Concept

Integral method — where it appears

A boundary-layer calculation that satisfies the momentum equation integrated across the layer rather than at every point within it. An assumed profile shape turns the layer into an ordinary differential equation for its thickness, which is why the methods of Pohlhausen and Thwaites are quick and approximate.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Two external flows that agree where it matters and nowhere else. The velocity just outside the boundary layer, for two pressure distributions, against distance along the surface. They cross at the half-way station with the same value and the same gradient, and they have nothing else in common: one accelerates steadily and the other does most of its accelerating at once.

A layer that is an integral of everything upstream

Two surfaces are given external velocity distributions that agree exactly at one station — the same speed and the same gradient. The boundary layers there differ by 38 per cent in momentum thickness, and the two surfaces separate five per cent of their length apart.

viscous · Boundary layer

Inside the layer the upper parcel's lead grows with depth. The transit lag, lower parcel minus upper, of parcels held at a quarter, a half and three-quarters of the boundary layer's thickness and just outside it, timed from either side of the attachment point to each chordwise station, on a thin cambered section at zero incidence, up to the upper layer's laminar separation at 62% chord. At mid-chord the lag outside the layer is 0.183 chord-over-speed units; at three-quarters of the thickness 0.195, at half 0.281 and at a quarter 0.695.

Inside the layer the upper parcel leads by more

Two parcels parting at a wing's attachment point arrive at different times, and outside the boundary layer the difference is the circulation over the speed squared. Inside the layer one might expect the slow, sticky fluid to wash the difference out. It does the opposite: deep in the layer the upper parcel's lead is several times the inviscid one, because the suction side's layer is fuller than the pressure side's. Only the layer's outer quarter reads the inviscid lead, and on the suction side the laminar layer gives out before the trailing edge.

misconceptions · Equal transit

Named alongside it

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

Boundary layer Separation Circulation Convolution Drag Equal transit time Kutta condition Lift Measurement Memory kernel Model limit Model validity

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