Date of Award

Summer 2019

Project Type

Dissertation

Program or Major

Mechanical Engineering

Degree Name

Doctor of Philosophy

First Advisor

Gregory P Chini

Second Advisor

John F Gibson

Third Advisor

Christopher White

Abstract

Direct numerical simulation (DNS) of wall-bounded turbulent flows in physically relevant parameter regimes remains infeasible in many cases of practical interest. Accordingly, this work further establishes the generalized quasilinear (GQL) approximation, introduced by Marston et al. (Phys. Rev. Lett., 116, 2016), as a robust, accurate, and efficient alternative to existing simulation and modeling schemes by investigating its effectiveness as a tool for simulating turbulent channel flow. The GQL reduction is achieved by separating the flow variables into low and high modes via a spectral filter rather than by decomposition into a strict mean and fluctuations, as for the quasilinear (QL) approximation, and then neglecting certain nonlinear interactions a priori. The effectiveness of GQL over the more common QL approximation scheme and the effect of varying the spectral cutoff on the flow dynamics is explored in two distinct parameter regimes and assessed using a multitude of turbulence statistics, including energy budgets. GQL is shown to be significantly more accurate than QL relative to DNS, even when only a modest number of low modes (e.g., 3-5) is retained. A primary conclusion of this work is that GQL accurately predicts the turbulence intensity and Reynolds stress profiles, captures the energy distribution across the entire dynamic range of scales, and recovers the characteristic dynamics and turbulence structure of wall-bounded shear flows. A second significant finding is the emergence of a discontinuity in the GQL energy spectra, which is conjectured to be attributable to the lack of modal instability in the high-mode set. A preliminary linear stability analysis about the turbulent mean velocity profile reveals a band of unstable low streamwise wavenumber modes, lending credence to this conjecture and pointing to a more precise methodology. Moreover, the success of the GQL approximation in quantitatively reproducing low-order turbulence statistics and instantaneous flow structure affirms the importance of both linear mechanisms and spectrally nonlocal energy transfers in fully-developed wall-turbulence.

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