  Previous work (S. Davidovits and N. J. Fisch, "Sudden viscous dissipation of
compressing turbulence," Phys. Rev. Lett., 116(105004), 2016) demonstrated that
the compression of a turbulent field can lead to a sudden viscous dissipation
of turbulent kinetic energy (TKE), and suggested this mechanism could
potentially be used to design new fast-ignition schemes for inertial
confinement fusion. We expand on previous work by accounting for finite Mach
numbers, rather than relying on a zero-Mach-limit assumption as previously
done. The finite-Mach-number formulation is necessary to capture a
self-consistent feedback mechanism in which dissipated TKE increases the
temperature of the system, which in turn modifies the viscosity and thus the
TKE dissipation itself. Direct numerical simulations with a tenth-order
accurate Pad\'e scheme were carried out to analyze this self-consistent
feedback loop for compressing turbulence. Results show that, for finite Mach
numbers, the sudden viscous dissipation of TKE still occurs, both for the
solenoidal and dilatational turbulent fields. As the domain is compressed,
oscillations in dilatational TKE are encountered due to the highly-oscillatory
nature of the pressure dilatation. An analysis of the source terms for the
internal energy shows that the mechanical work term dominates the viscous
turbulent dissipation. As a result, the effect of the suddenly dissipated TKE
on temperature is minimal for the Mach numbers tested. Moreover, an analytical
expression is derived that confirms the dissipated TKE does not significantly
alter the temperature evolution for low Mach numbers, regardless of compression
speed. The self-consistent feedback mechanism is thus quite weak for subsonic
turbulence, which could limit its applicability for inertial confinement
fusion.
