Classicité de formes modulaires surconvergentes

We prove in this paper a classicality result for overconvergent modular forms on PEL Shimura varieties of type (A) or (C) associated to an unramified reductive group on $mathbb{Q}_p$. To get this result, we use the analytic continuation method, first used by Buzzard and Kassaei

Drag reduction induced by superhydrophobic surfaces in turbulent pipe flow

The drag reduction induced by superhydrophobic surfaces is investigated in a turbulent pipe flow. Wetted superhydrophobic surfaces are shown to trap gas bubbles in their asperities. This stops the liquid from coming in direct contact with the wall in that location, allowing the flow to slip over the air bubbles. We consider a well-defined texture with streamwise grooves at the walls in which the gas is expected to be entrapped. This configuration is modeled with alternating no-slip and shear-free boundary conditions at the wall. With respect to the classical turbulent pipe flow, a substantial drag reduction is observed which strongly depends on the grooves’ dimension and on the solid fraction, i.e., the ratio between the solid wall surface and the total surface of the pipe’s circumference. The drag reduction is due to the mean slip velocity at the wall which increases the flow rate at a fixed pressure drop. The enforced boundary conditions also produce peculiar turbulent structures which on the contrary decrease the flow rate. The two concurrent effects provide an overall flow rate increase as demonstrated by means of the mean axial momentum balance. This equation provides the balance between the mean pressure gradient, the Reynolds stress, the mean flow rate, and the mean slip velocity contribution

Rearrangement of secondary flow over spanwise heterogeneous roughness

Turbulent flow over a surface with streamwise-elongated rough and smooth stripes is studied by means of direct numerical simulation (DNS) in a periodic plane open channel with fully resolved roughness. The goal is to understand how the mean height of roughness affects the characteristics of the secondary flow formed above a spanwise heterogeneous rough surface. To this end, while the statistical properties of roughness texture as well as the width and spacing of the rough stripes are kept constant, the elevation of the smooth stripes is systematically varied in different simulation cases. Utilizing this variation, three configurations – representing protruding, recessed and an intermediate type of roughness – are analysed. In all cases, secondary flows are present and the skin friction coefficients calculated for all the heterogeneous rough surfaces are meaningfully larger than what would result from the area-weighted average of those of homogeneous smooth and rough surfaces. This drag increase appears to be linked to the strength of the secondary flow. The rotational direction of the secondary motion is shown to depend on the relative surface elevation. The present results suggest that this rearrangement of the secondary flow is linked to the spatial distribution of the spanwise-wall-normal Reynolds stress component, which carries opposing signs for protruding and recessed roughness

Modelling spanwise heterogeneous roughness through a parametric forcing approach

Inhomogeneous rough surfaces in which strips of roughness alternate with smooth-wall strips are known to generate large-scale secondary motions. Those secondary motions are strongest if the strip width is of the order of the half-channel height and they generate a spatial wall shear stress distribution whose mean value can significantly exceed the area-averaged mean value of a homogeneously smooth and rough surface. In the present paper it is shown that a parametric forcing approach (Busse & Sandham, J. Fluid Mech., vol. 712, 2012, pp. 169–202; Forooghi et al., Intl J. Heat Fluid Flow, vol. 71, 2018, pp. 200–209), calibrated with data from turbulent channel flows over homogeneous roughness, can capture the topological features of the secondary motion over protruding and recessed roughness strips (Stroh et al., J. Fluid Mech., vol. 885, 2020, R5). However, the results suggest that the parametric forcing approach roughness model induces a slightly larger wall offset when applied to the present heterogeneous rough-wall conditions. Contrary to roughness-resolving simulations, where a significantly higher resolution is required to capture roughness geometry, the parametric forcing approach can be applied with usual smooth-wall direct numerical simulation resolution resulting in less computationally expensive simulations for the study of localized roughness effects. Such roughness model simulations are employed to systematically investigate the effect of the relative roughness protrusion on the physical mechanism of secondary flow formation and the related drag increase. It is found that strong secondary motions present over spanwise heterogeneous roughness with geometrical height difference generally lead to a drag increase. However, the physical mechanism guiding the secondary flow formation, and the resulting secondary flow topology, is different for protruding roughness strips and recessed roughness strips separated by protruding smooth surface strips

Numerical simulation of drop impingement and bouncing on a heated hydrophobic surface

The heat transfer of a single water droplet impacting on a heated hydrophobic surface is investigated numerically using a phase field method. The numerical results of the axisymmetric computations show good agreement with the dynamic spreading and subsequent bouncing of the drop observed in an experiment from literature. The influence of Weber number on heat transfer is studied by varying the drop impact velocity in the simulations. For large Weber numbers, good agreement with experimental values of the cooling effectiveness is obtained whereas for low Weber numbers no consistent trend can be identified in the simulations

Drag Assessment for Boundary Layer Control Schemes with Mass Injection

The present study considers uniform blowing in turbulent boundary layers as active flow control scheme for drag reduction on airfoils. The focus lies on the important question of how to quantify the drag reduction potential of this control scheme correctly. It is demonstrated that mass injection causes the body drag (the drag resulting from the stresses on the body) to differ from the wake survey drag (the momentum deficit in the wake of an airfoil), which is classically used in experiments as a surrogate for the former. This difference is related to the boundary layer control (BLC) penalty, an unavoidable drag portion which reflects the effort of a mass-injecting boundary layer control scheme. This is independent of how the control is implemented. With an integral momentum budget, we show that for the present control scheme, the wake survey drag contains the BLC penalty and is thus a measure for the inclusive drag of the airfoil, i.e. the one required to determine net drag reduction. The concept of the inclusive drag is extended also to boundary layers using the von Karman equation. This means that with mass injection the friction drag only is not sufficient to assess drag reduction also in canonical flows. Large Eddy Simulations and Reynolds-averaged Navier-Stokes simulations of the flow around airfoils are utilized to demonstrate the significance of this distinction for the scheme of uniform blowing. When the inclusive drag is properly accounted for, control scenarios previously considered to yield drag reduction actually show drag increase

Dynamic ductile to brittle transition in a one-dimensional model of viscoplasticity

We study two closely related, nonlinear models of a viscoplastic solid. These models capture essential features of plasticity over a wide range of strain rates and applied stresses. They exhibit inelastic strain relaxation and steady flow above a well defined yield stress. In this paper, we describe a first step in exploring the implications of these models for theories of fracture and related phenomena. We consider a one dimensional problem of decohesion from a substrate of a membrane that obeys the viscoplastic constitutive equations that we have constructed. We find that, quite generally, when the yield stress becomes smaller than some threshold value, the energy required for steady decohesion becomes a non-monotonic function of the decohesion speed. As a consequence, steady state decohesion at certain speeds becomes unstable. We believe that these results are relevant to understanding the ductile to brittle transition as well as fracture stability.Comment: 10 pages, REVTeX, 12 postscript figure