Scaling and dynamics of turbulence over sparseA canopies

Turbulent flows within and over sparse canopies are investigated using direct numerical simulations. We focus on the effect of the canopy on the background turbulence, the part of the flow that remains once the element-induced flow is filtered out. In channel flows, the distribution of the total stress is linear with height. Over smooth walls, the total stress is only the `fluid stress' $\tau_f$, the sum of the viscous and the Reynolds shear stresses. In canopies, in turn, there is an additional contribution from the canopy drag, which can dominate within. We find that, for sparse canopies, the ratio of the viscous and the Reynolds shear stresses in $\tau_f$ at each height is similar to that over smooth-walls, even within the canopy. From this, a height-dependent scaling based on $\tau_f$ is proposed. Using this scaling, the background turbulence within the canopy shows similarities with turbulence over smooth walls. This suggests that the background turbulence scales with $\tau_f$, rather than with the conventional scaling based on the total stress. This effect is essentially captured when the canopy is substituted by a drag force that acts on the mean velocity profile alone, aiming to produce the correct $\tau_f$, without the discrete presence of the canopy elements acting directly on the fluctuations. The proposed mean-only forcing is shown to produce better estimates for the turbulent fluctuations compared to a conventional, homogeneous-drag model. The present results thus suggest that a sparse canopy acts on the background turbulence primarily through the change it induces on the mean velocity profile, which in turn sets the scale for turbulence, rather than through a direct interaction of the canopy elements with the fluctuations. The effect of the element-induced flow, however, requires the representation of the individual canopy elements.Cambridge Commonwealth, European and International Trust PRACE DECI-15 European Research Counci

Examination of outer-layer similarity in wall turbulence over obstructed surfaces

Turbulent flows over canopies of rigid filaments with different densities, $\lambda_f$, are studied using direct simulations at Reynolds numbers $Re_\tau\approx550-1000$. The canopies have heights $h^+\approx110-220$, and are an instance of obstructing substrate. We show that conventional methods used to determine the zero-plane displacement can be at odds with proper outer-layer similarity and may not be applicable for flows at moderate $Re_\tau$. Instead, we determine $\Delta y$ and the length and velocity scales that recover outer-layer similarity by minimising the difference between the smooth-wall and canopy diagnostic function everywhere above the roughness sublayer, not just in the logarithmic layer. We also investigate if the zero-plane displacement and the friction velocity can be set independently, but find that outer-layer similarity is more consistently recovered when they are coupled. Our results suggest a modified outer-layer similarity, where the K\'arm\'an constant, $\kappa$, is not 0.39, but turbulence is otherwise smooth-wall-like. When the canopy is dense, the flow above the tips is essentially smooth-wall-like, with smooth-wall-like $\kappa\approx0.39$ and origin essentially at the tip plane. For intermediate densities, the overlying flow perceives a deeper zero-plane displacement, in agreement with previous studies, but exhibits a lower K\'arm\'an constant, $\kappa\approx0.34-0.36$. For sparse canopies, $\kappa$ tends back to its smooth-wall value, and the zero-plane-displacement height is at the canopy bed. For all canopies studied, the decrease in $\kappa$ never exceeds 15%, which is significantly less than that obtained in some previous works using conventional methods to assess outer-layer similarity.Comment: 30 pages, 18 figure

Spectral Analysis of the Slip-Length Model for Turbulence over Textured Superhydrophobic Surfaces.

We assess the applicability of slip-length models to represent textured superhydrophobic surfaces. From the results of direct numerical simulations, and by considering the slip length from a spectral perspective, we discriminate between the apparent boundary conditions experienced by different lengthscales in the overlying turbulent flow. In particular, we focus on the slip lengths experienced by lengthscales relevant to the near wall turbulent dynamics. Our results indicate that the apparent failure of homogeneous slip-length models is not the direct effect of the texture size becoming comparable to the size of eddies in the flow. The texture-induced signal scatters to the entire wavenumber space, affecting the perceived slip length across all lengthscales, even those much larger than the texture. We propose that the failure is caused by the intensity of the texture-induced flow, rather than its wavelength, becoming comparable to the background turbulence

Turbulent flows over dense filament canopies

Turbulent flows over dense canopies of rigid filaments of small size are investigated for different element heights and spacings using DNS. The flow can be decomposed into the element-coherent, dispersive flow, the Kelvin--Helmholtz-like rollers typically reported over dense canopies, and the background, incoherent turbulence. The canopies studied have spacings $s^+ = 3$--$50$, which essentially preclude the background turbulence from penetrating within. The dispersive velocity fluctuations are also mainly determined by the spacing, and are small deep within the canopy, where the footprint of the Kelvin--Helmholtz-like rollers dominates. Their typical streamwise wavelength is determined by the mixing length, which is essentially the sum of its height above and below the canopy tips. For the present dense canopies, the former remains roughly the same in wall-units, and the latter, which scales with the drag length, depends linearly on the spacing. This is the result of the drag being essentially viscous and governed by the planar layout of the canopy. In shallow canopies, the proximity of the canopy floor inhibits the formation of Kelvin--Helmholtz-like rollers, with essentially no signature for height-to-spacing ratios $h/s \approx 1$, and no further inhibition beyond $h/s \approx 6$. Very small spacings also inhibit the rollers, due to their obstruction by the canopy elements. The obstruction decreases with increasing spacing and the signature of the instability intensifies, even if for canopies sparser than those studied here the instability eventually breaks down. Simple models based on linear stability can capture some of the above effects.Cambridge Commonwealth, European and International Trust EPSRC Tier-2 grant EP/P020259/

Analysis of anisotropically permeable surfaces for turbulent drag reduction

The present work proposes the use of anisotropically permeable substrates as a means to reduce turbulent skin friction. We conduct an a priori analysis to assess the potential of these surfaces, based on the effect of small-scale surface manipulations on near-wall turbulence. The analysis, valid for small permeability, predicts a monotonic decrease in friction as the streamwise permeability increases. Empirical results suggest that the drag-reducing mechanism is however bound to fail beyond a certain permeability. We investigate the development of Kelvin-Helmholtz-like rollers at the surface as a potential mechanism for this failure. These rollers, which are a typical feature of turbulent flows over permeable walls, are known to increase drag, and their appearance to limit the drag-reducing effect. We propose a model, based on linear stability analysis, which predicts the onset of these rollers for sufficiently large permeability, and allows us to bound the maximum drag reduction that these surfaces can achieve

User's web page aesthetics opinion: a matter of low-level image descriptors based on MPEG-7

Analyzing a user's first impression of a Web site is essential for interface designers, as it is tightly related to their overall opinion of a site. In fact, this early evaluation affects user navigation behavior. Perceived usability and user interest (e.g., revisiting and recommending the site) are parameters influenced by first opinions. Thus, predicting the latter when creating a Web site is vital to ensure users’ acceptance. In this regard, Web aesthetics is one of the most influential factors in this early perception. We propose the use of low-level image parameters for modeling Web aesthetics in an objective manner, which is an innovative research field. Our model, obtained by applying a stepwise multiple regression algorithm, infers a user's first impression by analyzing three different visual characteristics of Web site screenshots—texture, luminance, and color—which are directly derived from MPEG-7 descriptors. The results obtained over three wide Web site datasets (composed by 415, 42, and 6 Web sites, respectively) reveal a high correlation between low-level parameters and the users’ evaluation, thus allowing a more precise and objective prediction of users’ opinion than previous models that are based on other image characteristics with fewer predictors. Therefore, our model is meant to support a rapid assessment of Web sites in early stages of the design process to maximize the likelihood of the users’ final approval