Energy cascade and scaling in supersonic isothermal turbulence
Energy cascade and scaling in supersonic isothermal turbulence
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DOI：
10.1017/jfm.2013.342
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发表时间：
2013-06
影响因子：
3.7
通讯作者：
A. Kritsuk;R. Wagner;M. Norman
中科院分区：
文献类型：
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作者：
A. Kritsuk;R. Wagner;M. Norman
摘要超声速湍流在许多极端的天体物理和地球环境中起着重要的作用，但对它的认识还很不成熟。我们使用来自超音速等温湍流的三维模拟的数据来重建从Navier-Stokes方程（Galtier & Banerjee，Phys. Rev. Lett.，第107卷，2011年，第134501页）。我们的分析支持先前在现象学水平上讨论的超音速湍流中的Kolmogorov惯性能量级联。我们发现，两个可压缩的类似物的五分之四定律存在描述第五和第四阶的相关性，但只有第四阶的关系仍然是“普遍的”在很宽的范围内的马赫数从不可压缩到高度可压缩的制度。导出并验证了一个新的近似关系式在强超声速区是有效的。我们还简要讨论了可压缩湍流模拟中瓶颈凸起的起源。
Abstract Supersonic turbulence plays an important role in a number of extreme astrophysical and terrestrial environments, yet its understanding remains rudimentary. We use data from a three-dimensional simulation of supersonic isothermal turbulence to reconstruct an exact fourth-order relation derived analytically from the Navier–Stokes equations (Galtier & Banerjee, Phys. Rev. Lett., vol. 107, 2011, p. 134501). Our analysis supports a Kolmogorov-like inertial energy cascade in supersonic turbulence previously discussed on a phenomenological level. We show that two compressible analogues of the four-fifths law exist describing fifth- and fourth-order correlations, but only the fourth-order relation remains ‘universal’ in a wide range of Mach numbers from incompressible to highly compressible regimes. A new approximate relation valid in the strongly supersonic regime is derived and verified. We also briefly discuss the origin of bottleneck bumps in simulations of compressible turbulence.