Concept

Parabolic — where it appears

The character of an equation whose solution marches in one direction, so that nothing at a station can depend on anything beyond it. Prandtl's boundary-layer equations are parabolic only because the pressure is prescribed, and letting the pressure respond destroys that character where it matters.

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

Also named here as triple deck — the same set of essays touches all of them, so they are one junction rather than several.

The singularity a layer makes for itself

March Prandtl's equations into an adverse pressure gradient and the wall shear reaches zero with an infinite slope at a finite station, and the solution cannot be continued past it. The singularity is real, it is not a numerical difficulty, and it belongs to the boundary condition rather than to the equations.

viscous · Boundary layer

The eighths nobody chose. Four physical statements — the inner layer sits in the classical one's shear, its inertia balances its own viscous stress, the pressure is of the order of that inertia, and the displacement it makes produces that pressure — are a linear system in four exponents. Solving it gives three eighths, five eighths, one eighth and a quarter, exactly.

The length the limit invents

Prandtl's equations are parabolic, so nothing at one station can depend on anything downstream of it. Every experiment shows the pressure rising ahead of a shock or a step. The resolution is a region three eighths of a power of the Reynolds number long, which the limit that produced the equations was supposed to have removed.

inviscid · Interaction

Named alongside it

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

Boundary layer Displacement thickness Model limit Separation Triple deck Adverse pressure gradient Airy function Asymptotic matching Discretisation Eigenvalue Goldstein singularity Interaction

All concepts