Characteristic speeds in a viscous, heat-conducting gas

5.6 Characteristic speeds in a viscous, heat-conducting gas

We recall from Section 2.4, in particular (14

), that the jumps $δu$ across acceleration waves and their speeds of propagation are to be calculated from the homogeneous system

In the present context, where the field equations are given by (79

, 80

) this homogeneous algebraic system spreads out into three equations, viz.

By (89

) and (91

) this is a fully explicit system, if the thermal equation of state $p = p(α, T)$ is known. The vanishing of its determinant determines the characteristic speeds. Seccia & Strumia [44 ] have calculated these speeds – one transversal and two longitudinal ones – for non-degenerate gases and obtained the following results in the non-relativistic and ultra-relativistic cases

$2 ∘ ----- mkcT- ≫ 1 : Vtrans = 75kmT$ ,	$∘ ----- Vl1ong = 43mkT$ ,	$∘ -------- Vl2ong = 5.18mkT$ ,

$∘ -- mc2 ≪ 1 : Vtrans = 1c kT 5$ ,	$∘ -- Vl1ong = 1c 3$ ,	$∘ -- Vl2ong = 3c 5$ .

All speeds are finite and smaller than c. Inspection shows that in the non-relativistic limit the order of magnitude of these speeds is that of the ordinary speed of sound, while in the ultra-relativistic case the speeds come close to c.