 Linear-profile spherical blast wave

ID: linear-profile-spherical-blast-wave

U = 2 ξ / (γ + 1)

D = (γ + 1) ξ / (γ - 1)

and

P = 2 ξ^{3} / (γ + 1)

solve the spherical blast equations at the displayed ambient exponent. For

γ = 5/3

β = 2

and

R^{3} = 3 E t^{2} / (2 π C)

. The dimensional fields are

u = r / (2 t)

ρ = 8 π C^{2} r / (3 E t^{2})

and

p = 2 π C^{2} r^{3} / (9 E t^{4})

for

0 < r < R

. Their kinetic and internal energies are equal. Substituting these profiles into all three equations and the shock conditions verifies the solution.

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