从turbulence的例子如何不使用李群对称的不变函数方法
An example from turbulence how not to use the invariant function method of Lie-group symmetries
摘要：
Oberlack等人最近的答复[Phys. Rev. Lett. 130，069403（2023）]未能反驳批评，数学解决方法已被误用在他们的原始工作。我们逐点证明，《复函》中提出的所有论点都是不正确的。因此，李群对称性的不变解方法不应该以与封闭系统相同的方式用于非封闭系统的事实仍然成立。忽视这一事实只会导致错误的结论。诸如从第一性原理导出统计纳维-斯托克斯方程的解，或找到湍流间歇性行为的量度，或特别是壁面湍流剪切流中的真实标度等主张都是不正确的。
英文摘要：
The recent Reply by Oberlack et al. [Phys. Rev. Lett. 130, 069403 (2023)] fails to rebut the critique that a mathematical solution method has been misapplied in their original work. On a point-by-point basis we prove that all arguments put forward in that Reply are incorrect. Therefore, the fact that the invariant solution method of Lie-group symmetries should not be used for unclosed systems in the same way as for closed systems still holds true. Ignoring this fact only leads to wrong conclusions. Claims such as having derived solutions of the statistical Navier-Stokes equations from first principles, or having found a measure for the intermittent behaviour of turbulence or particularly the true scaling in wall-bounded turbulent shear flows, are incorrect.
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