Resolvent Analysis for Turbulent Channel Flow with Riblets

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.

arXiv comment21 pages, 8 figures

References in corpus (8)

• A critical layer model for turbulent pipe flow
• Spectral analysis of jet turbulence
• On coherent structure in wall turbulence
• Resolvent-analysis-based design of airfoil separation control
• Model-based scaling of the streamwise energy density in high-Reynolds number turbulent channels
• A reduced-order model of three-dimensional unsteady flow in a cavity based on the resolvent operator
• A framework for studying the effect of compliant surfaces on wall turbulence
• On the design of optimal compliant walls for turbulence control

Cited by in corpus (9)

• From bypass transition to flow control and data-driven turbulence modeling: An input-output viewpoint
• Data-driven modal decomposition methods as feature detection techniques for flow problems: a critical assessment
• Nonlinear Stability Analysis of Transitional Flows using Quadratic Constraints
• Near-wall turbulence alteration with the Transpiration-Resistance Model
• Resolvent-based predictions for turbulent flow over anisotropic permeable substrates
• Resolvent-based design and experimental testing of porous materials for passive turbulence control
• Identification of cross-frequency interactions in compressible cavity flow using harmonic resolvent analysis
• Input-output framework for actuated boundary layers
• Linear models of strip-type roughness