Linear and Non-linear Interactions in a Rough-Wall Turbulent Boundary Layer

Author: Morgan, Jonathan Philip

Year: 2019

Degree: Dissertation (Ph.D.)

Advisor: McKeon, Beverley J.

Committee Members: Pullin, Dale Ian; Colonius, Tim; Meiron, Daniel I.; McKeon, Beverley J.

Option: Aeronautics

DOI: 10.7907/7RSR-3277

Abstract

This thesis explores the linear and non-linear interactions which take place in a rough-wall turbulent boundary through experiments and modeling. In order to derive physics-based models for the relation between roughness geometry and flow physics, two very simple periodic roughnesses were 3D printed and placed in a boundary layer wind tunnel for separate experiments. Hot-wire measurements were taken at a grid of points within a single period of the roughness in order to map the spatial variation of important flow statistics in way that allows correlation back to the roughness geometry. Time averaged streamwise velocity and the power spectrum of instantaneous streamwise velocity were both found to vary coherently with the roughness. The spatial variation of the time averaged velocity was identified as the linear result of the roughness, as it has identical wavenumber and frequency to the static roughness geometry. Modeling the time-averaged velocity field as a response mode of the linear resolvent operator was found to be reasonable for certain wavenumbers. The spatial distribution of the power spectrum was shown to be a non-linear effect of the roughness; the power spectrum only measures the energy of convecting modes, which necessarily have non-zero frequency and cannot correlate linearly to the static roughness. The spatial modulation of the power spectrum was found to be indicative of non-linear triadic interactions between the static velocity Fourier modes and pairs of convecting modes, as allowed by the Navier-Stokes equations. A low-order model for these interactions, and their effect on the power spectrum, was constructed using resolvent response modes to represent all velocity Fourier modes. The model was found to qualitatively predict the modulation of the power spectrum for several sets of wavenumbers. The success of such a simple model suggests that it presents a useful low-order understanding of non-linear forcing between scales in rough-wall boundary layers.

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