### Abstract

The converging shock problem was first solved by Guderley and later by Landau and Stanyukovich for infinitely strong shocks in an ideal gas with spherical and cylindrical symmetry. This problem is solved herein for finite-strength shocks and a non-ideal-gas equation of state with an adiabatic bulk modulus of the type B_{s}= -v∂p ∂v|_{s} = (p +B) f(v), where B is a constant with the dimensions of pressure, and f(v) is an arbitrary function of the specific volume. Self-similar profiles of the particle velocity and thermodynamic variables are studied explicitly for two cases with constant specific heat at constant volume; the Tait-Kirkwood-Murnaghan equation, f(v) = constant, and the Walsh equation, f(v) = v/A, where A = constant. The first case reduces to the ideal gas when B = 0. In both cases the flow behind the shock front exhibits an unbalanced buoyant force instability at a critical Mach number which depends upon equation-of-state parameters.

Original language | English (US) |
---|---|

Pages (from-to) | 194-202 |

Number of pages | 9 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 2 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1981 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics

### Cite this

*Physica D: Nonlinear Phenomena*,

*2*(1), 194-202. https://doi.org/10.1016/0167-2789(81)90073-7

**Converging finite-strength shocks.** / Axford, Roy A; Holm, D. D.

Research output: Contribution to journal › Article

*Physica D: Nonlinear Phenomena*, vol. 2, no. 1, pp. 194-202. https://doi.org/10.1016/0167-2789(81)90073-7

}

TY - JOUR

T1 - Converging finite-strength shocks

AU - Axford, Roy A

AU - Holm, D. D.

PY - 1981/1

Y1 - 1981/1

N2 - The converging shock problem was first solved by Guderley and later by Landau and Stanyukovich for infinitely strong shocks in an ideal gas with spherical and cylindrical symmetry. This problem is solved herein for finite-strength shocks and a non-ideal-gas equation of state with an adiabatic bulk modulus of the type Bs= -v∂p ∂v|s = (p +B) f(v), where B is a constant with the dimensions of pressure, and f(v) is an arbitrary function of the specific volume. Self-similar profiles of the particle velocity and thermodynamic variables are studied explicitly for two cases with constant specific heat at constant volume; the Tait-Kirkwood-Murnaghan equation, f(v) = constant, and the Walsh equation, f(v) = v/A, where A = constant. The first case reduces to the ideal gas when B = 0. In both cases the flow behind the shock front exhibits an unbalanced buoyant force instability at a critical Mach number which depends upon equation-of-state parameters.

AB - The converging shock problem was first solved by Guderley and later by Landau and Stanyukovich for infinitely strong shocks in an ideal gas with spherical and cylindrical symmetry. This problem is solved herein for finite-strength shocks and a non-ideal-gas equation of state with an adiabatic bulk modulus of the type Bs= -v∂p ∂v|s = (p +B) f(v), where B is a constant with the dimensions of pressure, and f(v) is an arbitrary function of the specific volume. Self-similar profiles of the particle velocity and thermodynamic variables are studied explicitly for two cases with constant specific heat at constant volume; the Tait-Kirkwood-Murnaghan equation, f(v) = constant, and the Walsh equation, f(v) = v/A, where A = constant. The first case reduces to the ideal gas when B = 0. In both cases the flow behind the shock front exhibits an unbalanced buoyant force instability at a critical Mach number which depends upon equation-of-state parameters.

UR - http://www.scopus.com/inward/record.url?scp=49149138828&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49149138828&partnerID=8YFLogxK

U2 - 10.1016/0167-2789(81)90073-7

DO - 10.1016/0167-2789(81)90073-7

M3 - Article

AN - SCOPUS:49149138828

VL - 2

SP - 194

EP - 202

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1

ER -