Schock-artige Fokussierung von Trägheitswellen – die lokale Erzeugung von Turbulenz

• Antragsteller: Professor Dr.-Ing. Martin Oberlack
• Fachliche Zuordnung: Strömungsmechanik
• Förderung: Förderung von 2018 bis 2023
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 407316090

• Erstellungsjahr: 2023

Zusammenfassung der Projektergebnisse

The general objective of the project was to develop the theoretical and numerical descriptions of the evolution of an initially axisymmetric rotating flow containing conical inertial waves. Inertial waves can be generated in rotating flows due to the restoring effect of the Coriolis force, whose propagation direction is determined solely by the ratio of the wave frequency to the fluid’s rotational velocity. Due to this property, the waves focus on the axis of symmetry when excited by an axisymmetric wave source, e.g. an oscillating torus, causing a dramatic increase in energy in the focal region and enabling the local generation of turbulence. The important milestones were (i) to develop a kinetic theory for rotating flows, (ii) to extend the linear theory to a weakly nonlinear case, and (iii) to develop a fully nonlinear theory describing the localized turbulence in the focal zone. To achieve these goals, both theoretical analyses and numerical simulations were carried out. The theoretical result of the linear theory was published and the weakly nonlinear theory described has been accepted for publication. These analytical studies show the phenomenon of generation, propagation and focusing of inertial waves. It was found that in the weakly nonlinear theory, in addition to the primary inertial waves predicted by the linear theory, secondary inertial waves are also excited. In particular, except for the fundamental focusing point, the secondary inertial waves form a new focal area. Furthermore, the newly derived statistical model for the rotating fluid with external forcing describing the fully nonlinear case will be published in the near future. In addition to the analytical investigations, the simulation workpackage included the numerical approach that was developed and exploited. It permitted to unveil the presence of the geostrophic mode, that has been found different depending on the regime of the flow, linear or nonlinear. The choice of regime has been shown to be directly related to the amplitude of the waves, but also to other parameters such as the non-dimensional Keulegan-Carpenter number and the Rossby number. When we sought to optimize the energy transfer as an important workpackage, we observed a rather well defined propagation angle, both in the numerical simulations and in the analytical theory. The conclusion is therefore assumed to be robust. The simulation database is available for comparison with the results of other groups, as is the 4D FFT analysis method. We also plan to further exploit this for an extended characterization of triadic interactions, augmented with respect to the statistical results obtained to date, that imply bicoherence spectra and spatio-temporal spectra.

Projektbezogene Publikationen (Auswahl)

• Study of the local turbulence generated from inertial waves focus in rotating fluids. In American Geophysical Union, Fall meeting, 2020, online
  A. Mohamed; A. Delache & F.S. Godeferd
  
• Focosing of inertial waves by a vertically oscillating annular forcing. In APS DFD Meeting, November 2022, Indianapolis, USA
  J. Liu; M. Oberlack & Y. Wang
  
• Focosing of inertial waves by a vertically oscillating annular forcing. In GAMM Annual Meeting, August 2022, Aachen, Germany
  J. Liu; M. Oberlack & Y. Wang
  
• Focusing of inertial waves by a vertically annular forcing. Physics of Fluids, 34(8).
  Liu, J.; Oberlack, M.; Wang, Y.; Delache, A. & Godeferd, F. S.
  
• Inertial waves focusing by vertically oscillating torus in rotating fluid. In Congrès Français de Mécanique, August 2022, Nantes, France
  A. Mohamed; A. Delache & F.S. Godeferd
  
• Inertial waves focusing into localized turbulence in rotating fluid. In European Fluid Mechanics Conference XIV, September 2022, Athens, France
  A. Mohamed; A. Delache & F.S. Godeferd
  
• Shock-like focusing of inertial waves - the localized generation of turbulence. In 12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP 12), July 2022, Osaka, Japan, online
  J. Liu; A. Mohamed; A. Delache; F.S. Godeferd; M. Oberlack & Y. Wang
  
• Focusing of weakly nonlinear inertial waves by a vertically oscillating annular forcing. Physics of Fluids, 35(11).
  Liu, J.; Wang, Y. & Oberlack, M.