Inviscid Transient Growth on Horizontal Shear Layers with Strong Vertical Stratification

Abstract

International audienceWe report an investigation of the three-dimensional stability of an horizontal free shear layer in an inviscid fluid with strong, vertical and constant density stratification. We compute the optimal perturbations for different optimization times and wavenumbers. The results allow comparing the potential for perturbation energy amplification of the free shear layer instability and the different mechanisms of transient growth. We quantify the internal wave energy content of the perturbations and identify different types of optimal perturbations. Intense excitation of gravity waves due to transient growth of perturbations is found in a broad region of the wavevector plane. Those gravity waves are eventually emitted away from the shear layer

Non-Modal Three-Dimensional Optimal Perturbation Growth in Thermally Stratified Mixing Layers

“…It is emphasized, however, that despite the obvious scatter in the results shown in Figure 1, they do show that significant non-modal growth can be expected even in cases of a strong, stable stratification. It also supports the results of [32], indicating that optimal perturbation can be located outside the shear layer.…”

“…It was shown recently that KH instability plays an important role in the formation of interfaces between coating and substrate materials and metallic materials [24,25]. The non-linear evolution of KH and Holmboe instabilities was studied in quite a large number of articles (e.g., [17,[26][27][28][29][30][31][32][33]). A difference in the nonlinear disturbances growth compared with the predictions of linear stability theory was reported in [31].…”

“…A difference in the nonlinear disturbances growth compared with the predictions of linear stability theory was reported in [31]. Surprisingly, the issue of non-modal growth of disturbances at short times was addressed only by [14] for non-stratified mixing layers and by [32] for a stratified inviscid model. The study [32] described the non-modal amplification of the stratified mixing layer in terms of the interaction of gravity wave and vortex energy of the optimal perturbation for large wavenumbers.…”

“…Surprisingly, the issue of non-modal growth of disturbances at short times was addressed only by [14] for non-stratified mixing layers and by [32] for a stratified inviscid model. The study [32] described the non-modal amplification of the stratified mixing layer in terms of the interaction of gravity wave and vortex energy of the optimal perturbation for large wavenumbers. It was shown that the amplified transient growth can be three-dimensional and is associated with wave generation due to a vertical motion at large wavenumbers.…”

Local stability analysis of homogeneous and stratified Kelvin–Helmholtz vortices

“…Our results also motivate a study on the effects of in-plane buoyancy gradients on previously known instabilities in idealized vortex models. Finally, apart from the secondary instabilities discussed in this study, transient growth could also represent an important mechanism for growth of perturbations in vortical flows, in both homogeneous (Ortiz & Chomaz 2011;Arratia, Caulfield & Chomaz 2013) and stratified (Ortiz, Donnadieu & Chomaz 2015;Arratia, Ortiz & Chomaz 2016) edge in the full analysis (figure 3d). As in the full analysis, the convective instability region moves away from the core in σ BG as well (t = 60, figure 15b).…”