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In this paper, we investigate the Turing instability and pattern formation mechanism of a Plant-Wrack model with both self-diffusion and cross-diffusion terms. Firstly, we study the effect of self-diffusion on the stability of equilibrium. Secondly, we derive the conditions for the occurrence of the Turing patterns induced by cross-diffusion based on self-diffusion stability. Thirdly, we analyze the pattern selection by using the amplitude equation and obtain the exact parameter ranges of different types of patterns, including stripe patterns, hexagonal patterns, and mixed states. Finally, numerical simulations confirm the theoretical results.

The turbulent boundary layer (TBL) is actively controlled by the synthetic jet generated from a circular hole. According to the datasets of velocity fields acquired by a time-resolved particle image velocimetry (TR-PIV) system, the average drag reduction rate of 6.2% in the downstream direction of the hole is obtained with control. The results of phase averaging show that the synthetic jet generates one vortex pair each period and the consequent vortex evolves into hairpin vortex in the environment with free-stream, while the reverse vortex decays rapidly. From the statistical average, it can be found that a low-speed streak is generated downstream. Induced by the two vortex legs, the fluid under them converges to the middle. The drag reduction effect produced by the synthetic jet is local, and it reaches a maximum value at x + = 400, where the drag reduction rate reaches about 12.2%. After the extraction of coherent structure from the spatial two-point correlation analysis, it can be seen that the synthetic jet suppresses the streamwise scale and wall–normal scale of the large scale coherent structure, and slightly weakens the spanwise motion to achieve the effect of drag reduction.

This work investigates the active control of a fully developed turbulent boundary layer by a submerged synthetic jet actuator. The impacts of the control are explored by measuring the streamwise velocities using particle image velocimetry, and reduction of the skin-friction drag is observed in a certain range downstream of the orifice. The coherent structure is defined and extracted using a spatial two-point correlation function, and it is found that the synthetic jet can efficiently reduce the streamwise scale of the coherent structure. Proper orthogonal decomposition analysis reveals that large-scale turbulent kinetic energy is significantly attenuated with the introduction of a synthetic jet. The conditional averaging results show that the induction effect of the prograde vortex on the low-speed fluid in a large-scale fluctuation velocity field is deadened, thereby suppressing the bursting process near the wall.

Based on a set of experimental databases of turbulent boundary layers obtained from particle image velocimetry in the streamwise-wall-normal plane at friction-velocity-based Reynolds number Reτ = 612, the influence of uniform momentum zones (UMZs) on the skin-friction drag is investigated. The skin-friction drag is measured by the single-pixel ensemble correlation method. The results show that the velocity fields with the number of UMZs larger than the mean value have a relatively low skin-friction drag, while the velocity fields with the number of UMZs less than the mean value have a relatively high skin-friction drag. By analyzing the statistical characteristics of UMZs, the dynamic correlation between the UMZs and skin-friction drag is explored. The velocity fields with a low number of UMZs present a sweep event. These sweep motions intensify the small-scale Reynolds shear stress in the near-wall region by modulation effects. The enhancement of small-scale Reynolds shear stress is the direct reason for the high skin-friction drag. Increasing the proportion of velocity fields with high UMZs amount may be a direction to reduce the skin-friction drag within the TBL.

Active control of a fully developed turbulence boundary layer (TBL) over a flat plate has been investigated with a statistical view. The piezoelectric (PZT) oscillator is employed to produce periodic input into the inner region of the TBL. A wall probe is fixed upstream of the oscillator to identify the high- or low-speed fluctuations as the detecting signals. Then, the impact of the detecting signals on the small-scale bursting process is investigated based on the data acquired by the traversing probe downstream of the oscillator. The results indicate that the small-scale bursting intensity is restrained more apparently at high-speed detecting fluctuations but less impacted at low-speed detecting fluctuations. Furthermore, the perturbed-scale fluctuations arrange the small-scale bursting process in the near-wall region. The detecting signals have an obvious impact on this arrangement, especially the high-intensity regions of the small-scale bursting events: the vibration enhances the intensity at high-speed detecting signals but weakens it at low-speed detecting signals in these regions, which gives a direct evidence on how detecting signals interfering the small-scale bursting process.

With a piezoelectric (PZT) oscillator, the predetermined controls of the turbulent boundary layer (TBL) are effective in reducing the drag force. The stream-wise velocities in the TBL are accurately measured downstream of the oscillator driven by an adjustable power source. The mean velocity profiles in the inner and outer scales are reported and the skin friction stresses with different voltage parameters are compared. Reduction of integral spatial scales in the inner region below y+ of 30 suggests that the oscillator at work breaks up the near-wall stream-wise vortices responsible for high skin friction. For the TBL at Reθ of 2183, the controls with a frequency of 160 Hz are superior among our experiments and a relative drag reduction rate of 26.83% is exciting. Wavelet analyses provide a reason why the controls with this special frequency perform best.

The present experimental work focuses on a new model for space-time correlation and the scale-dependencies of convection velocity and sweep velocity in turbulent boundary layer over a flat wall. A turbulent boundary layer flow at Re-theta = 2460 is measured by tomographic particle image velocimetry (tomographic PIV). It is demonstrated that arch, cane, and hairpin vortices are dominant in the logarithmic layer. Hairpins and hairpin packets are responsible for the elongated low-momentum zones observed in the instantaneous flow field. The conditionally-averaged coherent structures systemically illustrate the key roles of hairpin vortice in the turbulence dynamic events, such as ejection and sweep events and energy transport. The space-time correlations of instantaneous streamwise fluctuation velocity are calculated and confirm the new elliptic model for the space-time correlation instead of Taylor hypothesis. The convection velocities derived from the space-time correlation and conditionally-averaged method both suggest the scaling with the local mean velocity in the logarithmic layer. Convection velocity result based on Fourier decomposition (FD) shows stronger scale-dependency in the spanwise direction than in streamwise direction. Compared with FD, the proper orthogonal decomposition (POD) has a distinct distribution of convection velocity for the large-and small-scales which are separated in light of their contributions of turbulent kinetic energy.

Three different methods are used to manipulate and control phthalocyanine based single molecular rotors on Au (111) surface: (1) changing the molecular structure to alter the rotation potential; (2) using the tunnelling current of the scanning tunnelling microscope (STM) to change the thermal equilibrium of the molecular rotor; (3) artificial manipulation of the molecular rotor to switch the rotation on or off by an STM tip. Furthermore, a molecular 'gear wheel' is successfully achieved with two neighbouring molecules.

We investigate the transport dynamics of an interacting binary Bose—Einstein condensate in an incommensurate optical lattice and predict a novel splitting of a matter wavepacket induced by disorder potential and inter-species interaction. The effect of atomic interaction on the dynamics of the mobile and localized atoms are also studied in detail. We also discuss the behavior of the balanced and inbalanced mixtures in the incommensurate optical lattice.