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Linear Amplification in Nonequilibrium Turbulent Boundary Layers


Gomez De La Cruz, Salvador Rey (2024) Linear Amplification in Nonequilibrium Turbulent Boundary Layers. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/hn98-c285.


Resolvent analysis is applied to nonequilibrium incompressible adverse pressure gradient (APG) turbulent boundary layers (TBL) and hypersonic boundary layers with high temperature real gas effects, including chemical nonequilibrium. Resolvent analysis is an equation-based, scale-dependent decomposition of the Navier Stokes equations, linearized about a known mean flow field. The decomposition identifies the optimal response and forcing modes, ranked by their linear amplification. To treat the nonequilibrium APG TBL, a biglobal resolvent analysis approach is used to account for the streamwise and wall-normal inhomogeneities in the streamwise developing flow. For the hypersonic boundary layer in chemical nonequilibrium, the resolvent analysis is constructed using a parallel flow assumption, incorporating N₂, O₂, NO, N, and O as a mixture of chemically reacting gases.

Biglobal resolvent analysis is first applied to the zero pressure gradient (ZPG) TBL. Scaling relationships are determined for the spanwise wavenumber and temporal frequency that admit self-similar resolvent modes in the inner layer, mesolayer, and outer layer regions of the ZPG TBL. The APG effects on the inner scaling of the biglobal modes are shown to diminish as their self-similarity improves with increased Reynolds number. An increase in APG strength is shown to increase the linear amplification of the large-scale biglobal modes in the outer region, similar to the energization of large scale modes observed in simulation. The linear amplification of these modes grows linearly with the APG history, measured as the streamwise averaged APG strength, and relates to a novel pressure-based velocity scale.

Resolvent analysis is then used to identify the length scales most affected by the high-temperature gas effects in hypersonic TBLs. It is shown that the high-temperature gas effects primarily affect modes localized near the peak mean temperature. Due to the chemical nonequilibrium effects, the modes can be linearly amplified through changes in chemical concentration, which have non-negligible effects on the higher order modes. Correlations in the components of the small-scale resolvent modes agree qualitatively with similar correlations in simulation data.

Finally, efficient strategies for resolvent analysis are presented. These include an algorithm to autonomously sample the large amplification regions using a Bayesian Optimization-like approach and a projection-based method to approximate resolvent analysis through a reduced eigenvalue problem, derived from calculus of variations.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Fluid dynamics;turbulence;hypersonic flow;Bayesian Optimization;Reduced order modeling
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
  • Di Renzo, Mario
  • McKeon, Beverley J.
Defense Date:14 September 2023
Non-Caltech Author Email:rey.gomez (AT)
Funding AgencyGrant Number
U.S. Office of Naval Research (ONR)N00014-17-1-2307
U.S. Office of Naval Research (ONR)N00014-17-1-3022
Record Number:CaltechTHESIS:08312023-005517217
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Chapter 6 adapted for Chapter 6 adapted for Chapter 5 and 6
Gomez De La Cruz, Salvador Rey0000-0002-7568-721X
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16170
Deposited By: Salvador Gomez
Deposited On:05 Oct 2023 20:03
Last Modified:08 Nov 2023 00:33

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