Lombardini, M. and Pullin, D. I. and Meiron, D. I. (2014) Turbulent mixing driven by spherical implosions. Part 2. Turbulence statistics. Journal of Fluid Mechanics, 748 . pp. 113142. ISSN 00221120. http://resolver.caltech.edu/CaltechAUTHORS:20140708150458718

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Abstract
We present largeeddy simulations (LES) of turbulent mixing at a perturbed, spherical interface separating two fluids of differing densities and subsequently impacted by a spherically imploding shock wave. This paper focuses on the differences between two fundamental configurations, keeping fixed the initial shock Mach number ≈ 1.2, the density ratio (precisely A_0 ≈ 0.67) and the perturbation shape (dominant spherical wavenumber ℓ_0=40 and amplitudetoinitial radius of 3 %): the incident shock travels from the lighter fluid to the heavy one, or inversely, from the heavy to the light fluid. In Part 1 (Lombardini, M., Pullin, D. I. & Meiron, D. I., J. Fluid Mech., vol. 748, 2014, pp. 85112), we described the computational problem and presented results on the radially symmetric flow, the mean flow, and the growth of the mixing layer. In particular, it was shown that both configurations reach similar convergence ratios ≈2. Here, turbulent mixing is studied through various turbulence statistics. The mixing activity is first measured through two mixing parameters, the mixing fraction parameter Theta and the effective Atwood ratio A(e), which reach similar late time values in both lightheavy and heavylight configurations. The Taylorscale Reynolds numbers attained at late times are estimated ≈2000 in the lightheavy case and 1000 in the heavylight case. An analysis of the density selfcorrelation b, a fundamental quantity in the study of variabledensity turbulence, shows asymmetries in the mixing layer and nonBoussinesq effects generally observed in highReynoldsnumber RayleighTaylor (RT) turbulence. These traits are more pronounced in the lightheavy mixing layer, as a result of its flow history, in particular because of RTunstable phases (see Part 1). Another measure distinguishing lightheavy from heavylight mixing is the velocitytoscalar Taylor microscales ratio. In particular, at late times, larger values of this ratio are reported in the heavylight case. The latetime mixing displays the traits some of the traits of the decaying turbulence observed in planar RichtmyerMeshkov (RM) flows. Only partial isotropization of the flow (in the sense of turbulent kinetic energy (TKE) and dissipation) is observed at late times, the Reynolds normal stresses (and, thus, the directional Taylor microscales) being anisotropic while the directional Kolmogorov microscales approach isotropy. A spectral analysis is developed for the general study of statistically isotropic turbulent fields on a spherical surface, and applied to the present flow. The resulting angular power spectra show the development of an inertial subrange approaching a Kolmogorovlike 5/3 power law at high wavenumbers, similarly to the scaling obtained in planar geometry. It confirms the findings of Thomas & Kares (Phys. Rev. Lett., vol. 109, 2012, 075004) at higher convergence ratios and indicates that the turbulent scales do not seem to feel the effect of the spherical mixinglayer curvature.
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Additional Information:  © 2014 Cambridge University Press. Received 12 June 2013; revised 29 January 2014; accepted 20 March 2014;first published online 28 April 2014. This work has been supported in part by the Department of Energy under subcontract no. DEAC5206NA25396.  
Group:  GALCIT  
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Subject Keywords:  compressible turbulence; shock waves; turbulent mixing  
Record Number:  CaltechAUTHORS:20140708150458718  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20140708150458718  
Official Citation:  Lombardini, M., Pullin, D. I., & Meiron, D. I. (2014). Turbulent mixing driven by spherical implosions. Part 2. Turbulence statistics. Journal of Fluid Mechanics, 748, 113142. doi: doi:10.1017/jfm.2014.163  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  47081  
Collection:  CaltechAUTHORS  
Deposited By:  Joanne McCole  
Deposited On:  09 Jul 2014 17:50  
Last Modified:  21 Sep 2016 22:48 
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