Ultra-relativistic geometrical shock dynamics and vorticity

Jeremy Goodman, Andrew Macfadyen

    Research output: Contribution to journalArticle

    Abstract

    Geometrical shock dynamics, also called CCW theory, yields approximate equations for shock propagation in which only the conditions at the shock appear explicitly; the post-shock flow is presumed approximately uniform and enters implicitly via a Riemann invariant. The non-relativistic theory, formulated by G. B. Whitham and others, matches many experimental results surprisingly well. Motivated by astrophysical applications, we adapt the theory to ultra-relativistic shocks advancing into an ideal fluid whose pressure is negligible ahead of the shock, but is one third of its proper energy density behind the shock. Exact results are recovered for some self-similar cylindrical and spherical shocks with power-law pre-shock density profiles. Comparison is made with numerical solutions of the full hydrodynamic equations. We review relativistic vorticity and circulation. In an ultra-relativistic ideal fluid, circulation can be defined so that it changes only at shocks, notwithstanding entropy gradients in smooth parts of the flow.

    Original languageEnglish (US)
    Pages (from-to)325-338
    Number of pages14
    JournalJournal of Fluid Mechanics
    Volume604
    DOIs
    StatePublished - Jun 10 2008

    Fingerprint

    Vorticity
    vorticity
    shock
    Fluids
    Entropy
    Hydrodynamics
    ideal fluids
    fluid pressure
    hydrodynamic equations
    astrophysics
    flux density
    entropy
    gradients
    propagation
    profiles

    ASJC Scopus subject areas

    • Mechanics of Materials
    • Computational Mechanics
    • Physics and Astronomy(all)
    • Condensed Matter Physics

    Cite this

    Ultra-relativistic geometrical shock dynamics and vorticity. / Goodman, Jeremy; Macfadyen, Andrew.

    In: Journal of Fluid Mechanics, Vol. 604, 10.06.2008, p. 325-338.

    Research output: Contribution to journalArticle

    Goodman, Jeremy ; Macfadyen, Andrew. / Ultra-relativistic geometrical shock dynamics and vorticity. In: Journal of Fluid Mechanics. 2008 ; Vol. 604. pp. 325-338.
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