High-Resolution Simulation of Internal Waves Attractors and Impact of Interaction of High Amplitude Internal Waves With Walls on Dynamics of Waves Attractors

Abstract

Abstract.Internal wave attractors have received great attention since its discovery in 1995 by Leo Maas ([1, 2]). Now convectional theory describing the formation of attractors is generally accepted, and the principal interest of researchers in recent years is focused on nonlinear interactions. A number of theories had been proposed and now nonlinear interaction due to triadic resonance is accepted as a principle cause of instability of attractors, in which case the parent wave of large amplitude gives birth to two daughter waves, such that conditions of triadic resonance are fulfilled for all the three waves [3]. All this presumes that wave-wall interaction participate in the process only by focusing-defocusing of energy on the inclined boundaries. Here we address interactions of large amplitude internal waves with the boundaries in real laboratory conditions, where Prandtl-Schmidt number is equal to 700. We show that large amplitude waves produce folded structures which are clearly visible on density-gradient images, as if produced by "kneading the dough". These structures are not quickly dissipated due to high Schmidt number and with time they propagate to the interior of the domain, as was shown by our numerical simulation. These structures have visible impact on the instability of attractor and the whole picture of turbulent motion for large amplitudes. The mechanism of interaction of these structures with internal gravity waves structures is the subject of further research. Numerical simulation is quite challenging due to high Prandtl-Schmidt number and small scale of the folded structures in highly nonlinear regimes. Also study is performed on large time scales. As a consequence most of conventional computational approaches give unreliable results. We have applied spectral element approach base on code nek5000 by Paul Fischer. It allowed us to carefully follow the fine space structures on large time scales.

Mean flow generation by three-dimensional nonlinear internal wave beams

“…Possibly most importantly, our analysis in §3 illustrates that an appropriate mathematical representation of the wave maker is essential in studies on mean flow generation. The numerical code by Sibgatullin & Kalugin (2016), used in several studies involving wave makers, and the numerical code employed by Grisouard et al (2013); Raja (2018) for simulations of mean flow generation upon reflection at inclined bottoms, do not capture the vertical line vortices at the edges of the wave makers. While the absence of the vertical line vortices in simulations may be of no concern for the far field, one must be aware that the vertical line vortices are intrinsic to laboratory experiments, and may impact the non-linear dynamics in the vicinity of the wave maker.…”

Numerical Simulation of Three-Dimensional Wave Attractors

“…First qualitative and quantitative correspondence of laboratory and numerical simulation of wave attractors in the pseudo-2D laboratory tank with trapezoidal section was described in , and importance of dissipation on the lateral boundaries was shown (F. Beckebanze et al, 2018). For high Schdmidt number there appear the folded structures, which can interact with the background wave motion (Sibgatullin, Kalugin 2016). In (Brouzet et al, 2016b), (Dauxois et al, 2018) cascade of triadic resonances in (1,1) produced by a wave attractor was demonstrated.…”

“…Впервые хорошее качественное сопоставление вычислительного и лабораторного экспериментов в контейнере с трапецеидальной формой было приведено в работе , и показана важность диссипации энергии в пограничном слое на боковых поверхностях (Beckebanze et al, 2018). При большом числе Шмидта образуются складчатые структуры, взаимодействующие с фоновым течением (Sibgatullin, Kalugin 2016). В работах (Brouzet et al, 2016b;Dauxois et al, 2018) продемонстрирован каскад триадных неустойчивостей.…”