Lawrence Livermore National Laboratory, Livermore, California 94550, USA.
Phys Rev E. 2019 Jan;99(1-1):013107. doi: 10.1103/PhysRevE.99.013107.
Previous work [Davidovits and Fisch, Phys. Rev. Lett. 116, 105004 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.105004] demonstrated that the compression of a turbulent field can lead to a sudden viscous dissipation of turbulent kinetic energy (TKE), and that paper suggested this mechanism could potentially be used to design new fast-ignition schemes for inertial confinement fusion (ICF). 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 Padé 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, for both 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 ICF.
先前的工作[Davidovits 和 Fisch, Phys. Rev. Lett. 116, 105004 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.105004]表明，湍流场的压缩会导致湍流动能（TKE）的突然粘性耗散，并且该论文表明，这种机制可能被用于设计惯性约束聚变（ICF）的新型快速点火方案。我们通过考虑有限马赫数来扩展之前的工作，而不是像以前那样依赖于零马赫数极限假设。有限马赫数公式是捕捉自洽反馈机制所必需的，在这种机制中，耗散的 TKE 会增加系统的温度，进而改变粘性，从而改变 TKE 本身的耗散。采用第十阶精度的 Padé 格式进行了直接数值模拟，以分析压缩湍流的这种自洽反馈环。结果表明，对于有限马赫数，无论是涡旋还是膨胀湍流场，TKE 的突然粘性耗散仍然会发生。随着域的压缩，由于压力膨胀的高度振荡性质，会遇到膨胀 TKE 的振荡。对内能源项的分析表明，机械功项主导粘性湍流耗散。因此，对于测试的马赫数，突然耗散的 TKE 对温度的影响最小。此外，还推导出了一个解析表达式，该表达式确认在低马赫数下，无论压缩速度如何，耗散的 TKE 不会显著改变温度演化。因此，对于亚音速湍流，自洽反馈机制非常弱，这可能限制其在 ICF 中的适用性。
