Bursts and the law of the wall in turbulent boundary layers (original) (raw)

Shear-free turbulent boundary layers. Part 1. Physical insights into near-wall turbulence

Journal of Fluid Mechanics, 1995

Direct numerical simulation is used to examine the interaction of turbulence with a wall in the absence of mean shear. The in uence of a solid wall on turbulence is analyzed by rst considering two`simpler' types of boundaries. The rst boundary is an idealized permeable wall. This boundary isolates and elucidates the viscous e ects created by the wall. The second boundary is an idealized free surface. This boundary complements the rst by allowing one to isolate and investigate the kinematic e ects that occur near boundaries. The knowledge gained from these two simpler ows is then used to understand how turbulence is in uenced by solid walls where both viscous and kinematic e ects occur in combination.

Comparison between spatial and temporal wall oscillations in turbulent boundary layer flows

Direct numerical simulations have been performed to study the drag reduction resulting from spatial oscillations of a segment of the wall under a turbulent boundary layer. The oscillating motion is imposed by utilizing a streamwise modulated spanwise wall forcing. The results are compared with earlier simulations using temporal oscillations with an identical segment and forcing amplitudes, and with a frequency related to the wavelength through a convective velocity. Two different oscillation amplitudes with equal oscillation wavelength have been used, which allows for a direct comparison between a relatively weak and strong forcing of the flow. The weaker forcing results in 25 % drag reduction while the stronger forcing, with twice the amplitude, yields 41 % drag reduction. Comparison with the temporal cases reveals drastically improved energy savings for the spatial oscillation technique, in accordance with earlier channel flow investigations. The streamwise variation of spanwise shear is shown to follow the analytical solution to the laminar Navier-Stokes equations derived under the assumption of constant friction velocity. Furthermore, the spanwise velocity profiles at various phases are compared with the analytical solution, and show very good agreement. The downstream development of the spatial Stokes layer thickness is theoretically estimated to be ∼x 1/15 , in general agreement with the simulation data. The spatial variation of the spanwise Reynolds stress is investigated and compared with the variation in time for the temporal wall forcing cases. The controversy regarding a zero or non-zero production of spanwise Reynolds stress in the temporal case is elucidated. In addition, comparison with the spatial case reveals that a second production term originating from the downstream variation of the spanwise wall velocity has a negative contribution to the production, and hence relates to the larger drag reduction in the case of spatial forcing.

Mechanism of Wall Turbulence in Boundary Layer Flow

Modern Physics Letters B, 2009

The energy gradient method is used to analyze the turbulent generation in the transition boundary layer flow. It is found that the maximum of the energy gradient function occurs at the wall for the Blasius boundary layer flow. At this location under a sufficiently high Reynolds number, even a low level of free-stream disturbance can cause the turbulent transition and sustain the flow to be in a state of turbulence. This is an excellent explanation of the physics of self-sustenance of wall turbulence. The mechanism of receptivity for boundary layer flow can also be understood from the energy gradient criterion. That is, the free-stream disturbance can propagate towards the wall by the…

On the wave structure of the wall region of a turbulent boundary layer

Journal of Fluid Mechanics, 1975

Following the ideas suggested by Landahl (1967, 1975), some model calculations of the fluctuating velocity field in the wall region of a turbulent boundary layer have been carried out. It was assumed that the turbulent stresses are generated intermittently on small scales in time and space owing to bursting-type motions. The Reynolds-stress distribution during bursting periods and the mean velocity profile were assumed to be known, and the linear large-scale response to a random system of bursts was computed using an idealized model for the joint probability distribution in time and space of the occurrence of bursts. Computed energy spectra of the streamwise velocity fluctuations display scales in the spanwise and streamwise directions and time which are in good agreement with measurements by Morrison, Bullock & Kronauer (1971). However, the wavenumber band-widths of the computed spectra are narrower than those of the measured ones. This discrepancy is probably due to the crudeness ...

Effect of wall-boundary disturbances on turbulent channel flows

Journal of Fluid Mechanics, 2006

The interaction between the wall and the core region of turbulent channels is studied using direct numerical simulations at friction Reynolds number Re τ ≈ 630. In these simulations the near-wall energy cycle is effectively removed, replacing the smooth-walled boundary conditions by prescribed velocity disturbances with non-zero Reynolds stress at the walls. The profiles of the first-and second-order moments of the velocity are similar to those over rough surfaces, and the effect of the boundary condition on the mean velocity profile is described using the equivalent sand roughness. Other effects of the disturbances on the flow are essentially limited to a layer near the wall whose height is proportional to a length scale defined in terms of the additional Reynolds stress. The spectra in this roughness sublayer are dominated by the wavenumber of the velocity disturbances and by its harmonics. The wall forcing extracts energy from the flow, while the normal equilibrium between turbulent energy production and dissipation is restored in the overlap region. It is shown that the structure and the dynamics of the turbulence outside the roughness sublayer remain virtually unchanged, regardless of the nature of the wall. The detached eddies of the core region only depend on the mean shear, which is not modified beyond the roughness sublayer by the wall disturbances. On the other hand, the large scales that are correlated across the whole channel scale with U LOG = u τ κ −1 log(Re τ ), both in smooth-and in rough-walled flows. This velocity scale can be interpreted as a measure of the velocity difference across the log layer, and it is used to modify the scaling proposed and validated by delÁlamo et al. (J.

Turbulent boundary layer over 2D and 3D large-scale wavy walls

Physics of Fluids, 2015

An experimental investigation of the flow over two-and three-dimensional large-scale wavy walls was performed using high-resolution planar particle image velocimetry in a refractive-index-matching (RIM) channel. The 2D wall is described by a sinusoidal wave in the streamwise direction with amplitude to wavelength ratio a/λ x = 0.05. The 3D wall is defined with an additional wave superimposed on the 2D wall in the spanwise direction with a/λ y = 0.1. The flow over these walls was characterized at Reynolds numbers of 4000 and 40 000, based on the bulk velocity and the channel half height. Flow measurements were performed in a wall-normal plane for the two cases and in wall-parallel planes at three heights for the 3D wavy wall. Instantaneous velocity fields and time-averaged turbulence quantities reveal strong coupling between large-scale topography and the turbulence dynamics near the wall. Turbulence statistics show the presence of a well-structured shear layer that enhances the turbulence for the 2D wavy wall, whereas the 3D wall exhibits different flow dynamics and significantly lower turbulence levels. It is shown that the 3D surface limits the dynamics of the spanwise turbulent vortical structures, leading to reduced turbulence production and turbulent stresses and, consequently, lower average drag (wall shear stress). The likelihood of recirculation bubbles, levels and spatial distribution of turbulence, and rate of the turbulent kinetic energy production are shown to be severely affected when a single spanwise mode is superimposed on the 2D sinusoidal wall. Differences of one and two order of magnitudes are found in the turbulence levels and Reynolds shear stress at the low Reynolds number for the 2D and 3D cases. These results highlight the sensitivity of the flow to large-scale topographic modulations; in particular the levels and production of turbulent kinetic energy as well as the wall shear stress.

Wall turbulence at high friction Reynolds numbers

2022

A new direct numerical simulation of a Poiseuille channel flow has been conducted for a friction Reynolds number of 10 000, using the pseudospectral code LISO. The mean streamwise velocity presents a long logarithmic layer, extending from 400 to 2500 wall units, longer than it was thought. The maximum of the intensity of the streamwise velocity increases with the Reynolds number, as expected. Also, the elusive second maximum of this intensity has not appeared yet. In case it exists, its location will be around y + ≈ 120, for a friction Reynolds number extrapolated to approximately 13 500. The small differences in the near-wall gradient of this intensity for several Reynolds numbers are related to the scaling failure of the dissipation, confirming this hypothesis. The scaling of the turbulent budgets in the center of the channel is almost perfect above 1000 wall units. Finally, the peak of the pressure intensity grows with the Reynolds number and does not scale in wall units. If the pressure at the wall is modeled as an inverse quadratic power of Re τ , then p + ∞ ≈ 4.7 at the limit of infinite Reynolds number.

The large-scale dynamics of near-wall turbulence

Journal of Fluid Mechanics, 2004

The dynamics of the sublayer and buffer regions of wall-bounded turbulent flows are analysed using autonomous numerical simulations in which the outer flow, and on some occasions specific wavelengths, are masked. The results are compared with a turbulent channel flow at moderate Reynolds number. Special emphasis is put on the largest flow scales. It is argued that in this region there are two kinds of large structures: long and narrow ones which are endogenous to the wall, in the sense of being only slightly modified by the presence or absence of an outer flow, and long and wide structures which extend to the outer flow and which are very different in the two cases. The latter carry little Reynolds stress near the wall in full simulations, and are largely absent from the autonomous ones. The former carry a large fraction of the stresses in the two cases, but are shown to be quasi-linear passive wakes of smaller structures, and they can be damped without modifying the dynamics of other spectral ranges. They can be modelled fairly accurately as being infinitely long, and it is argued that this is why good statistics are obtained in short or even in minimal simulation boxes. It is shown that this organization implies that the scaling of the near-wall streamwise fluctuations is anomalous.