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Canonical Isotropic Turbulence/Shock Interaction and Beyond

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Homogeneous Turbulence Dynamics
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Abstract

This chapter displays the most advanced theoretical and numerical results dealing with shock/turbulence interaction. Both the wrinckled and the broken shock regimes are discussed, along with extensions beyond the canonical interaction case: spherical blast waves and converging spherical shock waves interacting with turbulence, interaction of a shock with a turbulent binary mixture and interaction of a detonation wave with turbulence.

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Notes

  1. 1.

    The turbulent Reynolds number based on the Taylor microscale \(Re_\lambda \) at the inlet plane of DNS presented in Lee et al. (1993, 1997) range from 11.6 to 21.6.

  2. 2.

    It is to note here that some interactions exist if the upstream field is composed of a single wave of each type, but these interactions cancel from a statistical viewpoint in fully developed isotropic turbulent flows.

References

  • Bhagatwala, A., Lele, S.K.: Interaction of a Taylor blast wave with isotropic turbulence (2012). Shock structure in shock-turbulence interaction. Phys. Fluids 23, 035103 (2011)

    Google Scholar 

  • Bhagatwala, A., Lele, S.K.: Interaction of a converging spherical shock wave with isotropic turbulence (2012). Shock structure in shock-turbulence interaction. Phys. Fluids 24, 085102 (2012)

    Google Scholar 

  • Donzis, D.A.: Shock structure in shock-turbulence interactions. Phys. Fluids 24, 126101 (2012a)

    Article  ADS  Google Scholar 

  • Donzis, D.A.: Amplification factors in shock-turbulence interactions: effect of shock thickness. Phys. Fluids 24, 011705 (2012b)

    Article  ADS  Google Scholar 

  • Dyakov, S.P.: On the stability of shock waves. Zh. Eksp. Teor. Fiz. 27, 288 (1954). At. Res. Agency Establ. AERE Lib./Trans. 648 (1956)

    Google Scholar 

  • Griffond, J.: Linear interaction analysis applied to a mixture of two perfect gases. Phys. Fluids 24, 115108 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Griffond, J., Soulard, O., Souffland, D.: A turbulent mixing Reynolds stress model fitted to match linear interaction analysis prediction. Phys. Scr. 142, 014059 (2010)

    Article  Google Scholar 

  • Griffond, J., Soulard, O.: Evolution of axisymmetric weakly turbulent mixtures interacting with shock or rarefaction waves. Phys. Fluids 17, 086101 (2012)

    Article  Google Scholar 

  • Huete, C., Wouchuk, J.G., Canaud, B., Velikovich, A.L.: Analytical linear theory for the shock and re-shock of isotropic density inhomogeneities. J. Fluid Mech. 700, 214–245 (2012a)

    Article  ADS  MATH  Google Scholar 

  • Huete, C., Wouchuk, J.G., Velikovich, A.L.: Analytical linear theory for the interaction of a planar shock wave with a two- or three-dimensional random isotropic acoustic wave field. Phys. Rev. E 85, 026312 (2012b)

    Article  ADS  Google Scholar 

  • Huete, C., Sanchez, A.L., Velikovich, A.L.: Theory of interactions of thin strong detonations with turbulent gases. Phys. Fluids 25, 076105 (2013)

    Article  ADS  Google Scholar 

  • Huete, C., Sanchez, A.L., Velikovich, A.L.: Linear theory for the interaction of small-scale turbulence with overdriven detonations. Phys. Fluids 26, 116101 (2014)

    Article  ADS  Google Scholar 

  • Huete, C., Jin, T., Martinez-Ruiz, D., Williams, F.A.: Reacting shock wave effects on isotropic turbulent flows. Linear Interaction Analysis and Direct Numerical Simulations. Private Communication (2016)

    Google Scholar 

  • Jacquin, L., Cambon, C., Blin, E.: Turbulence amplification by a shock wave and rapid distortion theory. Phys. Fluids A 5(10), 25309–2550 (1993)

    Article  MATH  Google Scholar 

  • Kontorovich, V.M.: To the question on stability of shock waves. Sov. Phys. JETP 6, 1179 (1957). At. Res. Agency Establ. AERE Lib./Trans. 648 (1956)

    Google Scholar 

  • Landau, L.D., Lifshitz, E.M.: Fluid Mechanics. Course of Theoretica Physics, vol. 6, 2nd edn. Butterworth-Heinemann (1987)

    Google Scholar 

  • Larsson, J., Lele, S.K.: Direct numerical simulation of canonical shock-turbulence interaction. Phys. Fluids 21, 126101 (2009)

    Article  ADS  MATH  Google Scholar 

  • Larsson, J., Bermejo-Moreno, I., Lele, S.K.: Reynolds- and Mach-number effects in canonical shock-turbulence interaction. J. Fluid Mech. 717, 293–321 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Lasseigne, D.G., Jackson, T.L., Hussaini, M.Y.: Nonlinear interaction of a detonation/vorticity wave. Phys. Fluids A 3, 1972–1979 (1991)

    Article  ADS  MATH  Google Scholar 

  • Lee, S., Lele, S.K., Moin, P.: Direct numerical simulation of isotropic turbulence interacting with a weak shock wave. J. Fluid Mech. 251, 533–562 (1993)

    Article  ADS  Google Scholar 

  • Lee, S., Lele, S.K., Moin, P.: Interaction of isotropic turbulence with shock waves: effect of shock strength. J. Fluid Mech. 340, 225–247 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Lele, S.K.: Shock-jump relations in a turbulent flow. Phys. Fluids A 4(12), 2900–2905 (1992)

    Article  ADS  MATH  Google Scholar 

  • Lubchich, A.A., Pudovkin, M.I.: Interaction of small perturbations with shock waves. Phys. Fluids 16(12), 4489–4505 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Mahesh, K., Lele, S.K., Moin, P.: The interaction of an isotropic field of acoustic waves with a shock wave. J. Fluid Mech. 300, 383–407 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Mahesh, K., Moin, P., Lele, S.K.: The interaction of a shock wave with a turbulent shear flow. Report No. TF-69, Department of Mecanical Engineering, Stanford University (1996)

    Google Scholar 

  • Mahesh, K., Lele, S.K., Moin, P.: The influence of entropy fluctuations on the interaction of turbulence with a shock wave. J. Fluid Mech. 334, 353–379 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Miller, G.H., Ahrens, T.J.: Shock wave viscosity measurement. Rev. Modern Phys. 63, 919–948 (1991)

    Article  ADS  Google Scholar 

  • Moore, F.K.: Unsteady oblique interaction of a shock wave with a plane disturbance. Technical report 2879, NACA (1954)

    Google Scholar 

  • Ribner, H.S.: Convection of a pattern of vorticity through a shock wave. Technical report 1164, NACA (1953)

    Google Scholar 

  • Ryu, J., Livescu, D.: Turbulence structure behind the shock in canonical shock-vortical turbulence interaction. J. Fluid Mech. 756(R1), 1–13 (2014)

    Article  ADS  Google Scholar 

  • Sinha, K.: Evolution of enstrophy in shock/homogeneous turbulence interaction. J. Fluid Mech. 707, 74–110 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Wouchuk, J.G., Huete, C., Velikovich, A.L.: Analytical linear theory for the interaction of a planar shock wave with an isotropic turbulent vorticity field. Phys. Rev. E 79, 066315 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  • Zank, P., Zhou, Y., Matthaeus, W.H., Rice, W.K.M.: The interaction of turbulence with shock waves: a basic model. Phys. Fluids 14(11), 3766–3774 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Zel’dovich, Y.B., Raizer, Y.P.: Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Dover Publications, Mineola (2002)

    Google Scholar 

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Correspondence to Pierre Sagaut .

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Sagaut, P., Cambon, C. (2018). Canonical Isotropic Turbulence/Shock Interaction and Beyond. In: Homogeneous Turbulence Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-319-73162-9_15

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