Dokoza, Toni (2024)
Influencing coherent structures in a plane Couette flow.
Technische Universität Darmstadt
doi: 10.26083/tuprints-00027582
Dissertation, Erstveröffentlichung, Verlagsversion

Kurzbeschreibung (Abstract)

Within shear flows, such as the plane Couette flow (PCF), beyond a certain Reynolds number threshold large-scale turbulent structures, so-called turbulent superstructures arise, where this organised motion of the fluid significantly influences various phenomena, such as the mass, momentum and heat transfer within the flow. To this day, the origin of these large-scale structures remains unsolved. The present thesis aims to improve the existing understanding on both the origin and the modification possibilities of these structures. The structures occurring in the PCF as well as its modification through added wall-transpiration and added pressure gradient in the streamwise direction are investigated using linear stability theory (LST), resolvent analysis (RA) and structured singular value analysis (SSVA) respectively. The application of LST on the PCF disclosed a Reynolds number induced growth of the largescale rolls by analysing the analytical solution of the underlying Orr–Sommerfeld equation (OSE). One of the key results in the present work is a distinct connection between decreasing streamwise wavenumbers and growing Reynolds numbers, where the product of both parameters acts as a global invariant in the resulting eigenvalue problem (EVP) in the limit of large Reynolds numbers and small streamwise wavenumbers. The significance of this invariant as a key parameter in the amplification mechanisms within the PCF is further shown by applying RA, where invariant structures are found for constant products of both parameters. A common way of shear flow control through the application of suction or blowing at the wall is investigated in this thesis by employing RA onto the flow. Hereby, the narrowing effect of the wall-transpiration on the large-scale structures is connected to the diminishing boundary layer thickness (BLT) of the laminar streamwise base flow as it continuously converges towards a boundary layer flow (BLF) for increasing wall-transpiration. Various invariant scaling laws predicting the optimal spatial wavelengths of the structures and optimal Reynolds numbers yielding largest amplification are discovered. In the final part of this thesis, the introduction of an added pressure gradient in the streamwise direction onto the PCF is analysed and the results obtained from employing both RA and SSVA are compared to results of a direct numerical simulation (DNS) at a transitional Reynolds number. The destructive effect of the pressure gradient on the large-scale rolls is shown for both approaches, where the uniform large-scale rolls split into two rows of rolls as the flow becomes increasingly pressure driven. The positions of the resulting large-scale structures are successfully connected to the occurrence of critical layers within the flow. The results stemming from SSVA upon investigating a turbulent mean flow are found to present the most promising results in capturing the structures observed in DNS.

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