cancellation.

Flows and fields

The floor that gives the drift back

In the open ocean the Coriolis force drives a current that cancels a swell's Stokes transport exactly. Over a continental shelf the sea floor holds a stress, and whatever it holds is transport the rotation does not take back. How much survives depends almost only on the depth in Ekman depths; which way it points depends on the wave.

7 figures

One number decides which pulse grows. The pressure pulse and the flow pulse at the far end of the tube, each as a multiple of its value at the entrance, against the load's reflection coefficient. A load that reflects pressure with the same sign — a stiffer or narrower continuation — amplifies the pressure pulse and damps the flow pulse. One that reflects it inverted — a wider continuation, or many branches — does the opposite. With no reflection both fall slightly, by the wave's own attenuation. The two curves cross near Γ = 0 and pull apart on either side.

Regimes and numbers

The pulse that grows as it leaves the heart

The pressure pulse measured at the wrist is larger than the pulse in the aorta that drives it, and the flow pulse is smaller. Nothing downstream is pumping. A wave reflected from the end of an elastic tube arrives back in step with the outgoing wave near the end and out of step near the start, and a single number — the reflection coefficient — decides whether it is the pressure or the flow that grows.

6 figures

What is taught wrongly

The spot a local theory cannot see

Newtonian theory gives every panel of a hypersonic vehicle a pressure set by its own angle to the stream, and no panel more than the stagnation pressure behind a normal shock. Let a shock from one part cross the bow shock of another and a supersonic jet forms that reaches the surface through weaker shocks. At Mach 8 it stagnates at 8.6 times the ceiling — and the worst amplification at every Mach number is close to the Mach number itself.

6 figures

The characteristic gets a wall, and the wall does not care about the discharge. One jet pump's characteristic, at an area ratio of 0.275, with the flow ratio at which its throat entry reaches vapour pressure drawn for three values of the cavitation parameter σ = (Pₛ − pᵥ)/(Pₘ − Pₛ). Left of a wall the machine runs on its curve. At the wall no lower discharge pressure raises the flow: the head ratio can fall to zero along the vertical and the flow ratio stays where it is. The wall's position contains the nozzle and suction losses and nothing downstream of the throat entry.

Fluids at work

The wall the suction puts in the curve

A liquid jet pump's lowest pressure is where the entrained stream enters the throat, and when that reaches vapour pressure the pump curve stops being a curve. The flow ratio freezes at a value no lower discharge pressure can move — and raising the motive pressure, the obvious cure, brings the wall closer.

7 figures

Compressible flow

A boom is aged in the thin air it starts in

The rays that reach the edge of a sonic-boom carpet travel two and a half times as far as the one under the track, and it is natural to expect their signatures to have aged accordingly. They have not. A pressure wave distorts thin air far faster than dense air, so two-thirds of a boom's ageing is done in the stratosphere near the aeroplane, and the extra kilometres near the ground add little — which decides how far out a boom shaped to be quiet stays quiet.

7 figures

Flat until the back pressure reaches a value, then gone. Entrainment ratio against back pressure, as a multiple of the suction pressure, for three mixing-section sizes of one steam ejector driven from a motive supply a hundred times its suction pressure. Each is exactly flat while the entrained stream is choked beside the jet, up to its critical back pressure. The dashed lines join that point to the back pressure at which the entrainment has fallen to nothing, 1.4 per cent higher for the middle machine. The model fixes those two ends and not the path between them. A larger mixing section entrains more and breaks at a lower back pressure.

Fluids at work

A choke that belongs to two streams

A steam ejector entrains a fixed amount of gas whatever its back pressure, up to a pressure where it stops. The flat part is a choke, and the entrained gas is not at Mach one when it happens: it is at 0.886, because the supersonic jet beside it is part of the same throat. One area ratio then trades that entrainment for compression, and the trade decides how a vacuum train is built.

7 figures $What every wing pays to bend its root less. Least induced drag against the root bending moment of the lift, both as fractions of the elliptic monoplane of the same span and lift, for the monoplane and for box wings with gaps of a tenth, a fifth and two-fifths of the span. Each curve is a parabola with its minimum at that wing's unconstrained optimum. The box wings' minima sit to the right of the monoplane's — they load their lift further out — and their parabolas are shallower: the gap-of-a-fifth box can bend its root 21 per cent less than the elliptic monoplane and still match its drag.$ Circulation and lift

A lighter spar turns a box wing into a biplane

Prandtl's best wing system has two-thirds of a monoplane's induced drag at a gap of a fifth of the span, and part of that saving is carried by circulation turning the corner into its fins. Ask the box to bend its root less and it pays about half what a monoplane pays — but a biplane with no fins pays nearly as little, and by the time the spar is a fifth lighter the fins carry almost nothing and the box has become the biplane it was built from.

7 figures

The part of a field 4 cameras cannot see. Middle, a field with no symmetry on a 16 × 16 grid. Left, the part of it that projects to exactly nothing in every one of 4 views, shaded one way above zero and the other below: a pattern of streaks and hollows that cancels along every ray. Right, the field with that part taken away. The middle and right fields give identical pictures in all 4 views, to 2e-13 of the largest ray, and no reconstruction from those views can tell them apart. The invisible part is one combination of 177 independent patterns the views cannot see.

What is taught wrongly

Four cameras and a field they cannot see

An axisymmetric flow can be rebuilt from one photograph because its symmetry supplies every other view. A flow without an axis has to be photographed from several directions, and a few directions do not merely give a noisy answer — they leave whole patterns of density that every camera records as nothing. Four views of a 16 × 16 field see 79 of its 256 independent patterns and are exactly blind to the rest.

7 figures

The plateau everybody looks for is a summit, and a low one. −Dₗₗₗ/((4/5)εr) against separation in decaying turbulence at five Taylor-scale Reynolds numbers. None has a plateau at one. Each rises through the viscous range and turns over, peaking at 0.49, 0.63, 0.75, 0.85, 0.90 for Reλ = 50, 100, 200, 500, 1000. A measurement of ε that takes the largest value of this curve as four-fifths reads each of those shortfalls as a smaller dissipation.

Transition and turbulence

The decay inside the four-fifths law

The four-fifths law gives the dissipation of turbulence from one measured moment with no constant in it, which makes it the obvious way to measure how the dissipation coefficient travels during a decay. But the law is exact only in a limit, and a decaying flow is not in it. The decay itself takes a quarter off the moment at the Reynolds numbers grids reach — and the bias moves as the flow decays, by a sixth, in the direction opposite to the effect being looked for.

6 figures

Regimes and numbers

The heat the eddies do not carry

In a laminar layer the temperature and the velocity have different thicknesses in every fluid but one. In a turbulent pipe the eddies carry both, and the difference nearly vanishes — for air, water and oil alike. It does not vanish for a liquid metal, whose molecules conduct heat faster than the eddies can, and the boundary between the two behaviours is a Péclet number of about four hundred at every Reynolds number.

6 figures $The best efficiency runs from nine-eighths of φ² to one. The best efficiency a peristaltic pump can reach, against the fraction of the channel its wave closes, with its two limits. For a shallow wave it is 9φ²/8, which is small — a wave closing a fifth of the channel is at best 4.5 per cent efficient. As the wave closes the channel the best efficiency tends to one, and its shortfall shrinks in proportion to the remaining gap: about 1.9(1 − φ). Nothing in between is independent of the amplitude.$ Flows and fields

The pump that is better the more it squeezes

A waving sheet swims at a cost per metre with no amplitude in it. A waving wall pumping fluid is the same mechanism turned round, and its efficiency is nothing like that: it starts at nine-eighths of the amplitude ratio squared, is exactly 2 − √3 at half closure, and rises towards one as the wave closes the tube — where the pump stops being a wave and becomes a piston.

8 figures

Three lobes, then a filament. An ellipse of aspect ratio 4 with a three-lobed bump of three thousandths, as contour dynamics carries it, drawn in the frame turning with the undisturbed ellipse at t = 0, 30 and 42. By t = 30 the bump has grown to a visible three-fold asymmetry — one end fattened, the other thinned — and by t = 42, about a turn and a tenth of the ellipse, the thinned end is being drawn out into a filament. The march is stopped there, while the area is still conserved to a few parts in a thousand; resolving the filament needs a contour that adds nodes, which this one does not.

Ideal flow

Past three, an ellipse is a shear layer

Kirchhoff's elliptical vortex turns for ever without changing shape, and Love showed in 1893 that it stops being stable at an aspect ratio of exactly three. Computed, that threshold turns out to be the first of a sequence — a new way of coming apart every one and a half aspect ratios — and the sequence ends somewhere recognisable. A long enough ellipse is a strip of vorticity, and it comes apart the way a shear layer does, at a rate Rayleigh found for the strip.

6 figures

At a fixed impulse every orbit is a curve of constant energy. Axial separation of two coaxial rings against the radius of the ring that started smaller, for six pairs with the same total impulse, all starting in one plane. Pairs starting nearer equal (inner curves) trace closed loops: the separation swings from one sign to the other as the rings take turns, and the radius swings with it. Pairs starting further apart run off to one side and never return. The pale curves are the separatrix, the energy of two equal free rings — it passes through the plane of the start at a ratio of 0.340 and its arms reach out to infinite separation.

Circulation and lift

Two rings leapfrog only if they start alike

Two coaxial smoke rings passing through each other in turn is the most famous thing vortices do, and it is not what two rings do in general. Set them off from one plane with different radii and below a definite ratio the smaller one draws ahead and never comes back. Which of the two happens is decided before either ring moves, by whether two separate rings could hold the pair's energy.

7 figures

Before that

Everything published earlier, newest first. Titles only — the cards are on the full listing.

15 September 2026

9 essays on transition and turbulence, viscosity and compressible flow

Universal, and one of five — transition and turbulence
The constant that travels — transition and turbulence
The solution that keeps its nonlinear term — viscosity
One channel, one flux, two flows — viscosity
The carpet an accelerating aeroplane folds — compressible flow
The fraction that is really four thirds — transition and turbulence
A relation with no turbulence in it — transition and turbulence
The edge is a rumble, not a quieter bang — compressible flow
Why the list is this long — viscosity

14 September 2026

18 essays on compressible flow, what is taught wrongly, flows and fields, fluids at work, transition and turbulence and regimes and numbers

A cone finishes its turn after the shock — compressible flow
The face Newton left in shadow — what is taught wrongly
The sign a stagnation point carries in space — flows and fields
Twice the margin, on top of the hammer — fluids at work
Matched at one speed and at no other — fluids at work
The drag a wake keeps however it rolls up — what is taught wrongly
The drift a rotating planet takes back — flows and fields
The profile Rayleigh cleared and viscosity did not — transition and turbulence
Three readings, and the one each answer leans on — compressible flow
Between hover and twice the hover inflow — fluids at work
The column the chord rule cannot settle — flows and fields
The gradient the heat never hears — compressible flow
The venturi that stops listening downstream — what is taught wrongly
A wave on the wall is a pump — flows and fields
The boom that turns back before the ground — compressible flow
The drop a no-slip wall would never let spread — what is taught wrongly
The gusts that cancel along the chord — regimes and numbers
The specific speed a pump spends its life at — fluids at work

12 September 2026

20 essays on what is taught wrongly, fluids at work, flows and fields, compressible flow and transition and turbulence

Where a liquid does pull — what is taught wrongly
A breaking strength that is the size of a flaw — what is taught wrongly
The margin friction lends a siphon — what is taught wrongly
The air that breaks a siphon nothing else can — what is taught wrongly
A cushion that changes its physics — what is taught wrongly
A tank that turns a hammer into a swing — fluids at work
The borrowed mass the boundary decides — what is taught wrongly
The better tunnel needs the bigger tank — fluids at work
The vorticity a clean surface cannot refuse — flows and fields
The window every vector is averaged over — what is taught wrongly
A breeze the boat cannot use — fluids at work
One view is enough, and the axis pays for it — what is taught wrongly
The jet a cone sprays sideways — compressible flow
Twice as slippery along as across — flows and fields
A keel flies wherever the course puts it — fluids at work
A wall puts in exactly its own speed — flows and fields
Friction moves the sonic point past the throat — compressible flow
The teapot effect is a tension, not a pressure — what is taught wrongly
The truncation that cannot carry three times the heat — transition and turbulence
Hexagons remember how the heat was turned up — transition and turbulence

10 September 2026

20 essays on what is taught wrongly, fluids at work, flows and fields and compressible flow

The one place the atmosphere pushes — what is taught wrongly
The siphon that does not break — what is taught wrongly
A roll that feeds itself — what is taught wrongly
A stall that is a place — what is taught wrongly
A force forgets the datum, a stress cannot — what is taught wrongly
The only theory simple enough to optimise — what is taught wrongly
Weighing what is missing — what is taught wrongly
The cushion that is there after all — what is taught wrongly
An instrument that takes a derivative — what is taught wrongly
The paint that measures the wrong field — what is taught wrongly
The duty that had no machine — fluids at work
The count computed on a body — flows and fields
The group with no head in it — fluids at work
Two kinds is a plane flow's privilege — flows and fields
What a turning frame keeps — fluids at work
The line the dye actually draws — flows and fields
The stress that picks the aerodynamics — fluids at work
The curve that measures a gradient — flows and fields
The skin that lags the flight — compressible flow
The thermometer that heats itself — compressible flow

5 September 2026

50 essays on what is taught wrongly, flows and fields, fluids at work, compressible flow, transition and turbulence, viscosity, regimes and numbers, circulation and lift and ideal flow

A calculation with no memory in it — what is taught wrongly
The shutter is part of the answer — what is taught wrongly
The same statistics, and a different load — what is taught wrongly
The bath that was only ever a wait — what is taught wrongly
Two strainings, and the order they came in — flows and fields
A scalar is a record of where its fluid was — flows and fields
The part of the closure a pipe cannot see — fluids at work
A drift made of two things that average to zero — flows and fields
The outlet is the inlet, a while ago — fluids at work
A boundary that only exists over a window — flows and fields
A gas that has not finished being shocked — compressible flow
A threshold that is also a duration — fluids at work
A surface that remembers the diaphragm — compressible flow
The ball that never forgets its spin — fluids at work
What a mean profile cannot tell anybody — flows and fields
How long the fluid has been in there — flows and fields
The sound now is the source then — compressible flow
A duct that cannot be run backwards — compressible flow
A puff that does not know how old it is — transition and turbulence
A gas that has not decided to react yet — compressible flow
How far downwind a surface is remembered — transition and turbulence
A dissipation that lags its production — transition and turbulence
Two totals, one of which a shock cannot touch — compressible flow
A closure with no memory at all — transition and turbulence
A dissipation correlated across every scale — transition and turbulence
The drag that integrates a whole history — viscosity
Two forces, and only one of them remembers — regimes and numbers
A wake that keeps the drag and forgets the body — transition and turbulence
The state a machine was started into — regimes and numbers
The wall the fluid is listening to — viscosity
A wake told what to do — regimes and numbers
The fluid that has not finished its last deformation — viscosity
A layer that is an integral of everything upstream — viscosity
Slip is a memory of one mean free path — regimes and numbers
The lag that makes flutter possible — circulation and lift
A particle is a low-pass filter — regimes and numbers
How long a fluid takes to forget it was not rotating — viscosity
The drift was the instrument — ideal flow
Two lifts at one incidence — circulation and lift
A duct that forgets everything but one number — viscosity
A spiral is a legible record — ideal flow
A wake that says what made it — circulation and lift
Every memory number is one time over another — regimes and numbers
A blade that flies through what it shed — circulation and lift
Reversible, and unusable — ideal flow
A row that meets the row before it — circulation and lift
Everything about the start, except one vector — ideal flow
Nothing in the present picks the flow — ideal flow
The inflow that takes time to arrive — circulation and lift
The theory with no memory in it — ideal flow

3 September 2026

20 essays on what is taught wrongly, fluids at work, flows and fields, compressible flow, transition and turbulence, regimes and numbers, viscosity, circulation and lift and ideal flow

A right total from a wrong picture — what is taught wrongly
The effect that is real, and where it stops — what is taught wrongly
Four Bernoullis and one name — what is taught wrongly
The wing that is flat, and flies — what is taught wrongly
The section that decides the river — fluids at work
A permeability that is only the geometry — fluids at work
The mesh that makes its own mass — flows and fields
The angle a junction chooses — fluids at work
Two averages of one flow — flows and fields
The profile a meter cannot see — fluids at work
The jump does not ask what made it — compressible flow
Slower than either of them — compressible flow
The scalar has its own cascade — transition and turbulence
Three buffer layers, one friction — transition and turbulence
Exact in the total, free in the profile — regimes and numbers
Four profiles, one drag — viscosity
The groups are not the only groups — regimes and numbers
The stress a pipe knows — viscosity
Three numbers out of a camber line — circulation and lift
The inside a flow does not decide — ideal flow

1 September 2026

20 essays on what is taught wrongly, fluids at work, flows and fields, compressible flow, transition and turbulence, viscosity, regimes and numbers, circulation and lift and ideal flow

An hour for every tenfold — what is taught wrongly
A number that is only the shape of the hole — fluids at work
The area that must not move — flows and fields
The drift a closed box will not allow — flows and fields
A compression that costs nothing in the end — compressible flow
Two numbers that do not change — compressible flow
Every unstable wave is inside one circle — transition and turbulence
Sufficient, and not necessary — transition and turbulence
Equal on average, and nothing else — transition and turbulence
The core that does not move — viscosity
The gap that carries the most — viscosity
The three that never converge — regimes and numbers
Exactly similar, and one number short — viscosity
Where a pure number comes from — regimes and numbers
One formula, and it does not ask what the shape is — circulation and lift
How much more than the least — ideal flow
The optimum that does not matter — circulation and lift
The mass a body has to borrow — ideal flow
The speed where the damping is exactly zero — circulation and lift
The lowest pressure is on the body — ideal flow

31 August 2026

20 essays on transition and turbulence, flows and fields, ideal flow and viscosity

A second length at the wall — transition and turbulence
The knot a flow cannot untie — flows and fields
The stretching rate that is not one number — flows and fields
What decay never forgets — transition and turbulence
The range a real Reynolds number does not have — transition and turbulence
The exponents that stop being thirds — transition and turbulence
A flux that runs both ways — transition and turbulence
Where the inverse cascade stops — transition and turbulence
The constant that makes a variance negative — transition and turbulence
A sheet that cannot stay a sheet — ideal flow
The shape a vortex keeps — ideal flow
The flow with no solution — viscosity
The part of the flow inside the body — ideal flow
The singularity a layer makes for itself — viscosity
The swirl that holds a wave still — ideal flow
The constant a hole leaves behind — ideal flow
The drag that is made of waves — ideal flow
What a point vortex is not — ideal flow
The corners that can be done with mirrors — ideal flow
The length the limit invents — ideal flow

30 August 2026

20 essays on regimes and numbers and circulation and lift

A solid, if it is not given time — regimes and numbers
The frequency a wake chooses — regimes and numbers
The number that cannot break a drop — regimes and numbers
Long enough to make a wake — regimes and numbers
The half that carries nothing — circulation and lift
A disc that knows no blades — circulation and lift
The number that is an answer — regimes and numbers
A transition that needs a second number — regimes and numbers
The side that cannot keep up — circulation and lift
A row is not a set of aerofoils — circulation and lift
A speed nobody imposed — regimes and numbers
One group, three exponents — regimes and numbers
The condition that can be bought — circulation and lift
An exponent dimensions cannot give — regimes and numbers
More lift than weight — circulation and lift
One formula for both ends — regimes and numbers
Where the line stops being a line — circulation and lift
The sweep a root does not have — circulation and lift
Two answers to one question — circulation and lift
The control that works backwards — circulation and lift

29 August 2026

20 essays on flows and fields and compressible flow

The picture belongs to whoever is watching — flows and fields
Every flow is two flows — flows and fields
A rate of change that will not hold still — flows and fields
Longer, with nothing pulling it — flows and fields
The other branch of the same curve — compressible flow
When a shock cannot bounce — compressible flow
Where a vortex stops — flows and fields
Incompressible is not a property of the fluid — flows and fields
The spin a shock leaves behind — compressible flow
A shock that lies on the body — compressible flow
The one number that runs out at three dimensions — flows and fields
A wave nothing in it travels with — flows and fields
The equation that changes type inside its own answer — compressible flow
Steady, three-dimensional, and mixing anyway — flows and fields
When gamma stops being a number — compressible flow
The signature that forgets the shape — compressible flow
A radius that gives the energy away — compressible flow
The least drag a volume can have — compressible flow
The discontinuity that has a thickness — compressible flow
Every compression becomes a shock in the end — compressible flow

27 August 2026

15 essays on ideal flow and circulation and lift

The flow with the least energy in it — ideal flow
The mirror that is a circle — ideal flow
Drag in the theory that forbids it — ideal flow
Where the unknown boundary is the known one — ideal flow
The momentum with no value — ideal flow
Inviscid does not mean irrotational — ideal flow
The one rotational solution anybody can write down — ideal flow
The vorticity nothing decides — ideal flow
The exact theory, drawn by viscosity — ideal flow
The body the outer flow actually sees — ideal flow
Three is the most that can be predicted — ideal flow
A finite force from an infinite speed — circulation and lift
Nothing turns a sharp corner — ideal flow
The pressure that depends on the past — ideal flow
The one thing that does not add up — ideal flow

26 August 2026

15 essays on viscosity

The price of a gradient — viscosity
Where the heat of a drag is made — viscosity
The cheapest shape the walls allow — viscosity
A force without the flow that makes it — viscosity
The last of the oil — viscosity
The film that heats itself — viscosity
What a plate takes with it — viscosity
A viscosity that depends on the question — viscosity
A viscosity made of particles — viscosity
The surface that moves with the flow — viscosity
The third thickness — viscosity
The energy a vortex cannot have — viscosity
A swimmer that cannot go backwards — viscosity
The viscosity nobody uses — viscosity
What a fluid takes out of a swing — viscosity

24 August 2026

15 essays on regimes and numbers and transition and turbulence

What "of order one" is worth — regimes and numbers
Where a fluid stops being one — regimes and numbers
Slow enough to be steady — regimes and numbers
How small is small enough — regimes and numbers
The size a drop is allowed — regimes and numbers
The drop that is not a tear — regimes and numbers
Which speed goes in the number — regimes and numbers
The balance that is its own error — regimes and numbers
The tracer that is not one — regimes and numbers
The threshold the walls decide — transition and turbulence
Where the parabola goes — regimes and numbers
Five numbers, one name — transition and turbulence
How far before the heat arrives — regimes and numbers
A limit nothing reaches — regimes and numbers
The number that really is one — regimes and numbers

22 August 2026

15 essays on flows and fields, what is taught wrongly, transition and turbulence, ideal flow, viscosity, compressible flow and circulation and lift

The mean is not the flow — flows and fields
The drift in a wave that has none — flows and fields
A wall that is not quite there — flows and fields
The randomness that is not in the equations — what is taught wrongly
The layer with no length in it — transition and turbulence
What a code says to a wall — transition and turbulence
What the far field remembers — ideal flow
An oscillation with somewhere to go — viscosity
The moment a spectrum cannot hold — transition and turbulence
The sound is what does not cancel — compressible flow
The one exact result — transition and turbulence
The limit that is not the value — transition and turbulence
How far a parcel gets — transition and turbulence
Turbulent some of the time — transition and turbulence
The lift at the mean angle — circulation and lift

21 August 2026

15 essays on flows and fields, regimes and numbers, what is taught wrongly, ideal flow, viscosity, compressible flow and circulation and lift

How many things a flow must be told — flows and fields
The other layer, and the one number that separates them — regimes and numbers
Where vorticity comes from — flows and fields
The cushion that is not there — what is taught wrongly
The wing the equation is really solving — regimes and numbers
Ask for the pressure, and see what shape that is — ideal flow
The air a wing does not carry — what is taught wrongly
Where the reaction to a wing's lift is — ideal flow
A body with no lift, and a moment anyway — ideal flow
The layer that stops at a depth — viscosity
The wall that heats itself — compressible flow
How far before a duct forgets what was fed into it — viscosity
The sound that only leaves — compressible flow
A wake that closes on itself — circulation and lift
The walls are in the answer — circulation and lift

20 August 2026

15 essays on what is taught wrongly and circulation and lift

Not half a venturi — what is taught wrongly
An angle, not a speed — what is taught wrongly
The bee that cannot fly — what is taught wrongly
Where lift starts — circulation and lift
Nothing but the edge — circulation and lift
A slot is not a nozzle — circulation and lift
The wind a swept wing feels — circulation and lift
Which part of a wing stalls first — circulation and lift
The loading nobody used — circulation and lift
A wing that leaves the plane — circulation and lift
Two wings and it does not matter where — circulation and lift
The lift beside a wing — circulation and lift
Where the wake ends up — circulation and lift
The shake that is not resonance — circulation and lift
The surface in the wake — circulation and lift

19 August 2026

15 essays on flows and fields, regimes and numbers, viscosity, ideal flow, circulation and lift, transition and turbulence and compressible flow

No randomness, and it mixes anyway — flows and fields
Where a jet stops being a jet — regimes and numbers
The count a pattern cannot break — flows and fields
Two slow things make a fast one — regimes and numbers
Too fast for a profile — regimes and numbers
Nothing but the shape of the gap — viscosity
Three dimensions are kinder — ideal flow
Lift out of a failure — circulation and lift
The eddies nobody stirs — viscosity
What survives being wound up — ideal flow
The cascade that runs backwards — transition and turbulence
What a jet keeps, and what it collects — viscosity
The number that stops the mixing — transition and turbulence
The wall that cancels its own waves — compressible flow
What viscosity cannot take away — viscosity

18 August 2026

15 essays on what is taught wrongly and fluids at work

The effect that explains nothing — what is taught wrongly
The bath does not know the hemisphere — what is taught wrongly
The siphon that does not need the air — what is taught wrongly
The hole that halves the flow — fluids at work
What a jet cannot push sideways — fluids at work
Half the jet speed takes everything — fluids at work
The price of knowing the flow rate — fluids at work
The instrument in the answer — fluids at work
Stopping water costs more than moving it — fluids at work
A pump with no engine — fluids at work
Mixing is a pump — fluids at work
One number picks the machine — fluids at work
A velocity nobody has — fluids at work
Where Darcy stops — fluids at work
The bed that weighs itself — fluids at work

16 August 2026

15 essays on what is taught wrongly, regimes and numbers, flows and fields, viscosity, ideal flow, circulation and lift, transition and turbulence and compressible flow

The theory that forbade flight — what is taught wrongly
Nothing sucks — what is taught wrongly
Counting what matters — regimes and numbers
What a parcel does in the first instant — flows and fields
The spin that feeds itself — flows and fields
Whether the droplet turns — regimes and numbers
The wall that shakes — viscosity
Vortices move each other — ideal flow
A ring moves because it is bent — circulation and lift
Pressure has no speed — ideal flow
The layer that stops growing — viscosity
The lift that arrives late — circulation and lift
Every mode decays and it grows anyway — transition and turbulence
One diaphragm, every wave — compressible flow
Two ways to choke — compressible flow

15 August 2026

15 essays on fluids at work

The most a disc can take — fluids at work
A big slow push — fluids at work
The wake that has to spin — fluids at work
The roughness a wall cannot feel — fluids at work
A loss with no viscosity in it — fluids at work
The shock in a river — fluids at work
The depth that costs least — fluids at work
The drag that falls as it speeds up — fluids at work
A ball that swings without spinning — fluids at work
Faster than the wind that drives it — fluids at work
The fastest way is not the straight one — fluids at work
The radius that costs least — fluids at work
When a body tears the water — fluids at work
The bubble that hammers — fluids at work
Work out of a change of swirl — fluids at work

13 August 2026

15 essays on transition and turbulence and viscosity

The solutions stop being chosen — transition and turbulence
The number that is not a number — transition and turbulence
A layer with a kink in it — transition and turbulence
Every wavelength at once — transition and turbulence
What averaging costs — transition and turbulence
The ladder that never closes — transition and turbulence
A guess with a constant in it — transition and turbulence
Where the energy goes — transition and turbulence
The gradient that does both — viscosity
The grid nobody can build — transition and turbulence
A threshold with a closed form — transition and turbulence
The cost of going turbulent — viscosity
Three numbers left of a fluid — transition and turbulence
A millionth is enough — transition and turbulence
The street this site cannot draw — transition and turbulence

11 August 2026

15 essays on compressible flow, what is taught wrongly and regimes and numbers

What a signal travels at — compressible flow
When the warning cannot arrive — compressible flow
Energy instead of pressure — compressible flow
The duct that works backwards — compressible flow
The throat that stops listening — compressible flow
What the airspeed indicator believes — what is taught wrongly
One area, two answers — compressible flow
The jump the equations allow — compressible flow
The pocket on top of the wing — regimes and numbers
The only law that forbids it — compressible flow
What a shock costs — compressible flow
A shock that leans — compressible flow
When the wedge is too blunt — compressible flow
Turning the other way is free — compressible flow
Drag with nothing to rub — compressible flow

4–10 August 2026

46 essays on what is taught wrongly, regimes and numbers, flows and fields, ideal flow, viscosity and circulation and lift

The story about air meeting up again — what is taught wrongly
One number decides which physics applies — regimes and numbers
Streamlines are not the paths particles take — flows and fields
The theory that solves everything — ideal flow
Everything happens in a layer you cannot see — viscosity
What actually holds a wing up — circulation and lift
Mass has nowhere to go — flows and fields
The exact theory says nothing has any drag — ideal flow
The sharp edge decides — circulation and lift
The Reynolds number, and the length in it — regimes and numbers
When the flow lets go — viscosity
Where Bernoulli's equation applies — what is taught wrongly
Air must be pushed down, and the usual sum is wrong — what is taught wrongly
Flows add up — ideal flow
The two theories, side by side — viscosity
The lift curve, and why it is a straight line — circulation and lift
What a flow is — flows and fields
When air stops being incompressible — regimes and numbers
Steady does not mean nothing is happening — flows and fields
How thick is thin — viscosity
Lift with no wing at all — circulation and lift
Fast means low pressure — ideal flow
The angle that does not care — regimes and numbers
What a photograph of a flow shows — what is taught wrongly
One function instead of two — ideal flow
Spin is not the same as going round — flows and fields
The model that cannot be matched — regimes and numbers
The two drags a wing pays — viscosity
The vortex a wing leaves behind — circulation and lift
Bodies made out of nothing — ideal flow
How much uphill a layer can take — viscosity
The number on a streamline is a flow rate — flows and fields
The world with no inertia — regimes and numbers
Where the lift acts — circulation and lift
A wall made by reflection — ideal flow
Circulation is vorticity, added up — flows and fields
The price of having ends — circulation and lift
Where the straight line stops — viscosity
From a circle to a wing — ideal flow
How much circulation is too much — circulation and lift
The cheapest way to stay up — viscosity
The number that does not depend on the tunnel — ideal flow
The wall that pushes back — circulation and lift
The force of getting going — ideal flow
What a flap does, and what it does not — circulation and lift
The span is the whole story — circulation and lift

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