### Abstract

A formalism for multidimensional simple waves in gas dynamics using ideas developed by Boillat is investigated. For simple-wave solutions, the physical variables depend on a single function φ(r, t). The wave phase φ(r, t) is implicitly determined by an equation of the form(φ) = r·n(φ)-λ(φ)t, where n(φ) denotes the normal to the wave front, λ is the characteristic speed of the wave mode of interest, r is the position vector, t is the time, and the function f(φ) determines whether the wave is a centred (f(φ) = 0) or a non-centred (f(φ) ≠ 0) wave. Examples are given of time-dependent vortex waves, shear waves and sound waves in one or two space dimensions. The streamlines for the wave reduce to two coupled ordinary differential equations in which the wave phase φ plays the role of a parameter along the streamlines. The streamline equations are expressed in Hamiltonian form. The roles of Clebsch variables, Lagrangian variables, Hamiltonian formulations and characteristic surfaces are briefly discussed.

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

Pages (from-to) | 417-460 |

Number of pages | 44 |

Journal | Journal of Plasma Physics |

Volume | 59 |

Issue number | 3 |

State | Published - 1998 |

### Fingerprint

### Keywords

- Dimethylene ketene radical cation
- Disulfides
- Ion-molecule reactions

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Journal of Plasma Physics*,

*59*(3), 417-460.

**Multidimensional simple waves in gas dynamics.** / Webb, G. M.; Ratkiewicz, R.; Brio, Moysey; Zank, G. P.

Research output: Contribution to journal › Article

*Journal of Plasma Physics*, vol. 59, no. 3, pp. 417-460.

}

TY - JOUR

T1 - Multidimensional simple waves in gas dynamics

AU - Webb, G. M.

AU - Ratkiewicz, R.

AU - Brio, Moysey

AU - Zank, G. P.

PY - 1998

Y1 - 1998

N2 - A formalism for multidimensional simple waves in gas dynamics using ideas developed by Boillat is investigated. For simple-wave solutions, the physical variables depend on a single function φ(r, t). The wave phase φ(r, t) is implicitly determined by an equation of the form(φ) = r·n(φ)-λ(φ)t, where n(φ) denotes the normal to the wave front, λ is the characteristic speed of the wave mode of interest, r is the position vector, t is the time, and the function f(φ) determines whether the wave is a centred (f(φ) = 0) or a non-centred (f(φ) ≠ 0) wave. Examples are given of time-dependent vortex waves, shear waves and sound waves in one or two space dimensions. The streamlines for the wave reduce to two coupled ordinary differential equations in which the wave phase φ plays the role of a parameter along the streamlines. The streamline equations are expressed in Hamiltonian form. The roles of Clebsch variables, Lagrangian variables, Hamiltonian formulations and characteristic surfaces are briefly discussed.

AB - A formalism for multidimensional simple waves in gas dynamics using ideas developed by Boillat is investigated. For simple-wave solutions, the physical variables depend on a single function φ(r, t). The wave phase φ(r, t) is implicitly determined by an equation of the form(φ) = r·n(φ)-λ(φ)t, where n(φ) denotes the normal to the wave front, λ is the characteristic speed of the wave mode of interest, r is the position vector, t is the time, and the function f(φ) determines whether the wave is a centred (f(φ) = 0) or a non-centred (f(φ) ≠ 0) wave. Examples are given of time-dependent vortex waves, shear waves and sound waves in one or two space dimensions. The streamlines for the wave reduce to two coupled ordinary differential equations in which the wave phase φ plays the role of a parameter along the streamlines. The streamline equations are expressed in Hamiltonian form. The roles of Clebsch variables, Lagrangian variables, Hamiltonian formulations and characteristic surfaces are briefly discussed.

KW - Dimethylene ketene radical cation

KW - Disulfides

KW - Ion-molecule reactions

UR - http://www.scopus.com/inward/record.url?scp=0032047891&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032047891&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032047891

VL - 59

SP - 417

EP - 460

JO - Journal of Plasma Physics

JF - Journal of Plasma Physics

SN - 0022-3778

IS - 3

ER -