Single Low-speed Streak Research Articles

Experimental study on dependence of streak breakdown on disturbance nature

Instability and breakdown of a low-speed streak initially forced by disturbances with a frequency-spectrum similar to that of wall turbulence were examined experimentally. A single low-speed streak was generated using a small piece of screen set normal to a boundary-layer plate, and disturbances made by two loudspeakers were introduced through two small holes. Turbulent velocity fluctuations with various spanwise coherences were used as driving signals to two loudspeakers to see how strongly the streak breakdown depended on the nature of disturbances. Signals were deduced at two spanwise locations with distance Δz+= 24–149 in the buffer region of a turbulent boundary layer by using a pair of hot-wires. The correlation coefficient Ct of the two turbulent signals ranged from −0.11 to 0.56. Both sinuous and varicose modes were excited but the former became dominant downstream in all cases. Development of the disturbance excited was compared to those for anti-symmetric (Ct=−1) and symmetric (Ct=1) excitations with the same turbulent spectrum. The comparison showed that the magnitude of the sinuous instability mode excited was dependent on the initial disturbances, but not strongly for −1≤Ct≤0. That is, in terms of the rms value of velocity fluctuations, the magnitude of the sinuous instability mode for the initial disturbance with Ct∼0 was about 75% of that in the case of anti-symmetric forcing. Even for Ct∼+0.56, the magnitude of the sinuous mode excited was as large as 50% of that in the anti-symmetric case.

POD analysis of the instability mode of a low-speed streak in a laminar boundary layer

The instability of one single low-speed streak in a zero-pressure-gradient laminar boundary layer is investigated experimentally via both hydrogen bubble visualization and planar particle image velocimetry (PIV) measurement. A single low-speed streak is generated and destabilized by the wake of an interference wire positioned normal to the wall and in the upstream. The downstream development of the streak includes secondary instability and self-reproduction process, which leads to the generation of two additional streaks appearing on either side of the primary one. A proper orthogonal decomposition (POD) analysis of PIV measured velocity field is used to identify the components of the streak instability in the POD mode space: for a sinuous/varicose type of POD mode, its basis functions present anti-symmetric/symmetric distributions about the streak centerline in the streamwise component, and the symmetry condition reverses in the spanwise component. It is further shown that sinuous mode dominates the turbulent kinematic energy (TKE) through the whole streak evolution process, the TKE content first increases along the streamwise direction to a saturation value and then decays slowly. In contrast, varicose mode exhibits a sustained growth of the TKE content, suggesting an increasing competition of varicose instability against sinuous instability.

Edge states as mediators of bypass transition in boundary-layer flows

The concept of edge states is investigated in the asymptotic suction boundary layer in relation to the receptivity process to noisy perturbations and the nucleation of turbulent spots. Edge tracking is first performed numerically, without imposing any discrete symmetry, in a large computational domain allowing for full spatial localisation of the perturbation velocity. The edge state is a three-dimensional localised structure recurrently characterised by a single low-speed streak that experiences erratic bursts and planar shifts. This recurrent streaky structure is then compared with predecessors of individual spot nucleation events, triggered by non-localised initial noise. The present results suggest a nonlinear picture, rooted in dynamical systems theory, of the nucleation process of turbulent spots in boundary-layer flows, in which the localised edge state plays the role of state-space mediator.

DNS of a Single Low-Speed Streak Subject to Spanwise Wall Oscillations

Direct numerical simulation (DNS) is performed to study the effect of steady streamwise oscillations of the spanwise wall velocity on a single low-speed streak in a laminar boundary layer. The low-speed streak is numerically generated by simulating a screen which creates a momentum loss. The wall oscillations are shown to reduce the skin friction which drops below the laminar Blasius flow value (without the presence of streaks) for certain cases of wall oscillations. In addition, the peak streamwise velocity fluctuation of the streaks are reduced drastically by up to 90 %, the trend in reduction being monotonic with respect to higher amplitude oscillations. The effect of oscillation is also studied during transition (breakdown of the streak) and it is found that the optimum wavenumber of the oscillation changes by nearly an order of magnitude during transition. The reduction of peak streamwise velocity fluctuations shows a phase dependent behaviour which is explained based on the regeneration of turbulence in the absence of a streamwise gradient of the spanwise velocity. The general trend of reduction in streamwise fluctuations across different wavenumbers does not correlate well with the decrease in skin friction. A much better qualitative correlation is found when comparing the relative trends for skin friction and wall-normal velocity fluctuations for different oscillation wavenumbers.

Development of subharmonic disturbance in spanwise-periodic low-speed streaks

Development of a subharmonic sinuous mode in spanwise-periodic low-speed streaks is studied experimentally. Periodic low-speed streaks are generated in a laminar boundary layer by using small pieces of screen set normal to the wall with an equal interval in the spanwise direction. Well-controlled disturbances are introduced to excite the subharmonic instablity mode whose spanwise wavelength is twice the streak spacing. The instability mode develops similar to that in a single low-speed streak in the linear instability stage. Beyond the nonlinear saturation stage of subharmonic instability, however, quasi-streamwise vortices developing along the neighboring low-speed streaks strongly interact with each other in each cycle, causing horseshoe vortices to develop in a staggered array. At the latest stage of subharmonic streak breakdown, near-wall low-speed streaks with a lateral spacing of 80 wall units in terms of the most probable value newly develop, leading to wall turbulence.

On the instability and reproduction mechanism of a laminar streak

The instability and spanwise reproduction process of one single low-speed streak evolved in a laminar flat-plate boundary layer is experimentally investigated. The primary goal of this experiment is to bridge the gap between the understandings on streak characteristics and the dynamic mechanisms of free stream turbulence-induced bypass transition. The wake of an upstream wall-normal positioned interference wire is used to generate a low-speed streak through the leading edge receptivity process. Moreover, the wire wake introduces irregular perturbations with quasi-antisymmetry into the boundary layer, thus triggers a sinuous-typed secondary instability of the streak. The downstream evolution of the streak presents a re-growth trend in streak strength statistics. The first growth stage is dominated by the streak instability, while the secondary growth stage might be associated with the unsteady breakdown of the streak. Streamwise vortices generated through breakdown process are frequently observed on either flank of the streak in the secondary growth stage. They always organize into streamwise-elongated train with alternating vorticity sign, thus introducing antisymmetric perturbations onto the streak with significant strength to trigger additional breakdown. In the far downstream, two new-born low-speed streaks appear on either side of the original one, indicating the completion of the spanwise reproduction of the streak. On considering the consistent lift-up inducement from the streamwise vortex trains onto the underlying inner fluid, the streak breakdown process provides a dynamical precondition for the streak reproduction process.

Influence of Surfactant on the Elementary Motions in Turbulent Flow

To investigate the effect of drag-reducing surfactant on typical elementary motions in turbulent flows, direct numerical simulation was carried out for a pair of streamwise vortices and a single low-speed streak. The surfactant solution was represented by a modified Bird-Carreau model. In surfactant solution, the streamwise vortices were inhibited immediately. On the other hand, the low-speed streak was less affected. Secondary streamwise vortices generated by low-speed streak were inhibited at downstream of surfactant solution. In such a sense, maintainance mechanism of low-speed streak was changed. In order to clarify the factor of modification of the elementary motions in turbulence, the energy budget was estimated. The inhibition of streamwise vortices resulted from strong viscous diffusion due to non-Newtonian effect. The influence of surfactant on the low-speed streak motion is mainly caused by the change in magnitude of energy redistribution. This is an indirect effect of streamwise vortices around a streak.

Numerical studies of the instability and breakdown of a boundary-layer low-speed streak

The experimental configuration in [M. Asai, M. Minagawa, M. Nishioka, The instability and breakdown of a near-wall low-speed streak, J. Fluid Mech. 455 (2002) 289–314] is numerically reproduced in order to examine the instability of a single low-speed streak in a laminar boundary layer and to investigate the resulting generation of coherent structures. Such a configuration is chosen since the experimental data show that the two instability modes, varicose and sinuous, are of comparable strength. The instability characteristics are retrieved from the simulation of the flow impulse response. The varicose instability is associated to higher frequencies and lower group velocities than those of the sinuous modes. The latter are less affected by the diffusion of the streak mean shear and are amplified for a longer streamwise distance. Analysis of the perturbation kinetic energy production reveals that both the varicose and the sinuous instability are driven by the work of the Reynolds stress against the wall-normal shear of the streak. The base flow considered here therefore presents an exception to the common knowledge, supported by several previous studies, that the sinuous instability is associated to the streak spanwise shear. The vortical structures at the late stage of the varicose breakdown are identified from the numerical data. By comparing them with those pertaining to other transition scenarios, it is confirmed that streaks and streamwise vortices are universal features of boundary layer transition.

Experimental investigation of the instability of spanwise-periodic low-speed streaks

The streak instability is examined experimentally by artificially generating spanwise-periodic low-speed streaks in a laminar boundary layer on a flat plate. Fundamental and subharmonic modes are excited for each of the sinuous and varicose instabilities and their development is compared with the corresponding result of a single low-speed streak. The development of subharmonic sinuous mode does not strongly depend on the streak spacing and it grows with almost the same growth rate as that for the single streak. By contrast, the development of fundamental sinuous mode is very sensitive to the streak spacing and is completely suppressed when the streak spacing is smaller than a critical value, about 2.5 times the streak width for the low-speed streaks examined. On the varicose instability, the fundamental mode is less amplified than the subharmonic mode, but the growth of both modes is weak compared with the case of the single streak.

The instability and breakdown of a near-wall low-speed streak

The instability of the three-dimensional high-shear layer associated with a near-wall low-speed streak is investigated experimentally. A single low-speed streak, not unlike the near-wall low-speed streaks in transitional and turbulent flows, is produced in a laminar boundary layer by using a small piece of screen set normal to the wall. In order to excite symmetric and anti-symmetric modes separately, well-controlled external disturbances are introduced into the laminar low-speed streak through small holes drilled behind the screen. The growth of the excited symmetric varicose mode is essentially governed by the Kelvin–Helmholtz instability of the in ectional velocity profiles across the streak in the normal-to-wall direction and it can occur when the streak width is larger than the shear-layer thickness. The spatial growth rate of the symmetric mode is very sensitive to the streak width and is rapidly reduced as the velocity defect decreases flowing to the momentum transfer by viscous stresses. By contrast, the anti-symmetric sinuous mode that causes the streak meandering is dominated by the wake-type instability of spanwise velocity distributions across the streak. As far as the linear instability is concerned, the growth rate of the anti-symmetric mode is not so strongly affected by the decrease in the streak width, and its exponential growth may continue further downstream than that of the symmetric mode. As for the mode competition, it is important to note that when the streak width is narrow and comparable with the shear-layer thickness, the low-speed streak becomes more unstable to the anti-symmetric modes than to the symmetric modes. It is clearly demonstrated that the growth of the symmetric mode leads to the formation of hairpin vortices with a pair of counter-rotating streamwise vortices, while the anti-symmetric mode evolves into a train of quasi-streamwise vortices with vorticity of alternate sign.