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


Morgan, Jonathan Philip (2019) Linear and Non-linear Interactions in a Rough-Wall Turbulent Boundary Layer. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7RSR-3277.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Turbulent boundary layer, amplitude modulation, rough wall, periodic roughness
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Awards:Charles D. Babcock Award, 2016.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • McKeon, Beverley J.
Thesis Committee:
  • Pullin, Dale Ian (chair)
  • Colonius, Tim
  • Meiron, Daniel I.
  • McKeon, Beverley J.
Defense Date:21 February 2019
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-17-1-2960
Office of Naval Research (ONR)N00014-13-1-0739
Record Number:CaltechTHESIS:04112019-234812867
Persistent URL:
Related URLs:
URLURL TypeDescription containing some experiments and analysis used in thesis.
Morgan, Jonathan Philip0000-0003-2898-4868
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11453
Deposited By: Jonathan Morgan
Deposited On:19 Apr 2019 23:10
Last Modified:25 Oct 2023 20:58

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