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      Resolvent Analysis for Turbulent Channel Flow with Riblets

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          Abstract

          This paper extends the resolvent formalism for wall turbulence proposed by McKeon and Sharma(2010) to account for the effect of streamwise-constant riblets. Under the resolvent formulation, the Navier-Stokes equations are interpreted as a forcing-response system: the nonlinear convective term is interpreted as a feedback forcing on the remaining linear terms, which generates a velocity and pressure response. A gain-based decomposition of the linear forcing-response transfer function --- the resolvent operator --- yields highly amplified velocity and pressure modes, which can be considered key building blocks of the turbulent flow field. Previous work has shown that these high-gain modes provide substantial insight into turbulence statistics, structure, and control of smooth-walled flows. To introduce the effect of riblets within this framework, a linear spatially-varying body force is added to the governing equations. In other words, volume penalization is used to approximate the surface features. Predictions for spanwise-periodic and streamwise-constant riblets show that specific high-gain modes identified from the modified governing equations reproduce observations made in prior direct numerical simulations with limited computation. The deterioration in performance with increasing riblet size is predicted well and so is the emergence of spanwise rollers resembling Kelvin-Helmholtz vortices. This new modeling framework is also used to pursue limited riblet shape optimization.

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          Regeneration mechanisms of near-wall turbulence structures

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            The autonomous cycle of near-wall turbulence

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              The immersed boundary method

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                Author and article information

                Journal
                18 December 2018
                Article
                1812.07178
                78c35fb5-d695-4557-aaf5-665f860ba308

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                21 pages, 8 figures
                physics.flu-dyn

                Thermal physics & Statistical mechanics
                Thermal physics & Statistical mechanics

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