Objections to a Reply of Oberlack et al. (Phys. Rev. E 92, 067002 (2015)) M. Frewer 1∗ , G. Khujadze 2 & H. Foysi 2 1 Tr¨ ubnerstr. 42, 69121 Heidelberg, Germany 2 Chair of Fluid Mechanics, Universit¨ at Siegen, 57068 Siegen, Germany December 24, 2015 Abstract The published Reply Phys. Rev. E 92, 067002 (2015) of Oberlack et al. to our Comment Phys. Rev. E 92, 067001 (2015) contains a new but central reasoning error which unfortu- nately passed the peer-review process, a mistake which when corrected would lead to an overall opposite conclusion. This notification serves to correct the mistake and will give its correct conclusion instead. Next to this issue, which is discussed in the first two sections, we also list four other, independent objections. Objection No. 1: In the Reply of Waclawczyk & Oberlack (2015) it is claimed that Eq. (13) results from Eq. (12) when considering the streamwise variation ∂/∂x of it. Although Eq. (12) † represents an integral equation for the pressure field P (x), its reduction to Eq. (13) under the given assumptions, however, only leads to a trivial identity relation from which no conclusions can be drawn; and not to an equation which can be explicitly solved for the pressure gradient as it is misleadingly claimed in the Reply. The problem is that Eq. (13) is presented in a form which does not immediately reveal itself as an identity, simply because the assumptions which were made on the unknown pressure field P (x) (for a laminar plane channel flow) were only made on the right-hand side of Eq. (12). But, in order to yield a consistent equation, these assumptions must also be made on its left-hand side. Hence, the correct formulation of Eq. (13) reads ΔP 2L x = - 1 8L z H ∂ ∂x  H -H  Lz -Lz  - ΔP 2L x |x - x ′ |     x ′ =-Lx +  ΔP 2L x |x - x ′ |     x ′ =Lx  dz ′ dy ′ . (1.1) Now, since the quantity ΔP/(2L x ) is treated as a constant, it can be taken in front of the integral operations; similar with the evaluations of |x - x ′ |, since the integrations are not performed in ∗ Email address for correspondence: frewer.science@gmail.com † Note that Eq. (12) is Green’s Theorem (see e.g. Jackson (1998))  V (φ∇ 2 ψ - ψ∇ 2 φ) d 3 x =  S n · (φ∇ψ - ψ∇φ) d 2 x, for φ = P and ψ = G, if the Green function G is normalized to ∇ 2 G = δ 3 (x - x ′ ). Further note that although Green’s Theorem is a valid integral relation, it’s not a constructive relation to solve for P in terms of boundary data if both the boundary values of P and ∂P/∂ n have to be specified simultaneously (Jackson, 1998). Only when choosing the appropriate Green function, this integral relation can be identified as a true integral equation for the unknown pressure field P . Hence, since for P (in the incompressible case) only Neumann boundary conditions can be placed, a consistent integral equation is only obtained if the Green function is chosen such that it satisfies the homogeneous Neumann boundary conditions ∂G(x, x ′ )/∂ n ′ = 0.