Abstract
Abstract
Highlights
Some textured surfaces, such as riblets (Walsh & Lindemann 1984), superhydrophobic surfaces (Rothstein 2010) and anisotropic permeable substrates (Gómez-de-Segura & García-Mayoral 2019), are designed to manipulate the flow to modify the turbulent skin-friction drag compared to a smooth surface
The result is an extension of Luchini’s theory where, rather than on the difference between the virtual origins perceived by the tangential velocities, ΔU+ depends on their positions relative to that perceived by the wall-normal velocity, regardless of the plane taken as reference
As long as the imposed virtual origins remain relatively small compared to the characteristic length scales of the near-wall turbulence cycle, the shift in the mean velocity profile, ΔU+, is determined by the offset between the virtual origin experienced by the mean flow and the virtual origin experienced by the turbulence, verifying (4.1)
Summary
Some textured surfaces, such as riblets (Walsh & Lindemann 1984), superhydrophobic surfaces (Rothstein 2010) and anisotropic permeable substrates (Gómez-de-Segura & García-Mayoral 2019), are designed to manipulate the flow to modify the turbulent skin-friction drag compared to a smooth surface. This effect has been observed in direct numerical simulations (DNSs) of certain textured surfaces (Gómez-de-Segura, Sharma & García-Mayoral 2018b), and in DNSs with active opposition control (Choi, Moin & Kim 1994) We impose such origins using Robin, slip-length-like boundary conditions. Effects of a small-textured surface on the flow, it may be necessary to consider virtual origins for all three velocity components, because the virtual origin for v can play an important role in setting the apparent origin for the quasi-streamwise vortices This implies that, when the virtual origins perceived by v and w differ, the quasi-streamwise vortices, and the overlying turbulence, might perceive a virtual origin at some intermediate plane between the two (Gómez-de-Segura et al 2018a; García-Mayoral et al 2019). Virtual origins for the three velocity components are introduced by imposing Robin, slip-length boundary conditions at the channel walls, following Gómez-de-Segura & García-Mayoral (2020). General, if large enough, the virtual origin perceived is not necessarily coincident with the virtual origin for the
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