title: Reply to "Comment on 'Statistical symmetries of the Lundgren-Monin-Novikov hierarchy' ".
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).
authors.affiliation: Chair of Fluid Dynamics, Department of Mechanical Engineering, TU Darmstadt, Otto-Berndt-Straße 2, 64287 Darmstadt, Germany.|Institute of Fluid Flow Machinery, Fiszera 14, 80-231 Gdask, Poland.
authors.forename: Marta
authors.initials: M
authors.lastname: Wacławczyk
authors.affiliation: Chair of Fluid Dynamics, Department of Mechanical Engineering, TU Darmstadt, Otto-Berndt-Straße 2, 64287 Darmstadt, Germany.|GS Computational Engineering, TU Darmstadt, Dolivostraße 15, 64293 Darmstadt, Germany.|Center of Smart Interfaces, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany.
authors.forename: Martin
authors.initials: M
authors.lastname: Oberlack
mesh_terms: D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical