Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Concept

Mach reflection — where it appears

The three-shock configuration that replaces an ordinary reflection when a reflected shock can no longer turn the flow back to the wall. A nearly normal Mach stem stands on the surface, three shocks meet at a triple point, and a slip line trails downstream.

Named by 2 essays across one field — 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 The shock radius against time, from an equation that was given no exponent. The thin-shell energy balance integrated forward from a small initial radius, on logarithmic axes. The two-fifths power is not put in: the ordinary differential equation is Ṙ = √(E/AρR³), and the straight line is what it does. The fitted slope is 0.39983 and the fitted prefactor is 0.90721 against a closed form of 0.90702 — the small residuals being the integration's memory of where it started, which the similarity solution has no equivalent of.

A radius that gives the energy away

Four quantities, three dimensions, one group. The radius of a strong blast must be a constant times (Et²/ρ)¹⁄⁵, and nothing about the device, the chemistry or the initial size can appear. The exponent is free and the constant is not.

compressible · Blast wave

Named alongside it

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

MeasurementModel limitNormal shockShock waveBifurcationBlast waveBuckingham's pi theoremDimensional analysisDiscontinuityEnergy equationHysteresisN-wave

All concepts