AI 中文总结
该研究通过高分辨率直接数值模拟，发现等温可压缩湍流的耗散异常呈依赖马赫数的双分支特性，虽为耗散异常提供证据，但未明确其强弱属性。
AI 中文摘要
采用一套全面的三维高分辨率直接数值模拟，研究由无散驱动产生的均匀各向同性等温可压缩湍流中耗散异常的存在性。研究发现，总动能耗散率及其无散分量、胀量分量均随雷诺数Re增大趋近于有限渐近值。归一化平均耗散率分为两个不同分支：对应亚声速与跨声速区域的分支，其均方根马赫数（$M_{\rm rms}\lesssim 1$）；对应高超声速区域的分支，其均方根马赫数（$M_{\rm rms}\ge 3$）。这种依赖马赫数的双分支特性在总动能耗散中最为显著。对于无散与胀量耗散率分量，其对Re的依赖还取决于积分尺度与均方根速度的具体选择。尽管网格分辨率高达$2048^3$个点，可达到的雷诺数仍不足以明确区分弱耗散异常与强耗散异常。研究通过三种互补方法验证上述发现：（i）基于对应耗散率平衡方程及其各自产生项，对耗散产生机制进行详细分析；（ii）采用扩展至可压缩流动的Duchon-Robert框架，研究异常耗散的前兆；（iii）对强耗散区域进行几何表征。综合而言，这些分析为等温可压缩湍流中存在耗散异常提供了一致证据，但仍未明确其为弱异常还是强异常。
英文摘要
Using a comprehensive set of three-dimensional, high-resolution direct numerical simulations, we investigate the existence of a dissipative anomaly in isothermal, homogeneous, isotropic compressible turbulence driven by solenoidal forcing. We find that the total kinetic-energy dissipation rate, as well as its solenoidal and dilatational components, approaches finite asymptotic values with increasing Reynolds number $Re$. The normalized mean dissipation rates collapse onto two distinct branches: one corresponding to the subsonic and transonic regimes, with root-mean-square Mach numbers ($M_{\rm rms}\lesssim 1$), and another to the highly supersonic regime, with ($M_{\rm rms}\ge 3$). This two-branch Mach-number dependence is most pronounced for the total kinetic-energy dissipation. For the solenoidal and dilatational dissipation rate components, the dependence on $Re$ depends in addition on the specific choice of the integral scale and root-mean-square velocity. Despite grid resolutions of up to $2048^3$ points the Reynolds numbers accessible are not sufficiently large to distinguish conclusively between a weak and a strong dissipative anomaly. We substantiate these findings using three complementary approaches: (i) a detailed analysis of the mechanisms responsible for dissipation generation, based on the corresponding dissipation-rate balance equations and their individual production terms; (ii) an investigation of precursors of anomalous dissipation using the Duchon--Robert framework extended to compressible flows; and (iii) a geometrical characterization of regions of intense dissipation. Taken together, these analyses provide consistent evidence for the existence of a dissipative anomaly in isothermal compressible turbulence, while leaving its precise weak or strong character unresolved.
Comments39 pages, 20 figures
