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Turbulence over rough/textured walls does not obey Navier-Stokes equations

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TURW04 - Wall-bounded turbulence: beyond current boundaries

This talk will discuss the effect of surface texture on the overlying turbulence. For very small textures, turbulence remains smooth-wall-like, and the only effect is an apparent origin offset for different flow components, which results in a drag increase or reduction through a change in the so-called ‘roughness function’. In this regime, the texture can be replaced by equivalent, homogeneous boundary conditions, and thus the change in drag can be predicted a priori. Unfortunately, this regime breaks down once the texture size becomes comparable to the smallest lengthscale in the overlying flow (typically 15 wall units) so its practical relevance is limited. Beyond this regime, drag predictions often resort to correlations for known textures, overlooking that ‘roughness’ is a hydrodynamic property, so it is not difficult to find examples of surfaces for which existing correlations do not work. Instead, we focus on understanding the mechanisms through which the dynamics of the overlying turbulence are modified by the texture. As a first step in this direction, we focus on the effect of slip/no-slip textures – a popular model for superhydrophobic surfaces – which make the problem particularly simple. For these textures, effective homogeneous boundary conditions can be shown to hold for sizes much larger than 15 wall units. However, for larger sizes, the texture-coherent flow interacts directly with the background turbulence and modifies its equations of motion, which are no longer Navier-Stokes’. We provide evidence for this comparing texture-resolved simulations and texture-less simulations with homogeneous boundary conditions and modified governing equations.

This talk is part of the Isaac Newton Institute Seminar Series series.

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