Concept

Bow shock — where it appears

The curved shock that stands ahead of a blunt body in supersonic flow, detached from its nose by a small gap of subsonic gas. Close to the nose it is nearly normal and strong; far out it weakens and bends back towards the Mach angle of the free stream.

Named by 4 essays across one field — each of them below, with the objects they name alongside it.

Past 23.0° at Mach 2.00 there is no attached shock. The same wedge at two half-angles. On the left the θ–β–M relation has a root and the shock sits on the nose. On the right it has none, and the solver throws rather than returning the nearest thing — which matters, because a solver that quietly clamped to the maximum would draw a neat attached shock on a body that cannot carry one. The bow shock on the right is indicative: its shape is not solved here.

When the wedge is too blunt

Every curve of shock angle against deflection has a maximum. Past it there is no attached shock at any angle — the solver has no root to return and must say so, rather than quietly handing back the nearest thing and drawing a picture that cannot exist.

compressible · Oblique shock

A bow shock that grows as a line explosion does. The radius of the bow shock around a hemisphere-nosed cylinder, in body diameters, against distance behind the nose: the blast-wave analogy, R/d = 0.795 C^¼ (x/d)^½ with C, the drag coefficient, 0.919, which contains no Mach number, and Billig's correlation of measured bow shocks on spheres at Mach 5, 10 and 20, anchored at the nose and continued as a hyperbola to the Mach cone. Both grow as the square root of the distance; at Mach 20 the analogy's shock is a steady 0.71 of Billig's.

A hypersonic body leaves a line explosion behind it

A blunt body at hypersonic speed does work on the air at a rate equal to its drag, and each slice of air it passes through is struck once and left to expand. Seen from the ground, that is a line explosion, and Sedov's cylindrical blast wave gives the bow shock's width and the pressure on the afterbody without a Mach number in either. The analogy's classical constants come straight out of the blast solution. So do its limits: it holds only while its own shock stays strong, over a length that grows as the square of the flight Mach number, and it puts the body inside a core hotter than anything the flow can reach.

compressible · Blast wave

Next to the body the gas remembers the nose. The gas temperature, over the free stream's, against distance from the axis of a hemisphere-nosed cylinder at Mach 15, at 2, 20 and 200 diameters behind the nose; the body's surface is at a half. The gas next to the body crossed the nearly normal part of the bow shock and carries its entropy: 16.7 times the free stream's temperature at 2 diameters, 9.29 at 200, falling outwards to the gas that crossed the weaker, oblique shock. The blast-wave analogy's core at 2 diameters, dashed, runs off the top of the frame on its way to infinity.

The gas beside a hypersonic body remembers its nose

The blast-wave analogy gets a blunt body's bow shock and afterbody pressure right and its temperature absurdly wrong: it puts the body in the empty core of an explosion, where the temperature has no bound. The real gas beside the body crossed the nearly normal shock at the nose and carries that crossing's entropy all the way down. Expanded to the afterbody's pressure, it is ten to twenty times the free stream's temperature at Mach 15, it never falls below a floor set by the nose alone, and the sheath that carries it is wider than the body.

compressible · Blast wave

A laminar boundary layer eats through the sheath a Reynolds number of diameters back. How far out the boundary layer has eaten into the entropy layer, as the upstream radius of the streamline at its edge in nose diameters, against distance behind the nose, at Mach 15 for Reynolds numbers on the diameter of 10⁴ to 10⁷, laminar, and 10⁶ turbulent. The sheath's edge is the streamline whose entropy is half the axis's, 1.22 diameters out. The laminar layer reaches it at 3.3·10³ diameters for the smallest Reynolds number and 3.4·10⁶ for the largest; turbulent at 10⁶, at 536.

The sheath outlasts the body

A blunt hypersonic body wraps itself in a sheath of hot, thin gas from its nose's shock, and its boundary layer grows by eating that gas from the inside. The usual picture has the boundary layer through the sheath within a few nose diameters. It is not: a laminar boundary layer takes about a third of a Reynolds number of diameters to swallow the sheath at Mach 15, which is thousands to millions of diameters, and a turbulent one hundreds. On any body of ordinary length the boundary layer never sees the cooler gas outside, and it is heated by the sheath's gas all the way down.

compressible · Blast wave

Named alongside it

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

Blunt body Entropy Entropy layer Hypersonic Model limit Similarity solution Blast wave Stagnation temperature Analogy Boundary layer Detachment Drag

All concepts