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Resolvent-based study of compressibility effects on supersonic turbulent boundary layers

Bae, H. Jane and Dawson, Scott T. M. and McKeon, Beverley J. (2020) Resolvent-based study of compressibility effects on supersonic turbulent boundary layers. Journal of Fluid Mechanics, 883 . Art. No. A29. ISSN 0022-1120. https://resolver.caltech.edu/CaltechAUTHORS:20200128-124558577

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Abstract

The resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) is applied to supersonic turbulent boundary layers to study the validity of Morkovin’s hypothesis, which postulates that high-speed turbulence structures in zero-pressure-gradient turbulent boundary layers remain largely the same as their incompressible counterparts. Supersonic zero-pressure-gradient turbulent boundary layers with adiabatic wall boundary conditions at Mach numbers ranging from 2 to 4 are considered. Resolvent analysis highlights two distinct regions of the supersonic turbulent boundary layer in the wave parameter space: the relatively supersonic region and the relatively subsonic region. In the relatively supersonic region, where the flow is supersonic relative to the free-stream, resolvent modes display structures consistent with Mach wave radiation that are absent in the incompressible regime. In the relatively subsonic region, we show that the low-rank approximation of the resolvent operator is an effective approximation of the full system and that the response modes predicted by the model exhibit universal and geometrically self-similar behaviour via a transformation given by the semi-local scaling. Moreover, with the semi-local scaling, we show that the resolvent modes follow the same scaling law as their incompressible counterparts in this region, which has implications for modelling and the prediction of turbulent high-speed wall-bounded flows. We also show that the thermodynamic variables exhibit similar mode shapes to the streamwise velocity modes, supporting the strong Reynolds analogy. Finally, we demonstrate that the principal resolvent modes can be used to capture the energy distribution between momentum and thermodynamic fluctuations.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1017/jfm.2019.881DOIArticle
https://arxiv.org/abs/1905.12680arXivDiscussion Paper
ORCID:
AuthorORCID
Bae, H. Jane0000-0001-6789-6209
Dawson, Scott T. M.0000-0002-0020-2097
McKeon, Beverley J.0000-0003-4220-1583
Additional Information:© 2019 Cambridge University Press. Received 28 May 2019; revised 23 August 2019; accepted 22 October 2019. The authors acknowledge support from the Air Force Office of Scientific Research grant FA9550-16-1-0232. The authors also thank Dr A. Lozano-Durán and Dr M. Cho for their insightful comments on the manuscript.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-16-1-0232
Subject Keywords:compressible boundary layers, compressible turbulence, turbulence modelling
Record Number:CaltechAUTHORS:20200128-124558577
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200128-124558577
Official Citation:Bae, H., Dawson, S., & McKeon, B. (2020). Resolvent-based study of compressibility effects on supersonic turbulent boundary layers. Journal of Fluid Mechanics, 883, A29. doi:10.1017/jfm.2019.881
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100963
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:28 Jan 2020 23:25
Last Modified:29 Jan 2020 17:10

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