Study on Coherent Structures in Turbulent Channel Flows

Abstract

This thesis concentrates on coherent structures, including vortices and attached eddies, in turbulent channel flows. Due to the chaos and randomness of turbulence, coherent structures, i.e., recurrent flow patterns, as organized elements, are effective media to investigate and understand turbulent flows. Additionally, these studies on fundamental structures could provide explanations for mean statistics such as the success and failure of velocity transformations, which are concerned merely with mean values.

This thesis first assesses velocity transformations that map compressible mean stream-wise velocity profiles to the incompressible logarithmic law in several types of noncanonical wall turbulence. These transformations are developed using Morkovin’s hypothesis and the semi-local scaling, i.e., the compressibility effect can be absorbed by the variation of mean flow properties. Some of them work well in canonical wall turbulence. For noncanonical cases, all these popular methods fail to provide an overall satisfactory performance for noncanonical compressible wall-bounded flows.

In order to examine the physical mechanism behind mean profiles, coherent structures responsible for the dynamics of wall turbulence are investigated in detail. For vortical structures, a study of the kinematic properties (orientation, size, strength, and population) of vortical structures in compressible and incompressible channel flows is provided. Overall, a quantitative consistency of most features between compressible and incompressible channel flows after applying the semi-local scaling is observed.

Regarding the attached eddy, an important parameter, the streamwise inclination angle, is investigated. Spectral linear stochastic estimation (SLSE) can extract instantaneous attached-eddy signatures by modeling the inner-outer interaction model (IOIM) as a single-input/single-output (SI/SO) system. After isolating signatures of eddies at a targeted scale, the inclination angle using u' (streamwise velocity fluctuations) approaches 45◦as the Reynolds number increases, showing a minor Mach-number influence among cases in this thesis. A high similarity can be seen between u' and temperature fluctuations.

Finally, this thesis further refines the SLSE prediction framework. The near-wall uni-versal signal, the input noise of the SI/SO system, impacts the extraction accuracy. To eliminate the noise effect, an extra input, near-wall wall-normal velocity fluctuation v'_i, is introduced, which transfers the original SI/SO system to a multi-input/single-output (MI/SO) system. Then, this thesis re-examines more properties of attached eddies, especially the logarithmic decay rate A₁ of u^r2. The decay rate A₁ becomes, overall, much larger, reducing the Reynolds number variation.

This thesis provides concrete evidence supporting the structural similarity between compressible and incompressible flows by applying the semi-local scaling. In other words, Morkovin’s hypothesis and semi-local scaling, which have been widely verified using mean values in previous studies, also work for instantaneous features of turbulent structures. It is a crucial piece of knowledge for developing advanced modeling approaches and extending incompressible theories and models to compressible flows. This thesis also improves the SLSE approach to extract attached-eddy signatures by taking the noise of the SI/SO system into consideration and extending the SI/SO system into a MI/SO one. The refinement framework of the noise effect in this thesis is also applicable to other systems.

This thesis also takes the development of new velocity transformations one step further. The effectiveness of Morkovin’s hypothesis and the semi-local scaling shown in this thesis implies that the success of the Trettel-Larsson and total-stress-based transformations can be attributed to the application of the semi-local wall normal coordinate. Further examinations of coherent structures in higher Reynolds-number and Mach-number cases, and all kinds of non-canonical wall turbulence are required. If this consistency still exists by applying the semi-local scaling or other scalings, new velocity transformations can be expected based on the obtained uniform wall-normal coordinate.

Date of Award	2025
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology
Supervisor	Lin FU (Supervisor)