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Strong cylindrical shocks in a rotating gas

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Abstract

Similarity solutions describing the flow behind a diverging strong cylindrical shock wave, advancing into a nonuniform gas having solid body rotation, are studied. The effects of the angular velocity variation on the shock velocity are shown graphically. It is found that an increase in the initial angular velocity leads to a decrease in the shock velocity.

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Abbreviations

c 0 :

sound velocity in unperturbed state

c′ :

sound velocity in unperturbed state at the axis of symmetry

D :

nondimensional density in unperturbed state

E :

energy release per unit length

f :

nondimensional radial velocity in perturbed state

g :

nondimensional pressure in perturbed state

h :

nondimensional density in perturbed state

k :

nondimensional azimuthal velocity in perturbed state

M :

an integral

N :

another integral

P :

nondimensional pressure in unperturbed state

p :

pressure in perturbed state

p 0 :

pressure in unperturbed state

p′ :

pressure at the axis in unperturbed state

p 1 :

pressure immediately behind the shock front

R :

shock front radius

r :

radial coordinate

R 0 :

a characteristic length parameter

t :

time coordinate

U :

shock front velocity

u :

particle velocity (radial) in perturbed state

u 0 :

particle velocity (radial) in unperturbed state

u 1 :

particle velocity (radial) immediately behind the shock front

v :

particle velocity (azimuthal) in perturbed state

v 0 :

particle velocity (azimuthal) in unperturbed state

v 1 :

particle velocity (azimuthal) immediately behind the shock

w :

nondimensional azimuthal velocity in unperturbed state

x :

a nondimensional independent variable

z :

axial coordinate of cylindrical coordinates

Z :

a nondimensional independent variable

Ω 0 :

angular velocity in unperturbed state

Ω 1 :

angular velocity immediately behind the shock

ρ :

density in perturbed state

ρ 0 :

density in unperturbed state

ρ 1 :

density immediately behind the shock

ρ′ :

density at r=0 in unperturbed state

γ :

adiabatic index of the gas

Χ 0 :

R 20 Ω 20 /(c′)2

References

  1. Fraenkel, L. E., J. Fluid Mech. 5 (1959) 637.

    Google Scholar 

  2. Sakurai, A., J. Fluid Mech. 1 (1956) 436.

    Google Scholar 

  3. Chandrasekhar, S., Hydrodynamic and Hydromagnetic stability, Clarendon Press, Oxford (1961) Chapter III.

    Google Scholar 

  4. Whitham, G. B., J. Fluid Mech. 4 (1958) 337.

    Google Scholar 

  5. Sakurai, A., J. Phys. Soc. Japan 8 (1953) 662.

    Google Scholar 

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Authors and Affiliations

  1. Dept. of Mathematics, Indian Institute of Technology, Bombay-76, India

    P. Chaturani

Authors
  1. P. Chaturani
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Chaturani, P. Strong cylindrical shocks in a rotating gas. Appl. Sci. Res. 23, 197–211 (1971). https://doi.org/10.1007/BF00413198

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  • DOI: https://doi.org/10.1007/BF00413198

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