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A framework for studying the effect of compliant surfaces on wall turbulence

Luhar, M. and Sharma, A. S. and McKeon, B. J. (2015) A framework for studying the effect of compliant surfaces on wall turbulence. Journal of Fluid Mechanics, 768 . pp. 415-441. ISSN 0022-1120.

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This paper extends the resolvent formulation proposed by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to consider turbulence–compliant wall interactions. Under this formulation, the turbulent velocity field is expressed as a linear superposition of propagating modes, identified via a gain-based decomposition of the Navier–Stokes equations. Compliant surfaces, modelled as a complex wall admittance linking pressure and velocity, affect the gain and structure of these modes. With minimal computation, this framework accurately predicts the emergence of the quasi-two-dimensional propagating waves observed in recent direct numerical simulations. Further, the analysis also enables the rational design of compliant surfaces, with properties optimized to suppress flow structures energetic in wall turbulence. It is shown that walls with unphysical negative damping are required to interact favourably with modes resembling the energetic near-wall cycle, which could explain why previous studies have met with limited success. Positive-damping walls are effective for modes resembling the so-called very-large-scale motions, indicating that compliant surfaces may be better suited for application at higher Reynolds number. Unfortunately, walls that suppress structures energetic in natural turbulence are also predicted to have detrimental effects elsewhere in spectral space. Consistent with previous experiments and simulations, slow-moving spanwise-constant structures are particularly susceptible to further amplification. Mitigating these adverse effects will be central to the development of compliant coatings that have a net positive influence on the flow.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Sharma, A. S.0000-0002-7170-1627
McKeon, B. J.0000-0003-4220-1583
Additional Information:© 2015 Cambridge University Press. Received 4 November 2014; revised 21 January 2015; accepted 3 February 2015; first published online 10 March 2015. This material is based on work supported by the Air Force Office of Scientific Research under awards FA9550-12-1-0469 (program manager D. Smith) and FA9550-14-1-0042 (program manager G. Abate).
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-12-1-0469
Air Force Office of Scientific Research (AFOSR)FA9550-14-1-0042
Subject Keywords:boundary layer control, drag reduction, turbulent boundary layers
Record Number:CaltechAUTHORS:20150420-130124855
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:56778
Deposited By: Tony Diaz
Deposited On:20 Apr 2015 20:33
Last Modified:03 Oct 2019 08:17

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