The linear evolution of acoustic waves in a fluid flow with uniform mean density and uniform shear of velocity is investigated. The process of the mean flow energy extraction by the three-dimensional acoustic waves, stimulated by the non-normal character of the linear dynamics in the shear flow, is analyzed. The thorough examination of the dynamics of different physical variables characterizing the wave evolution is presented. The physics of gaining of the shear energy by acoustic waves is described.

The article by M. Wacławczyk et al. [Phys. Rev. E 90, 013022 (2014)] proposes two new statistical symmetries in the classical theory for turbulent hydrodynamic flows. In this Comment, however, we show that both symmetries are unphysical due to violating the principle of causality. In addition, they must get broken in order to be consistent with all physical constraints naturally arising in the statistical Lundgren-Monin-Novikov (LMN) description of turbulence. As a result, we state that besides the well-known classical symmetries of the LMN equations no new statistical symmetries exist. Finally, we criticize the relation between intermittency and global symmetries as it is presented throughout that study.

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The recent study by Wac lawczyk et al. [J. Phys. A: Math. Theor. 50, 175501 (2017)] possesses three shortcomings: (i) The analysis misses a key aspect of the LMN equations which makes their Lie-group symmetry results incomplete. In particular, two essential symmetries will break when including this aspect. (ii) The statements on the constraints regarding the infinite-dimensional symmetry groups are misleading. (iii) The particular symmetries originating solely from the linearity of the LMN hierarchy violate the classical principle of cause and effect and therefore are unphysical. Within this Comment we present a detailed proof to this claim and conclude with the note that the new study by Wac lawczyk et al. gives an unrealistic outlook on deriving invariant symmetry solutions for velocity correlations that arise from intermittent processes.

Aerodynamic sound generation in shear flows is investigated in the light of the breakthrough in hydrodynamics stability theory in the 1990s, where generic phenomena of non-normal shear flow systems were understood. By applying the thereby emerged short-time/non-modal approach, the sole linear mechanism of wave generation by vortices in shear flows was captured [G. D. Chagelishvili, A. Tevzadze, G. Bodo, and S. S. Moiseev, “Linear mechanism of wave emergence from vortices in smooth shear flows,” Phys. Rev. Lett. 79, 3178-3181 (1997); B. F. Farrell and P. J. Ioannou, “Transient and asymptotic growth of two-dimensional perturbations in viscous compressible shear flow,” Phys. Fluids 12, 3021-3028 (2000); N. A. Bakas, “Mechanism underlying transient growth of planar perturbations in unbounded compressible shear flow,” J. Fluid Mech. 639, 479-507 (2009); and G. Favraud and V. Pagneux, “Superadiabatic evolution of acoustic and vorticity perturbations in Couette flow,” Phys. Rev. E 89, 033012 (2014)]. Its source is the non-normality induced linear mode-coupling, which becomes efficient at moderate Mach numbers that is defined for each perturbation harmonic as the ratio of the shear rate to its characteristic frequency. Based on the results by the non-modal approach, we investigate a two-dimensional homentropic constant shear flow and focus on the dynamical characteristics in the wavenumber plane. This allows to separate from each other the participants of the dynamical processes — vortex and wave modes — and to estimate the efficacy of the process of linear wave-generation. This process is analyzed and visualized on the example of a packet of vortex modes, localized in both, spectral and physical, planes. Further, by employing direct numerical simulations, the wave generation by chaotically distributed vortex modes is analyzed and the involved linear and nonlinear processes are identified. The generated acoustic field is anisotropic in the wavenumber plane, which results in highly directional linear sound radiation, whereas the nonlinearly generated waves are almost omni-directional. As part of this analysis, we compare the effectiveness of the linear and nonlinear mechanisms of wave generation within the range of validity of the rapid distortion theory and show the dominance of the linear aerodynamic sound generation. Finally, topological differences between the linear source term of the acoustic analogy equation and of the anisotropic non-normality induced linear mechanism of wave generation are found.