title: Analytical linear theory for the interaction of a planar shock wave with a two- or three-dimensional random isotropic acoustic wave field.
abstract: We present an analytical model that describes the linear interaction of a planar shock wave with an isotropic random sonic field. First, we study the interaction with a single-mode acoustic field. We present the exact evolution for the pressure, velocity, vorticity, and density field generated behind the shock wave, and we also calculate exact and closed analytical expressions for the asymptotic behavior of these modes. Applying superposition, we use the results obtained from the single-mode analysis in order to compute the interaction with 2D/3D isotropic random acoustic fields. We present analytical expressions for the average turbulent kinetic energy generated behind the shock, as well as the averaged vorticity and the density perturbations as a function of the shock strength M(1) and the gas compressibility γ. We also study the acoustic energy flux emitted by the shock front. Exact asymptotic analytical scaling laws are given for all the 3D averages downstream. A detailed comparison with previous works is shown.
authors.affiliation: Escuela Técnica Superior de Ingenieros Industriales, Instituto de Investigaciones Energéticas, Universidad de Castilla La Mancha, Campus, E-13071 Ciudad Real, Spain. cesar.huete@uclm.es
authors.forename: C
authors.initials: C
authors.lastname: Huete
authors.forename: J G
authors.initials: JG
authors.lastname: Wouchuk
authors.forename: A L
authors.initials: AL
authors.lastname: Velikovich