The phase-locked mean impulse response of a turbulent channel flow

We describe the first DNS-based measurement of the complete mean response of a turbulent channel flow to small external disturbances. Space-time impulsive perturbations are applied at one channel wall, and the linear response describes their mean effect on the flow field as a function of spatial and temporal separations. The turbulent response is shown to differ from the response a laminar flow with the turbulent mean velocity profile as base flow.Comment: Accepted for publication in Physics of Fluid

Uniform representation of the turbulent velocity profile in an open channel

A uniform representation of the mean turbulent velocity profile in the sum of a wall function and a wake function is applied to an open channel, quantitatively determining its components. The open channel is thus found to coherently fit in to the same theoretical picture previously drawn for plane Couette, plane closed channel and circular pipe flow, and to share with them a universal law of the wall and a universal logarithmic law with a common value of von K\'arm\'an's constant.Comment: submitted to the Journal of Fluid Mechanic

Streamwise oscillation of spanwise velocity at the wall of a channel for turbulent drag reduction

Steady forcing at the wall of a channel flow is studied via DNS to assess its ability of yielding reductions of turbulent friction drag. The wall forcing consists of a stationary distribution of spanwise velocity that alternates in the streamwise direction. The idea behind the forcing builds upon the existing technique of the spanwise wall oscillation, and exploits the convective nature of the flow to achieve an unsteady interaction with turbulence. The analysis takes advantage of the equivalent laminar flow, that is solved analytically to show that the energetic cost of the forcing is unaffected by turbulence. In a turbulent flow, the alternate forcing is found to behave similarly to the oscillating wall; in particular an optimal wavelength is found that yields a maximal reduction of turbulent drag. The energetic performance is significantly improved, with more than 50% of maximum friction saving at large intensities of the forcing, and a net energetic saving of 23% for smaller intensities. Such a steady, wall-based forcing may pave the way to passively interacting with the turbulent flow to achieve drag reduction through a suitable distribution of roughness, designed to excite a selected streamwise wavelength

On the large difference between Benjamin's and Hanratty's formulations of perturbed flow over uneven terrain

Flow over an uneven terrain is a complex phenomenon that requires a chain of approximations in order to be studied. In addition to modelling the intricacies of turbulence if present, the problem is classically first linearized about a flat bottom and a locally parallel flow, and then asymptotically approximated into an interactive representation that couples a boundary layer and an irrotational region through an intermediate inviscid but rotational layer. The first of these steps produces a stationary Orr–Sommerfeld equation; since this is a one-dimensional problem comparatively easy for any computer, it would seem appropriate today to forgo the second sweep of approximation and solve the Orr–Sommerfeld problem numerically. However, the results are inconsistent! It appears that the asymptotic approximation tacitly restores some of the original problem’s non-parallelism. In order to provide consistent results, Benjamin’s version of the Orr–Sommerfeld equation needs to be modified into Hanratty’s. The large difference between Benjamin’s and Hanratty’s formulations, which arises in some wavenumber ranges but not in others, is here explained through an asymptotic analysis based on the concept of admittance and on the symmetry transformations of the boundary layer. A compact and accurate analytical formula is provided for the wavenumber range of maximum laminar shear-stress response. We highlight that the maximum turbulent shear-stress response occurs in the quasi-laminar regime at a Reynolds-independent wavenumber, contrary to the maximum laminar shear-stress response whose wavenumber scales with a power of the boundary-layer thickness. A numerical computation involving an eddy-viscosity model provides a warning against the inaccuracy of such a model. We emphasize that the range $k\unicode[STIX]{x1D708}/u_{\unicode[STIX]{x1D70F}} of the spectrum remains essentially unexplored, and that the question is still open whether a fully developed turbulent regime, similar to the one predicted by an eddy-viscosity model, ever exists for open flow even in the limit of infinite wavelength

Turbulent drag reduction over curved walls

This work studies the effects of skin-friction drag reduction in a turbulent flow over a curved wall, with a view to understanding the relationship between the reduction of friction and changes to the total aerodynamic drag. Direct numerical simulations (DNS) are carried out for an incompressible turbulent flow in a channel where one wall has a small bump; two bump geometries are considered, that produce mildly separated and attached flows. Friction drag reduction is achieved by applying streamwise-travelling waves of spanwise velocity (StTW). The local friction reduction produced by the StTW is found to vary along the curved wall, leading to a global friction reduction that, for the cases studied, is up to 10\% larger than that obtained in the plane-wall case. Moreover, the modified skin friction induces non-negligible changes of pressure drag, which is favorably affected by StTW and globally reduces by up to 10\%. The net power saving, accounting for the power required to create the StTW, is positive and, for the cases studied, is one half larger than the net saving of the planar case. The study suggests that reducing friction at the surface of a body of complex shape induces further effects, a simplistic evaluation of which might lead to underestimating the total drag reduction

Effects of base-flow variations on the secondary instability in the wake of a circular cylinder

L'abstract si trova nella sezione S1-3