Slightly two- or three-dimensional self-similar solutions

Re'em Sari, Nate Bode, Almog Yalinewich, Andrew MacFadyen

    Research output: Contribution to journalArticlepeer-review


    Self-similarity allows for analytic or semi-analytic solutions to many hydrodynamics problems. Most of these solutions are one-dimensional. Using linear perturbation theory, expanded around such a one-dimensional solution, we find self-similar hydrodynamic solutions that are two- or three-dimensional. Since the deviation from a one-dimensional solution is small, we call these slightly two-dimensional and slightly three-dimensional self-similar solutions, respectively. As an example, we treat strong spherical explosions of the second type. A strong explosion propagates into an ideal gas with negligible temperature and density profile of the form ρ(r, θ, φ{symbol}) = r-ω[1 + σF(θ, φ{symbol})], where ω > 3 and σ ≪ 1. Analytical solutions are obtained by expanding the arbitrary function F(θ, φ{symbol}) in spherical harmonics. We compare our results with two-dimensional numerical simulations, and find good agreement.

    Original languageEnglish (US)
    Article number087102
    JournalPhysics of Fluids
    Issue number8
    StatePublished - Aug 16 2012

    ASJC Scopus subject areas

    • Computational Mechanics
    • Condensed Matter Physics
    • Mechanics of Materials
    • Mechanical Engineering
    • Fluid Flow and Transfer Processes


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