Mathematical framework for analysis of internal energy dynamics and spectral distribution in compressible turbulent flows

Compressibility effects on energy exchange mechanisms in a spatially developing plane free shear layer

“…Based on our DNS results of all the budget terms in the three transport equations, five terms are found to be mainly responsible for the turbulent energy conversion among TKE, MKE and MIE: turbulent production, Figure 4 shows the simplified schematic of the kinetic energy transfer corresponding to the current DNS results (for the detailed schematic of kinetic energy balance, readers are referred to Lele (1994) and Mittal & Girimaji (2019)). In the figure, we only present the dominant terms responsible for energy exchange among TKE, MKE and MIE.…”

Physical Processes in Star Formation

“…For that reason, w has been often used to compute the kinetic energy spectrum in compressible turbulence (e.g. Cook and Zhou, 2002;Wang et al, 2013;Grete et al, 2017;Mittal and Girimaji, 2019). Empirically, it was noticed that in supersonic turbulenceK(k) shows a very strong "bottleneck" (present in bothK s (k) andK d (k) spectra), which can be traced to shock fronts (section 3.5 in Kritsuk et al, 2007a).…”

“…√ ρc s √ ρ c s /γ(γ−1) (Schmidt and Grete, 2019;Mittal and Girimaji, 2019). The most popular option (i) uses point splitting between a conserved variable ρ and the specific thermodynamic energy e. Option (ii) mimics the momentum-velocity point splitting for the kinetic energy by replacing the velocity u with the sound speed c s .…”

Scale-space energy density function transport equation for compressible inhomogeneous turbulent flows

“…Interscale energy transfer is further complicated in compressible flows owing to the interactions between kinetic and internal energy enabled by the emergence of a dilatational flow field. Mittal & Girimaji (2019) developed a self-consistent framework for describing turbulent kinetic and internal energy interactions in physical and spectral space. The authors identified the appropriate internal energy state variable that emulates the role of velocity in kinetic energy spectral transfer.…”