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Reply to "Comment on 'Statistical symmetries of the Lundgren-Monin-Novikov hierarchy' "
Marta Wacławczyk1,2, Martin Oberlack1,3,4
1Chair of Fluid Dynamics, Department of Mechanical Engineering, TU Darmstadt, Otto-Berndt-Straße 2, 64287 Darmstadt, Germany.
Abstract:
In this Reply we respond to the criticism of Frewer et al. presented in the Comment on "Statistical symmetries of the Lundgren-Monin-Novikov hierarchy" by Wacławczyk et al. [Phys. Rev. E 90, 013022 (2014)]. We discuss physical interpretation of the statistical symmetries, and respond to criticism on the violation of the causality principle. We derive the Lundgren-Monin-Novikov equations for a flow with boundaries. Last, we stress that our work addressed the phenomenon of "external intermittency" (separation between laminar and turbulent flow), and not "internal intermittency" (strong fluctuations at small scales).
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