Propagation Of Spherical Shock Waves Research Articles

Propagation of Shock Waves in Inhomogeneous Gases. III

The propagation of spherical shock waves in the stellar interior is considered, extending the method developed in previous papers. A differential equation of the shock strength is derived, which can be applied to any stellar models. It is found that the spherical damping effect is pronounced near the center of stars, and this guarantees the stability of the stellar core in general. In the envelope, this effect becomes negligible, and it is justified near the stellar surface to treat the shock waves as plane.

Propagation of spherical shock waves in stars

Propagation of spherical shock waves through self-gravitating polytropic gas spheres such as stars, caused by an instantaneous central explosion of finite energy E, is discussed theoretically. The problem is characterized by two lengths R0, L, where $R_0 = \left(\frac {E}{4\pi p_0}\right)^{1|3},\;\;\;\;\; L = \left(\frac {3C^2_0}{2\pi \rho_0G} \right)^{1|2}$p0 and C0 are the values of pressure, density and velocity of sound at the centre of the equilibrium pre-explosion state, and G is the constant of gravitation. R0 and L are scales connected with the power of the explosion and the dimensions of the star respectively, and their ratio A = R0/L has a fundamental significance. A solution especially suitable in the case of A = O(1) is developed in the form of power series in R/R0 (R is the distance between the shock front and the centre) by a method similar to that used in previous papers by the present author (1953, 1954). An approximation to this solution is carried out up to the term in R3. In particular, the velocity of the shock wave U is found to be $\frac {U}{C_0} = 1\cdot30 \left(\frac{R}{R_0}\right)^{-3|2} \{1 +0\cdot41A^2\left(\frac{R}{R_0}\right)^2 + 0\cdot 57\left(\frac{R}{R_0}\right)^3 +\ldot\}$ for the case of λ = 1.4, where λ is the ratio of specific heats.

Propagation of Spherical Shock Waves in Stellar Interiors

Propagation of Spherical Shock Waves in Stellar Interiors

Propagation of Spherical Shock Waves in Water

Propagation of Spherical Shock Waves in Water