Concept

Hysteresis — where it appears

A dependence of the present state on the path taken to reach it, so that a quantity traced up and down a parameter does not retrace itself. The area of the loop is work done, and its presence proves a state variable is being carried that the parameter does not determine.

Named by 6 essays across 5 fields — each of them below, with the objects they name alongside it.

The two ways a shock can meet a wall. Left: the incident shock from the wedge reaches the wall and a second shock turns the flow back parallel to it, meeting at a point. Right: at a larger wedge angle no reflected shock can turn the flow that far, and the intersection lifts off the wall into a triple point with a nearly normal Mach stem standing on the surface and a slip line trailing downstream. The two configurations are drawn at the angles the solver returns, with every shock angle computed rather than sketched.

When a shock cannot bounce

A shock reflects off a wall until the reflected shock runs out of turning, which happens at a wedge angle well below the free stream's own limit. Between the two boundaries both configurations exist, both are stable, and which one appears depends on which direction the experiment came from.

compressible · Mach reflection

A high tail buys a second trim point, at 31.52 degrees. The pitching moment of two layouts against incidence, with the stable trim points marked. Both cross zero with a negative slope near 0.76°, which is the ordinary cruise trim. Past the stall the conventional layout's tail is caught only glancingly by the wake and its moment stays nose-down, so it has no second crossing; the T-tail's tail is swept into the wake and sees 12 per cent of the dynamic pressure, its download collapses, and the wing's own nose-up moment carries the curve back across zero at 31.52°. That second crossing is stable — the slope there is negative too — which means an aircraft that reaches it stays there.

A stall that is a place

A stall is an event, and the usual accounts treat it as one — a boundary reached, a damping lost. A high tailplane makes it something else. Swept into the wing's wake, the tail loses the download that held the nose up, and the aircraft finds a second stable trim point thirty degrees past the stall from which the elevator cannot bring it back.

misconceptions · Stall speed

A skin lags the air by a time its own thickness sets. A skin held at one flight condition, relaxing towards the adiabatic wall temperature. The approach is exponential with a time constant ρc τ / h — 8.37 s at 2 mm, 25.1 s at 6 mm, 50.2 s at 12 mm — so the temperature a steady recovery calculation gives is reached after several minutes rather than at once. The fluid supplies one number to this calculation, the adiabatic wall temperature, and the structure supplies everything else.

The skin that lags the flight

A wall can be told its temperature or told nothing, and both are solved problems. A real skin is told neither. It has heat capacity, so its temperature is a transient whose time constant is its own thickness divided by what the layer delivers — and the number the steady calculation returns is an upper bound a short exposure never collects.

compressible · Recovery

The curve that lets in more than one answer. The neutral stability curve: the driving needed to sustain a disturbance of a given wavelength. It has a minimum, so at any driving above the minimum there is a whole band of wavelengths that can grow — and the system has to pick one.

The state a machine was started into

Above the critical driving there is not one flow but a band of them, and a container of a given size can hold several. Which one appears is decided by how the apparatus was brought up to speed, and at twice critical there are eight to choose from.

regimes · Taylor

The same wavelength drawn as rolls and as hexagons. Plan views of a convecting layer with one critical wavelength, drawn from the amplitude equations' two stable states. On the left, rolls: a single set of parallel bands, rising fluid along one set of lines and sinking along the next. On the right, hexagons: three sets of rolls at 120° to each other with equal amplitudes, whose sum has its maxima on a triangular lattice with spacing 2/√3 of the wavelength, each maximum at the centre of a hexagonal cell. At ε = 0.0250, inside the window, both are stable: rolls with amplitude 0.158 and hexagons with 0.081 in each of their three rolls. A hexagon is not a different kind of cell; it is three roll patterns that the quadratic term lets reinforce one another.

Hexagons remember how the heat was turned up

A layer heated from below convects in rolls, unless its top and bottom are not mirror images of each other. Then three sets of rolls at 120° can feed one another through a term the symmetry used to forbid, hexagonal cells appear before the layer is formally unstable, and there is a range of heating in which rolls and hexagons are both stable — so the pattern a layer shows depends on whether the heat was turned up or down to get there.

turbulence · Convection

One incidence, two lifts. Lift coefficient against incidence for a wing pitched sinusoidally through the stall, with the static curve for comparison. The loop is traversed anticlockwise: at twelve degrees the wing carries 0.22 more lift going up than coming down.

Two lifts at one incidence

A wing pitched up and down through the stall does not retrace its own lift curve. At twelve degrees it carries 0.22 more lift going up than coming down, and the loop that opens between the two is the work the airstream does on it — which is where the energy for a stall flutter comes from.

circulation · Vortex lift

Named alongside it

The objects these essays reach for when they reach for this one.

Bifurcation Measurement Memory kernel Model limit Initial condition Model validity Separation Stability Stall Adiabatic wall Aerodynamic heating Aeroelasticity

All concepts