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Resolvent-Based Modeling of Flows in a Channel


Rosenberg, Kevin Thomas (2018) Resolvent-Based Modeling of Flows in a Channel. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/PHDW-Z389.


This thesis concerns the continued development of the resolvent framework (McKeon and Sharma, 2010) to model wall-bounded turbulent flows. Herein, we introduce novel modifications and extensions of the framework to improve the compact representation of flows in a channel. In particular, inspired by ideas rooted in classical linear stability theory, we introduce a decomposition of the velocity field into Orr-Sommerfeld (OS) and Squire (SQ) modes in a nonlinear context via the resolvent operator. We demonstrate through the analysis of a number of exact coherent states (ECS) of the Navier-Stokes equations (NSE) in Couette and Poiseuille flow that this decomposition offers a significant improvement in the low-dimensional representation of these flows. With this efficient basis, we are able to develop through the notion of interaction coefficients a method to compute accurate, self-consistent solutions of the NSE with knowledge of only the mean velocity profile. We also highlight the role of the solenoidal component of the nonlinear forcing in the solution process. In addition, the resolvent framework is extended to the analysis of 2D/3C flows. This approach, again applied to ECS, sheds light on the underlying scale interactions which sustain these solutions. Notably, it reveals that lower branch ECS can be effectively described in their entirety with a single resolvent response mode. This discovery is leveraged to construct a method to compute accurate approximations of ECS starting from a laminar profile using a single parameter model. This thesis also utilizes a constant time-step DNS of a turbulent channel to perform a direct characterization of the nonlinear forcing terms. We compute power spectra and confirm that the nonlinear forcing has a non-trivial signature in the wavenumber-frequency domain. We also compute and analyze spectra for the OS/SQ vorticity and discuss the potential benefit of this decomposition technique to the study of fully turbulent flows as well.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Turbulence, modeling, resolvent analysis, exact coherent states
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • McKeon, Beverley J.
Thesis Committee:
  • Meiron, Daniel I. (chair)
  • Leonard, Anthony
  • Colonius, Tim
  • McKeon, Beverley J.
Defense Date:21 May 2018
Non-Caltech Author Email:kevin.t.rosenberg (AT)
Funding AgencyGrant Number
Record Number:CaltechTHESIS:06012018-114927289
Persistent URL:
Related URLs:
URLURL TypeDescription DocumentArticle adapted for Chap. 2, 3.
Rosenberg, Kevin Thomas0000-0001-6101-3823
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10998
Deposited By: Kevin Rosenberg
Deposited On:05 Jun 2018 22:54
Last Modified:25 Oct 2023 21:00

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